Math in 60 Seconds
One idea per video — 60-second math lessons by Selena Bui, Math Expert. Watch, learn, and save your favorites.
244 lessons in the bank
Factoring Quadratics in 60 Seconds
Learn how to factor x²+7x+12: find two numbers that multiply to 12 and add to 7 — that’s 3 and 4, so the answer is (x+3)(x+4). Remember to watch the signs, and double-check with FOIL!
Watch the Signs! Factoring x²−5x+6
The #1 factoring mistake: ignoring the signs. For x²−5x+6, (x+2)(x+3) is WRONG — a positive product with a negative sum means BOTH numbers are negative, so the answer is (x−2)(x−3). Signs first, numbers second!
Why You Can't Divide by Zero
Stop saying you just can't — here's why you really can't. Division asks one question: how many groups? Twelve divided by three is four, because four groups of three make twelve. But twelve divided by zero? Adding zero forever never reaches twelve, and no number times zero equals twelve. It's not a rule to memorize — it's impossible.
Why Place Value Decides What a Digit Is Worth
What is the 3 in 3,482 really worth? Three thousand! Every digit's value comes from its place: thousands, hundreds, tens, ones. In 3,482, the 3 means 3,000, the 4 means 400, the 8 means 80, and the 2 means 2 — add them up and you get 3,482. The place decides the value.
Why Rounding Works: Close Enough Counts
4,763 to the nearest hundred — is it 4,700 or 4,800? Look at the tens digit: 6 is five or more, so round the hundreds digit up from 7 to 8, giving 4,800. Check: 4,800 is only 37 away, while 4,700 is 63 away. Five or more, round up; four or less, round down.
Why 3 + 4 × 2 = 11, Not 14
3 + 4 × 2: is it 11 or 14? Math has an order of operations — PEMDAS. Multiplication beats addition, so 4 × 2 = 8 comes first, then 3 + 8 = 11. Going left to right gives 14: wrong order, wrong answer. Multiply and divide before you add and subtract.
Why You Compare Numbers From the Left
How do you compare 12,405 and 12,540 without subtracting? Line the numbers up and walk from the left: the left places are worth the most, so the first difference you meet decides everything. Here the hundreds digit differs — 4 versus 5 — so 12,540 is bigger. The leftmost different digit always wins.
How to Break a Number Into Place Values
A 60-second walkthrough of breaking 3,482 into its place values. Name each digit's place, multiply each digit by its place value, and add the parts: 3,000 + 400 + 80 + 2 = 3,482. Then check by adding back to the whole. Place, multiply, add — that's the method.
Word Problem: The 3,482-Can Food Drive
A school food drive collected 3,482 cans — what is each digit worth? Pull out the number, name each digit's place (thousands, hundreds, tens, ones), and answer in a sentence: 3,000 plus 400 plus 80 plus 2 equals 3,482 in all. The trick: underline the numbers, name their places, and the words become math.
How to Compare Big Numbers in 3 Steps
Comparing 12,405 and 12,540 the right way: line the digits up by place value, scan from the left for the first difference (4 vs 5), and let the bigger digit decide — 5 beats 4, so 12,540 is bigger. Then check by subtracting: 12,540 − 12,405 = 135, and since 135 is positive, the answer is confirmed.
How to Round Any Number in 3 Steps
Round 4,763 to the nearest hundred using three simple steps: circle the hundreds digit (7), peek at the next digit (6 — five or more means round up), and turn everything after into zero to get 4,800. Verify with the distance check: 4,800 is only 37 away while 4,700 is 63 away.
Why Estimation Works: Close Enough Counts
Discover why estimation works using 198 × 21 as an example. Rounding each number to a friendly value — 198 up to 200, 21 down to 20 — gives 200 × 20 = 4,000 in just three seconds. Because the numbers barely move (up 2, down 1), the exact answer of 4,158 falls within 4% of the estimate.
How to Estimate 198 × 21 in 3 Seconds
Estimate 198 × 21 in three seconds: round each number to a friendly value — 198 to 200, 21 to 20 — then multiply: 200 × 20 = 4,000. Check: the exact answer is 4,158, so the estimate lands within 4%. Round first, compute easy, stay close.
Word Problem: The Stadium Attendance
A stadium announcer said “about 4,800 fans” came — the turnstile counted 4,763. Was he right? The word “about” is the clue: round to the nearest hundred. 4,763 rounds up to 4,800, so yes — the announcer rounded correctly.
Word Problem: The Grocery Estimate
You have $50 and four items: $18.95, $12.49, $9.99, $6.75. Is it enough? Round each price to a friendly number — $19 + $12 + $10 + $7 = $48 — and answer in a sentence: about $48, so yes, $50 is enough. The trick: whenever a problem asks “about how much,” round everything first, then add.
How to Use PEMDAS in 3 Steps
Is 3 + 4 × 2 equal to 11 or 14? Walk through PEMDAS in 3 steps: check parentheses and exponents (none here), multiply and divide left to right (4 × 2 = 8), then add and subtract left to right (3 + 8 = 11). Most people add first and get 14 — this video shows why the answer is really 11.
Challenge: Nested PEMDAS — 2 + 3 × (4 − 1)²
Think you can crack 2 + 3 × (4 − 1)²? Most people get this wrong. Walk through the nested-PEMDAS trap: parentheses first — (4 − 1) = 3; exponents next — 3² = 9; then multiply — 3 × 9 = 27; then add — 2 + 27 = 29. The insight: always work inside-out.
Why Divisibility Rules Work
Why do divisibility rules work? Test 4,320 for divisibility by 2, 3, 5, 9, and 10 without dividing — and see the real math hiding behind each shortcut. Perfect for building number sense in homework, quizzes, and test prep.
Why 13 Is Prime but 15 Is Not
Why is thirteen prime but fifteen not? A prime number has exactly two divisors — one and itself. Thirteen only divides by one and thirteen, so it is unbreakable. Fifteen breaks apart as three times five, giving it four divisors: one, three, five, and fifteen. Builds number sense with the break test for primes.
How to Test Divisibility in Seconds
Test 4,320 for divisibility by 2, 3, 5, 9, and 10 in seconds. Step 1: check the last digit — 0 is even, ends in 0 or 5, ends in 0 — so it passes 2, 5, and 10. Step 2: add the digits — 4+3+2+0 = 9 — so it passes 3 and 9. Last digit, then digit sum: that is the method.
How to Check Prime or Composite
Learn how to decide prime vs composite in 60 seconds. Test divisors 2, 3, 5, and so on — only up to the square root of the number. Thirteen is prime (neither 2 nor 3 divides it), while fifteen is composite since 3 × 5 = 15. One number-sense idea per video, by Selena Bui, Math Expert.
How to Prime-Factor 60 in 3 Steps
Prime-factor 60 in three steps: split 60 into 6 × 10, factor each piece (6 = 2 × 3, 10 = 2 × 5), then collect the primes: 2² × 3 × 5. Verify by multiplying back: 4 × 15 = 60. The method that always works: keep splitting until every piece is prime.
Why 60 = 2² × 3 × 5
Prime factorization breaks a number into its prime building blocks: 60 = 2² × 3 × 5, seen in the factor tree 60 = 6 × 10 = (2×3) × (2×5). Every number has exactly one prime factorization — its unique DNA. Bonus check: 1,000 = 2³ × 5³, since 8 × 125 = 1,000.
Challenge: Prime-Factor 1,000
A 60-second challenge: prime-factor 1,000 before the reveal. See why 1,000 = 10 × 10 × 10 = (2×5)³ = 2³ × 5³, verify with 8 × 125 = 1,000, and learn the trick that every ten splits into 2 × 5.
Why LCM(4, 6) = 12
Two buses leave the station together — one every 4 minutes, one every 6. When do they leave together again? Answer with the least common multiple: list multiples of 4 (4, 8, 12, 16…) and of 6 (6, 12, 18…) to find the first match, 12. Check: 12 ÷ 4 = 3 and 12 ÷ 6 = 2. The big idea: the LCM is the first time the lists meet.
How to Find GCF(12, 18) in 3 Steps
Find the greatest common factor of 12 and 18 in just three steps: list the divisors of each number, circle the common ones (1, 2, 3, 6), and take the greatest — 6. Verify with a quick check: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. A 60-second method you can reuse for simplifying fractions and factoring.
Why GCF(12, 18) = 6
Why is the greatest common factor of 12 and 18 equal to 6? Answer it with a ribbon-cutting story: two ribbons of 12 and 18 inches must be cut into equal pieces with nothing wasted, so the longest possible piece is the GCF. Listing the divisors of 12 and 18 shows the common divisors 1, 2, 3, and 6 — and 6 is the greatest. GCF is the biggest equal piece.
Word Problem: The Ribbon Pieces
Maya has two ribbons — 12 inches and 18 inches — and wants to cut both into the longest equal pieces with nothing left over. Learn the translation trick: “longest equal pieces” is a GCF problem in disguise. Listing the divisors of 12 and 18 gives common divisors 1, 2, 3, 6, so each piece is 6 inches long — two from the 12-inch ribbon and three from the 18-inch. Perfect for number sense practice.
How to Find LCM(4, 6) in 3 Steps
Learn how to find the least common multiple of 4 and 6 in three easy steps: list the multiples of each number, find the first match (12), then check that it divides both numbers evenly (12 ÷ 4 = 3 and 12 ÷ 6 = 2). The method recap is simple: list, match, check. A 60-second math lesson by Selena Bui, Math Expert.
Word Problem: The Two Buses
Two buses leave the station together at noon — the Blue bus every 4 minutes, the Red bus every 6 minutes. When do they leave together again? This 60-second word-problem lesson shows how to translate “together again” into a least common multiple problem: list the multiples of 4 and 6, find the first match (12), and check that 12 ÷ 4 = 3 and 12 ÷ 6 = 2 leave no leftovers. The buses leave together again 12 minutes after noon — at 12:12.
Why (−5) + 8 = 3
Can you add to a negative number? This 60-second concept lesson shows why (−5) + 8 = 3: start at −5 on the number line and take 8 steps right — you land on 3. A temperature story (−5°C at night warming up 8 degrees → 3°C by noon) makes the intuition stick. The one idea: adding a positive always moves you right on the number line, even from a negative start.
How to Add Integers with Different Signs
A 31-second lesson on adding integers with different signs. Using (−5) + 8 as the worked example, walk through a 3-step method: subtract the smaller absolute value from the bigger (8 − 5 = 3), take the sign of the number with the bigger absolute value (positive), then verify on the number line from −5 moving 8 steps right to land on 3. The rule: different signs — subtract, keep the bigger’s sign.
Word Problem: The Temperature Rise
At midnight the temperature was −5°C, and by noon it had risen 8 degrees. This 42-second lesson walks through three steps of a classic integer word problem: translating “rose 8 degrees from −5” into (−5) + 8, counting 8 steps right on the number line from −5 to land on 3, and checking with the different-signs rule (subtract 8−5=3, keep the sign of the bigger number). Ends with the answer stated as a full sentence: the noon temperature is 3 degrees Celsius.
Why (−4) × (−3) = +12
Why is (−4) × (−3) = +12? The rule: same signs give positive, different signs give negative. Think of each negative as flipping direction — one flip gives −12, flip again and you are back at +12. Plus the parentheses trap: (−2)² = +4 but −2² = −4, because the exponent only hits what is inside the parentheses.
How to Multiply Integers: The Sign Rule
Multiply integers with the 3-step sign rule in 60 seconds! First multiply the absolute values (4 × 3 = 12), then decide the sign — same signs give positive, different signs give negative — so (−4) × (−3) = +12. The video covers the full sign chart and a classic trap: (−2)² = +4 but −2² = −4, because parentheses decide what the exponent hits. A 60-second lesson by Selena Bui, Math Expert.
Challenge: (−2)³ vs −2³
Can you predict (−2)² vs −2² before the reveal? First the twist: (−2)³ and −2³ both equal −8, so where is the real trap? It is the square — (−2)² = (−2)(−2) = +4, but −2² = −(2²) = −4. The exponent binds to whatever is inside the parentheses, and only that; without parentheses, the negative sign stays outside. A 60-second challenge from Selena Bui's Math in 60 Seconds series.
Why |−7| = 7
Why is the absolute value of negative seven equal to seven? Because absolute value is distance from zero on the number line — and negative seven is 7 steps away from zero, so |−7| = 7. Distance is never negative (you cannot be −7 miles from home), which is why the bars strip the sign. A 60-second concept lesson by Selena Bui.
How to Evaluate |−7| in 2 Steps
Evaluate absolute value in two steps! This 60-second lesson shows that |−7| measures the distance from zero on the number line: negative seven sits 7 units away, and distance is never negative, so |−7| = 7. Quick practice with |5|, |−3|, and |0| reinforces the rule: find the distance, drop the sign. A daily 60-second math lesson by Selena Bui, Math Expert.
Why 2⁵ = 32
What does the little five in two to the fifth power actually mean? This 60-second lesson shows that an exponent is shorthand for repeated multiplication: two to the fifth means two times two times two times two times two — five twos multiplied together — which equals thirty-two. The one-sentence takeaway: the exponent counts the factors.
How to Compute 2⁵ in 3 Steps
Learn to compute 2⁵ in 60 seconds with a simple 3-step method: expand the exponent into repeated multiplication, multiply left to right, and count your factors to double-check. You will see that 2⁵ = 2×2×2×2×2 = 32, and discover the key insight — the exponent tells you how many times to multiply the base. A 60-second math lesson by Selena Bui, Math Expert.
Why x³ × x⁴ = x⁷
Why does x³ × x⁴ = x⁷? Write out the factors: x cubed is three x's and x to the fourth is four x's — put them together and you get seven x's, which is exactly why we add the exponents when multiplying powers. The lesson also covers the two companion rules: dividing cancels factors, so subtract exponents (x⁶÷x²=x⁴), and a power of a power means multiply ((x³)²=x⁶).
Challenge: Simplify (2x³)² × x
A 60-second exponent-rules challenge: simplify (2x³)² × x. The classic trap is writing 2x⁶ — the exponent must hit everything inside the parentheses, including the coefficient 2. Squaring gives (2x³)² = 4x⁶, then multiplying by x (adding exponents) gives 4x⁷. Verify it with x = 2: both sides equal 512. A 60-second math challenge by Selena Bui, Math Expert.
How to Multiply Powers: x³ × x⁴
Learn how to multiply powers in 60 seconds! This video walks through a three-step method: check that the bases match, add the exponents for multiplication (x³ × x⁴ = x⁷), and verify with the companion rules — division subtracts exponents and a power of a power multiplies them. A numeric check with 2³ × 2⁴ = 8 × 16 = 128 = 2⁷ seals the understanding. A 60-second math lesson by Selena Bui, Math Expert.
Why x⁰ = 1
Why does anything to the zero power equal 1? This 60-second concept lesson walks down the dividing-by-the-base pattern — 2³=8, 2²=4, 2¹=2 — showing that 2⁰=1, and that going further, negative exponents flip into fractions (2⁻¹=½, 2⁻²=¼, so x⁻²=1/x²). A clear visual explanation of zero and negative exponents for algebra students.
How to Evaluate 2⁻² in 2 Steps
Learn how to evaluate zero and negative exponents in 60 seconds with a simple two-step method. First, any zero power equals one: 5 to the zero is 1, and negative seven quantity to the zero is 1. Then, a negative exponent flips into a fraction: two to the negative two is one over two squared, which is one quarter, and three to the negative one is one over three. The pattern divides by the base each step — zero power is one, negative power flips it. A 60-second math lesson by Selena Bui, Math Expert.
Why We Write 3,400,000 as 3.4 × 10⁶
Why does scientific notation exist? Because writing numbers like 93,000,000 by hand invites a mistake! This 60-second lesson shows that scientific notation is shorthand for big numbers — one digit before the decimal point, times ten to a power. The exponent simply counts the decimal jumps: 3,400,000 becomes 3.4 × 10⁶, and the sun is 93,000,000 miles away, or 9.3 × 10⁷ miles.
How to Write 3,400,000 in Scientific Notation
Learn how to write 3,400,000 in scientific notation in three simple steps: place the decimal so exactly one digit sits before it (3.4), count the decimal's jumps back to the start (6 places), then write 3.4 × 10⁶. The same method works for small numbers — 0.00045 = 4.5 × 10⁻⁴, where the decimal moved 4 places right, so the exponent is negative. One idea per video: one digit before the decimal, count the jumps, ten to that power.
Word Problem: How Far Is the Sun?
A real-world word problem in 60 seconds! Light travels 186,000 miles every second and takes about 500 seconds to reach Earth from the Sun — how far is the Sun? Distance = speed × time, so 186,000 × 500 = 93,000,000 miles (186 × 5 = 930, then add the six zeroes). Convert to scientific notation: 9.3 × 10⁷ miles. Multiply, then convert — that is why scientists live in scientific notation. A 60-second math lesson by Selena Bui, Math Expert.
Why √49 = 7
Why does the square root of forty-nine equal seven? Because seven squared is forty-nine — squaring and square roots are opposite operations. This 60-second concept video shows how the square root asks ‘what number, squared, gives this?’, works through √25 = 5, lists the perfect squares 1 through 49 with their roots 1 through 7, and warns of the classic trap: √49 has ONE answer, 7 — never ±7. The payoff: the square root undoes the square. Part of Selena Bui’s Math in 60 Seconds lecture series.
How to Find √49 in 2 Steps
Learn the two-step method for finding square roots of perfect squares: step one, ask what number squared gives the value; step two, check by squaring. Works through √49 = 7 and √81 = 9, plus the full list of perfect squares from 1 to 100 with their roots one through ten. A 60-second math lesson by Selena Bui, Math Expert.
How to Read 3/4 in 2 Steps
Learn how to read a fraction in two simple steps: read the bottom number for how many equal parts the whole is cut into, then read the top number for how many parts you have. For 3/4, that means three of four equal parts — and since 3 is less than 4, it is less than one whole. Remember: bottom cuts, top counts. A 60-second math lesson by Selena Bui, Math Expert.
Why 3/4 Means 3 of 4 Parts
What do the two numbers in 3/4 actually say? This 60-second lesson explains that a fraction describes parts of a whole: the denominator (bottom number) tells how many EQUAL parts the whole is cut into, and the numerator (top number) tells how many of those parts we have. Using a pizza cut into 4 equal slices with 3 taken, it shows why 3/4 means 3 of 4 parts — and why the parts must be equal for the fraction to mean anything. The one-sentence takeaway: denominator cuts, numerator counts.
Why 1/2 = 2/4
Why does one half equal two fourths? This 60-second concept video explains equivalent fractions: multiplying the top and bottom of 1/2 by 2 is the same as multiplying by 2/2, which equals 1 — so the value never changes. A quick cross-check (1×4 = 2×2 = 4) confirms it, and the payoff is a one-sentence rule students can keep forever. A 60-second math lesson by Selena Bui, Math Expert.
How to Make 1/2 into 2/4
Learn how to build equivalent fractions in 60 seconds! Pick a multiplier — 2 — and multiply the top AND the bottom of 1/2 by it: 1×2 = 2 and 2×2 = 4, giving 2/4. Going the other way, reduce 6/9 by dividing top and bottom by 3 to get 2/3, verified by cross multiplication (6×3 = 18 = 9×2). The rule to remember: scale the top and bottom by the same number. A 60-second math lesson by Selena Bui, Math Expert.
Why 12/18 = 2/3
Why does twelve eighteenths equal two thirds? This 60-second lesson reveals the secret behind simplifying fractions: dividing the top and bottom by the same number (6) is really dividing by 6/6 — and dividing by one changes nothing, so the value stays the same. Verified with a cross-multiplication check (12×3 = 18×2 = 36), and it ends with a challenge: simplify 84/126 before the challenge video reveals the answer (2/3). A 60-second math lesson by Selena Bui, Math Expert.
How to Simplify 12/18 in 2 Steps
Learn how to simplify fractions in 60 seconds. This lesson simplifies 12/18 in two steps: find the greatest common divisor of 12 and 18, which is 6, then divide the top and bottom by 6 to get 2/3. Includes a cross-multiplication check and the reason 2/3 is fully simplified. By Selena Bui, Math Expert.
Challenge: Simplify 84/126
A 60-second fraction challenge: simplify 84/126. The slow way divides three times (÷2 → 42/63, ÷3 → 14/21, ÷7 → 2/3) — the fast way finds the GCD first. Since 84 and 126 share 2 × 3 × 7, the GCD is 42: divide once (84÷42 = 2, 126÷42 = 3) for 2/3. Check: 84×3 = 252 = 126×2. Divide once, not three times! A 60-second math challenge by Selena Bui, Math Expert.
Why 3/5 Beats 4/7
Why is 3/5 bigger than 4/7? Cross-multiply: 3×7=21 and 4×5=20 — 21 beats 20, so 3/5 wins. The trick works because it secretly gives both fractions the same bottom: 21/35 vs 20/35. Same bottom, bigger top wins! Learn why cross-multiplying is just a shortcut for comparing with a common denominator. A 60-second math lesson by Selena Bui, Math Expert.
How to Compare 3/5 and 4/7
Learn how to compare fractions in 60 seconds: 3/5 vs 4/7 in three steps. Step 1: cross-multiply — 3×7=21 and 4×5=20. Step 2: compare the products — 21 beats 20, so 3/5 is bigger. Step 3: double-check with the common denominator 35: 21/35 vs 20/35, same answer. Important: this trick works for comparing, not adding. A 60-second math lesson by Selena Bui, Math Expert.
How to Add 1/3 + 1/6
Learn HOW to add fractions in 60 seconds with a worked example: to add 1/3 + 1/6, (1) find the common bottom — 3 and 6 share 6; (2) convert — 1/3 = 2/6; (3) add the tops — 2/6 + 1/6 = 3/6 = 1/2. Subtraction works the same way: 2/3 − 1/6 = 4/6 − 1/6 = 3/6 = 1/2. The method recap: common bottom, then add the tops. A 60-second math lesson by Selena Bui, Math Expert.
Why 1/3 + 1/6 = 1/2
Why does adding fractions need a common denominator? This 60-second lesson shows that 1/3 + 1/6 can not be solved by just adding the tops — the pieces are different sizes. Convert 1/3 to 2/6, add 2/6 + 1/6 to get 3/6, and simplify to 1/2. The takeaway: same pieces can combine, so convert first, then add — verified with a recipe check (1/3 cup + 1/6 cup = 1/2 cup). A 60-second math lesson by Selena Bui, Math Expert.
Recipe Story: 1/3 Cup + 1/6 Cup
A 60-second lesson on fraction word problems through a recipe story: 1/3 cup of sugar plus 1/6 cup of cocoa. Learn the translation trick — turn words into math, convert to a common denominator (1/3 = 2/6) before adding, then simplify to 1/2 cup. Ends with a sanity check confirming 1/2 sits between 1/3 and 2/3. A 60-second math lesson by Selena Bui, Math Expert.
Why 7/3 = 2 1/3
Why does 7/3 equal 2 1/3? This 60-second concept lesson builds the intuition both directions: seven thirds means seven thirds of a whole — group them and six thirds make two wholes with one third left over; going back, two wholes give six thirds plus the one leftover, so (2 × 3 + 1)/3 = 7/3. The reason it works is division with a remainder: seven divided by three is two remainder one, and the remainder becomes the new top. A 60-second math lesson by Selena Bui, Math Expert.
How to Convert 7/3 to 2 1/3
Learn how to convert an improper fraction to a mixed number in three easy steps! Divide seven by three to get two remainder one, then write the whole number two with the remainder on top as two and one third. Check your work by going back: two times three plus one is seven. You will also see why eleven fourths equals two and three fourths. A 60-second math lesson by Selena Bui, Math Expert.
Why 2/3 × 3/4 = 1/2
Why do we multiply the tops and the bottoms when multiplying fractions? Because “off” means multiply: 2/3 × 3/4 means two thirds of three fourths of a pizza — take three fourths of the pizza, then take two thirds of that. Multiplying the pieces (2 × 3 = 6) and the splits (3 × 4 = 12) gives 6/12, which simplifies to 1/2 — or cancel first to land on 1/2 directly. Fractions of fractions: multiply straight across. A 60-second math lesson by Selena Bui, Math Expert.
Pizza Story: Half of 2/3 Left
A pizza has two thirds left, and you eat half of what is left — how much of the whole pizza did you eat? This word-problem lesson translates the story into math: “off” means multiply, so 1/2 × 2/3 = 2/6 = 1/3. A sanity check confirms 1/3 is less than 2/3 — you can not eat more than what is left. One idea per video, by Selena Bui, Math Expert.
How to Multiply 2/3 × 3/4
Learn how to multiply fractions in 60 seconds! Multiply the tops (2 × 3 = 6), multiply the bottoms (3 × 4 = 12), then simplify 6/12 to 1/2. The cancel-first shortcut skips the big numbers entirely: 2 and 4 share 2, 3 and 3 cancel, leaving 1/2. Includes a bonus worked example: 1/2 × 4/5 = 4/10 = 2/5. A 60-second math lesson by Selena Bui, Math Expert.
Why 1/2 ÷ 1/4 = 2
Why is one half divided by one quarter equal to two? This 60-second concept lesson shows that division asks a fitting question: how many quarters fit inside a half? Two of them — picture half a meter of ribbon cut into quarter-meter pieces. That intuition is exactly why flip-and-multiply works: 1/2 × 4/1 = 4/2 = 2, and the check is 2 × 1/4 = 1/2. The big idea: division asks how many fit, so the answer can be bigger than what you started with. A 60-second math lesson by Selena Bui, Math Expert.
How to Divide 1/2 ÷ 1/4
Dividing fractions is easy with three steps: keep the first fraction, flip the second, then multiply. Watch 1/2 ÷ 1/4 become 1/2 × 4/1 = 2, plus a second worked example: 2/3 ÷ 5/6 = 4/5. One idea per video — perfect for fraction homework and test prep. A 60-second math lesson by Selena Bui, Math Expert.
Why Flipping Works in Division
Why is dividing by a half the same as multiplying by two? This 60-second concept video shows the intuition: 1 ÷ 1/2 asks “off” how many halves fit inside one? — two! The reciprocal is simply the flip, so 3 ÷ 2/5 = 3 × 5/2 = 15/2, and multiplying back (15/2 × 2/5 = 3) proves it undoes itself. Remember: zero has no reciprocal, because you can not flip nothing. A 60-second math lesson by Selena Bui, Math Expert.
Ribbon Story: Half Meter ÷ Quarter
A 60-second word-problem story by Selena Bui, Math Expert: with half a meter of ribbon and a quarter meter needed per bow, how many bows can you make? The video translates the words into math (how many quarters fit inside a half?), solves 1/2 ÷ 1/4 = 2 with keep-flip-multiply, and runs a sanity check (2 × 1/4 = 1/2) to confirm the ribbon is used up exactly. The payoff: division asks how many fit — and the answer can be bigger than what you started with.
How to Find the Reciprocal
Learn how to find the reciprocal of any number in 60 seconds. Flip the fraction — the reciprocal of 2/5 is 5/2 — then check your answer: 2/5 times 5/2 equals 10/10, which is 1, because reciprocals always multiply to 1. This lesson also covers the special cases: whole numbers (7 goes to 1/7), mixed numbers (1 1/2 becomes 3/2, so its reciprocal is 2/3), and why zero has no reciprocal. A 60-second math lesson by Selena Bui, Math Expert.
How to Find 2/3 of 18
Learn how to find a fraction of a number in 60 seconds. This lesson shows the three-step method on 2/3 of 18: remember “off” means multiply, divide by the bottom (18 ÷ 3 = 6), then multiply by the top (6 × 2 = 12). A second example finds 2/5 of a class of 30 the same way. Perfect for fraction practice and homework help. A 60-second math lesson by Selena Bui, Math Expert.
Class Story: 2/5 of 30 Walk
A class has 30 students and two fifths walk to school — how many walk? This 60-second lesson shows the translation trick: “off” means multiply, so 2/5 of 30 becomes 2/5 × 30 = 12. Divide by the bottom first (30 ÷ 5 = 6), then multiply by the top (6 × 2 = 12 walkers), and sanity-check that 2/5 < 1/2 means fewer than 15 walk. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: The Complex Fraction
Take the challenge: simplify the complex fraction (2/3)/(4/9)! This 60-second lesson reveals the twist — the longest bar is the main division — then flips and multiplies to get 3/2 = 1 1/2. Includes a sanity check: dividing by less than 1 gives more than you started with. Perfect for fraction fluency and test prep. A 60-second math lesson by Selena Bui, Math Expert.
Baking Story: (2/3)/(4/9)
A 60-second word-problem story: you have 2/3 cup of sugar and each batch of cookies needs 4/9 cup — how many full batches can you make? This lesson translates the words into math (2/3 ÷ 4/9), flips and multiplies to get 18/12 = 3/2 = 1 1/2, and runs a sanity check: dividing by less than 1 gives more than you started with. One full batch plus half of another! A 60-second math lesson by Selena Bui, Math Expert.
Why 0.1 Beats 0.01
Which is bigger: 0.1 or 0.01? This 60-second lesson explains why place value makes all the difference: 0.1 is one tenth, 0.01 is one hundredth, and each place to the right is ten times smaller. Viewers learn that ten hundredths make one tenth, that the first digit after the decimal point matters most, and why 0.2 beats 0.19 — one clear idea per video. A 60-second math lesson by Selena Bui, Math Expert.
How to Read Decimal Places
Learn how to read decimal places and compare decimals in 60 seconds: name the places (tenths, hundredths, thousandths), line up the decimal points and pad zeros (0.45 becomes 0.450), then compare digit by digit from the left — thousandths gives 0 vs 9, so 0.459 is bigger. The same trick cracks 0.2 vs 0.19: pad to 0.20 vs 0.19 and 20 beats 19. A 60-second math lesson by Selena Bui, Math Expert.
Why 0.45 Beats 0.405
Why does 0.45 beat 0.405, even though 0.405 has more digits? This 60-second lesson shows why comparing decimals by digit count is a trap: line up by place value (0.450 vs 0.405), compare tenths then hundredths, and stop the moment a place differs. Five hundredths beats zero hundredths — the hundredth place is ten times bigger than the thousandth place. The takeaway: decimals compare by place value, never by digit count. A 60-second math lesson by Selena Bui, Math Expert.
How to Compare 0.45 and 0.405
This 60-second lesson teaches a 3-step method for comparing decimals: line up the decimal points, pad zeros so both numbers have the same number of digits, then compare left to right. We work 0.45 vs 0.405 (pad to 0.450, compare tenths 4=4 then hundredths 5>0, so 0.45 wins) and 0.6 vs 0.59 (pad to 0.60, tenths 6>5, so 0.6 wins). Padding zeros never changes a decimal's value — 0.450 is exactly 0.45. A 60-second math lesson by Selena Bui, Math Expert.
Why You Must Line Up Decimal Points
Why must you line up the decimal points when adding decimals? This 60-second concept video explains the WHY: adding decimals means combining the same place values — tenths with tenths, hundredths with hundredths — and the decimal point is what keeps them matched. Watch $2.45 + $0.35 = $2.80 worked column by column, and see the chaos of misaligned points (27.95?!) versus the clean lined-up answer of 5.95. Perfect for decimals homework and test prep. A 60-second math lesson by Selena Bui, Math Expert.
How to Add 2.45 + 3.50
Learn how to add and subtract decimals in 60 seconds. Line up the decimal points, pad zeros so every column has a digit, then add from the right and bring the point straight down: 2.45 + 3.50 = 5.95. Subtraction works the same way — just borrow when you must: 7.20 − 4.65 = 2.55. A Math in 60 Seconds lesson by Selena Bui, Math Expert.
Grocery Math: What's the Total?
Grocery Math: What's the Total? A 60-second word problem: at the store you grab a $2.45 snack and a $3.50 drink — what's your total? Translate the story to math, line up the decimal points (dollars on the left, cents on the right), and add from the right: 2.45 + 3.50 = 5.95. A quick sanity check confirms it: 2 + 3 dollars and 45 + 50 cents. A 60-second math lesson by Selena Bui, Math Expert.
Why 0.3 × 0.2 = 0.06
Why isn't 0.3 × 0.2 = 0.6? Because 0.3 is three tenths and 0.2 is two tenths, so (3/10) × (2/10) = 6/100 = 0.06 — two decimal places, not one. Each tenth factor shrinks the answer ten times, so two tenth-factors shrink it a hundred times. A quick sanity check: the answer must be smaller than each factor, and 0.06 < 0.3 and 0.06 < 0.2. One idea per video: count the places! A 60-second math lesson by Selena Bui, Math Expert.
How to Multiply 0.3 × 0.2
Learn how to multiply decimals in 60 seconds: ignore the decimal points and multiply as whole numbers (3 × 2 = 6), count the total decimal places (1 + 1 = 2), then place the point to get 0.06. Includes a second worked example: 2.5 × 1.4 = 3.5. A 60-second math lesson by Selena Bui, Math Expert.
Why Moving the Point Works in Division
Why does "moving the decimal point" work in decimal division? Because moving both points multiplies the top AND bottom by the same power of 10 — and 10/10 cancels, so the division is unchanged. Watch 4.8 ÷ 0.6 become 48 ÷ 6 = 8, and 0.0144 ÷ 0.12 become 1.44 ÷ 12 = 0.12, with the rule that you count the moves from the DIVISOR. A 60-second math lesson by Selena Bui, Math Expert.
How to Divide 4.8 ÷ 0.6
Learn the 3-step method for dividing decimals: count the digits after the divisor's decimal point, move both points that many places right, then divide as usual. Works through 4.8 ÷ 0.6 = 8 and a bonus example, 0.0144 ÷ 0.12 = 0.12. Perfect for middle-school students who get stuck when the divisor isn't a whole number. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: Divide 7.2 ÷ 0.08
A 60-second challenge: divide 7.2 by 0.08. Most students count decimal places from the dividend and get 0.9 or 9 — the twist is that the move count comes from the divisor. Since 0.08 has 2 digits, move both points 2 places: 720 ÷ 8 = 90. A quick sanity check (the divisor is less than 1, so the answer must exceed 7.2) confirms 90 is right. A 60-second math lesson by Selena Bui, Math Expert.
Why 1/3 = 0.333… Forever
Why does 1 ÷ 3 equal 0.333… forever? This 60-second concept lesson long-divides 1 by 3 to show the remainder 1 cycling forever, then reveals the key idea: when dividing by 3, remainders can only be 0, 1, or 2, so a repeated remainder means repeating digits. It closes with a bonus shocker — the classic proof that 0.999… = 1. A Selena Bui Math Expert micro-lesson.
Challenge: 0.67 vs 0.666…
Most people guess 0.666… is bigger — infinite sixes feel like they should win. But decimals compare by place value, never by length: line them up as 0.670 versus 0.666…, and the first differing digit is in the hundredths place, where 7 beats 6. So 0.67 is bigger, and the repeating sixes never catch up. A 60-second challenge lesson by Selena Bui, Math Expert.
Change from $20: Three Items
A 60-second word-problem story by Selena Bui, Math Expert: you hand over a twenty-dollar bill for a snack ($2.45), a drink ($3.50), and gum ($1.25) — how much change? The video works it in two steps: add the three prices ($2.45 + $3.50 + $1.25 = $7.20), then subtract the total from the bill ($20.00 − $7.20 = $12.80), and runs a sanity check ($20 − $7 = $13, minus $0.20 = $12.80) to confirm. The payoff: add first, subtract from the bill — that's the method.
How to Write 35% Three Ways
Learn how to write 35% three ways in this 60-second lesson: as a fraction (35/100 simplifies to 7/20), as a decimal (0.35), and in reverse (0.8 = 80%, 3/4 = 75%). Percent, fraction, decimal — same idea, three faces. A 60-second math lesson by Selena Bui, Math Expert.
What 35% Really Means
What does 35% really mean? This 60-second lesson explains that percent means per hundred: 35% is 35 out of every 100. See the three faces of 35% — the fraction 35/100, the decimal 0.35, and the simplified fraction 7/20 — and check the famous ones: 50% = 1/2 (one half) and 100% = 100/100 = 1 (the whole thing). The takeaway: the % sign is just shorthand for over a hundred. A 60-second math lesson by Selena Bui, Math Expert.
Why 3/8 = 0.375 = 37.5%
Why do fraction, decimal, and percent conversions work? Three eighths equals zero point three seven five equals thirty-seven point five percent — it's the same number in three costumes. This 60-second lesson reveals that the fraction bar IS division (3 ÷ 8 = 0.375) and percent just means per hundred, so converting decimal to percent is moving the point two places right. The same trick handles repeating values: 5/6 = 0.833… = 83.33…%. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: Order 40%, 3/8, 0.4
A 60-second challenge: order 40%, 3/8, and 0.4 from least to greatest. The twist is that 40% and 0.4 are secretly equal (40% = 40/100 = 0.4), while 3/8 = 0.375 is the smallest. Converting all three to the same costume — decimals — gives 0.375 < 0.40 = 0.40: three eighths first, then 40% and 0.4 tied. A 60-second math lesson by Selena Bui, Math Expert.
Why 20% of 150 = 30
Why does 20% of 150 equal 30? In math, the word "of" means multiply — so 20% of 150 becomes 0.20 × 150 = 30. The video also shows the fraction shortcut (20% = one fifth, so 150 ÷ 5 = 30) and a real-life restaurant-tip example: a 20% tip on a $60 bill is $12. One idea, 60 seconds. A 60-second math lesson by Selena Bui, Math Expert.
How to Convert 3/8 to a Percent
Learn the three-step method for converting between fractions, decimals, and percents: 3/8 becomes 0.375 (the bar means division), then 37.5% (move the point two places right). Includes the reverse chain — 83.33…% → 0.8333… → 5/6 — and a recap of the method: divide, move the point, move it back. A 60-second math lesson by Selena Bui, Math Expert.
How to Find 20% of 150
Learn the 3-step method for finding a percent of any number: convert the percent to a decimal, remember that "of" means multiply, then compute. Worked examples: 20% of 150 = 30, 15% of 80 = 12, and a real-life restaurant tip — 20% of $60 = $12. A 60-second "how to" lesson by Selena Bui, Math Expert.
Tip Story: 20% of $60
Tip Story: 20% of $60. A 60-second word problem: your restaurant bill is $60 and the tip should be 20% — how much tip? Translate the story to math — "of" means multiply — so 0.20 × 60 = $12. A quick sanity check confirms it: 10% of 60 is 6, and 20% is twice that; total with tip is 60 + 12 = $72. A 60-second math lesson by Selena Bui, Math Expert.
Test Score Story: 18 of 20
You got 18 questions right out of 20 — what percent is that? This 60-second lesson shows how to translate the word story into math: part divided by whole, so 18 ÷ 20 = 0.90 = 90%, with a sanity check (90% of 20 = 18) and a second story — $15 saved of a $60 allowance is 25%. The payoff: stories become math — part over whole, then times a hundred. A 60-second math lesson by Selena Bui, Math Expert.
What Percent Is 12 of 48?
What percent is 12 of 48? Learn the two-step method: divide the part by the whole, then multiply by 100 — 12 ÷ 48 = 0.25 gives 25%. The same trick cracks test scores like 18 out of 20 (90%) and 7 out of 35 (20%). A 60-second "Math in 60 Seconds" lesson by Selena Bui, Math Expert.
Why $40 to $50 Is a 25% Increase
Why does $40 to $50 count as a 25% increase, but $50 back to $40 is only a 20% decrease? Because percent change is always relative to the original: 10 ÷ 40 = 25%, while 10 ÷ 50 = 20%. Same ten dollars, different original, different percent — plus the sale-check trick (a $100 jacket marked down to $70 is 30% off) and the formula change ÷ original × 100. A 60-second math lesson by Selena Bui, Math Expert.
How to Find Percent Change
Learn how to find percent change in three steps: find the change (new minus old), divide by the original, then times a hundred. Worked examples: $40 to $50 is a 25% increase, a sale markdown from $80 to $60 is a 25% decrease, and a population rising from 200 to 260 is a 30% increase. The key rule is to always divide by the original number, never the new one. A 60-second math lesson by Selena Bui, Math Expert.
$80 with 25% Off, Then 8% Tax
A real-world percent word problem in 60 seconds: an $80 jacket with 25% off, then 8% sales tax — translate words into math (0.75 × 80 = 60, then 60 × 1.08 = $64.80). Bonus twist: two 20% discounts are NOT 40% off (0.8 × 0.8 = 0.64 = 36% off), because percent changes stack by multiplying, never adding. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: Two 20% Discounts
A $100 jacket gets 20% off, then another 20% off the sale price — is that 40% off? Most people guess $60, but the real final price is $64. First discount: 100 × 0.8 = 80; second: 80 × 0.8 = 64 — that's 36% off, not 40%. The twist: percent changes stack by multiplying (0.8 × 0.8 = 0.64), never by adding. A 60-second math lesson by Selena Bui, Math Expert.
Reverse: $64 After 20% Off
Reverse percentages in 60 seconds! When a jacket costs $64 after 20% off, the trap is adding 20%: 64 + 20% = $76.80 — but that's 20% of the sale price, not the original. The correct method is to think forward (original × 0.80 = 64) and undo it by dividing: 64 ÷ 0.80 = $80, confirmed by the check 80 × 0.80 = 64. It works for any sale: $51 after 15% off → 51 ÷ 0.85 = $60. The takeaway: reverse percents by dividing by the pay rate, never by adding. A 60-second math lesson by Selena Bui, Math Expert.
Sale Story: $80 to $60
A jacket was $80 and now it's on sale for $60 — what percent markdown? This 60-second lesson shows how to translate the word problem into math: the change is 80 minus 60 ($20), and dividing by the original gives 20 ÷ 80 = 0.25, a 25% markdown. A sanity check (25% of 80 is 20, and 80 minus 20 is 60) confirms the answer, and you saved $20. Remember the trick: change divided by original, times 100. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: Undo a 20% Off
A shirt costs $68 after 25% off — what was the original price? This challenge video exposes the classic trap of multiplying by 1.25 (68×1.25 = 85), which is wrong because it adds 25% of the sale price, not the original. The correct move is to think forward (original × 0.75 = 68) and undo it with division: 68÷0.75 = 90.67, verified by 90.67×0.75 ≈ 68, plus a bonus example ($51 after 15% off → 51÷0.85 = $60). The payoff: reversing a percent is division, not multiplication. A 60-second math lesson by Selena Bui, Math Expert.
Commission Story: 6% of $250,000
A realtor earns 6% commission on a $250,000 house — how much? This 60-second lesson translates the word problem into math (6% = 0.06, then 0.06 × 250,000 = $15,000) and sanity-checks the answer with the 1% trick, plus a bonus example: 3% of $320,000 = $9,600. A 60-second math lesson by Selena Bui, Math Expert.
Why 3:2 Means 3 Out of 5
Why does 3 to 2 mean 3 out of 5? A ratio compares part to part, but a fraction needs part over the whole — 3 + 2 = 5 total parts, so 3 girls to 2 boys means girls are three fifths of the class, not three halves. Learn why order matters and how 12:8 simplifies to 3:2, all in 60 seconds. A 60-second math lesson by Selena Bui, Math Expert.
How to Simplify 12:8
Simplify the ratio 12:8 in 60 seconds! Three steps: find the GCF (the greatest common factor of 12 and 8 is 4), divide both parts by it (12 ÷ 4 = 3, 8 ÷ 4 = 2), then check that 3 and 2 share no common factor — simplest form is 3:2. Two bonus examples: 25:15 → 5:3 and 6:9 → 2:3. GCF, divide, check — that's the method. A 60-second math lesson by Selena Bui, Math Expert.
Why 120 Miles in 2 Hours Is 60 MPH
A 60-second lesson on why a rate is distance divided by time: 120 miles in 2 hours means 120 ÷ 2 = 60 mph, and the units tell the story — miles per hour literally means miles over hours. Reversed, 90 mph for 2 hours gives 90 × 2 = 180 miles, since distance equals rate times time. The takeaway: divide the quantities, keep the units together. A 60-second math lesson by Selena Bui, Math Expert.
Simplify 12:18 to 2:3
Learn how to simplify ratios in 60 seconds. This video teaches the three-step method — find the GCF of both parts, divide both by it, and check that the result is simplest — using 12:18 → 2:3 as the worked example, plus 25:15 → 5:3 and 6:9 → 2:3 as bonus examples. Part of Selena Bui's Math in 60 Seconds series. A 60-second math lesson by Selena Bui, Math Expert.
Why $6 for 4 Apples Is $1.50 Each
A 60-second concept lesson on unit rates: why you divide price by count to compare deals fairly. Works through $6 for 4 apples ($1.50 each) vs $8 for 5 apples ($1.60 each), plus a bonus ounces example at $0.25/oz. Takeaway: unit rate means price per one — then compare. A 60-second math lesson by Selena Bui, Math Expert.
Unit Rate: Which Cereal Box Is Cheaper?
A 60-second lesson on unit rates using a grocery-store comparison: an 18 oz cereal box for $4.50 versus a 24 oz box for $5.28. The video walks through three steps — write price over quantity, divide to get $0.25/oz and $0.22/oz, then compare — showing the bigger box is cheaper. It closes with a bonus example ($6 for 4 apples is $1.50 each) and the recap: price per one, then compare fairly. A 60-second math lesson by Selena Bui, Math Expert.
Grocery Shopping Word Problem: Which Bag Is Cheaper?
A story-form unit-rate lesson: Maya buys 4 apples for $6 while her brother buys 5 for $8. Students translate the story into math by dividing each price by its count — $6 ÷ 4 = $1.50 per apple vs $8 ÷ 5 = $1.60 per apple, so Maya got the better deal. A bonus juice-pack comparison ($5.28 ÷ 24 = $0.22/oz vs $3.60 ÷ 12 = $0.30/oz) shows the bigger pack wins. The payoff: stories hide numbers — unit rates reveal them.
Why x/4 = 9/12 Means x = 3
A 60-second lesson on why x/4 = 9/12 means x = 3. Selena explains that a proportion is just equivalent fractions grown up — two ratios with the same value. Find the scale factor (4 grew into 12 by times 3) and apply it to both sides to get x = 3, then verify by cross-multiplying 12x = 36. Includes a bonus problem, 2/3 = x/9 → x = 6. A 60-second math lesson by Selena Bui, Math Expert.
Solve x/4 = 9/12: Cross-Multiply
Learn how to solve a proportion by cross-multiplying. Step one: write the proportion x/4 = 9/12. Step two: cross-multiply to get 12x = 36. Step three: divide to find x = 3, then verify that 3/4 = 9/12. Includes a bonus round: solving 5/8 = x/16 gives x = 10. A 60-second math lesson by Selena Bui, Math Expert.
Cross-Multiply: 5/8 = x/40
Learn to cross-multiply in 60 seconds. Solve the proportion 5/8 = x/40 by multiplying the diagonals to get 8x = 200, then dividing: x = 200 ÷ 8 = 25. A bonus bracket version, (x+1)/3 = 7/9, is worked through as well — cross-multiplying gives 9(x+1) = 21, so 9x = 12 and x = 4/3. Cross-multiply, divide, verify: that's the method. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: Bracket Proportion (x+1)/3 = 7/9
A 60-second challenge on bracket proportions: cross-multiply (x+1)/3 = 7/9 to get 9(x+1) = 21, distribute and solve for x = 4/3, then tackle a second twist 2/(x−1) = 4/10 to find x = 6. Takeaway: brackets mean distribute first, and cross-multiplying still works when the unknown is below the bar. A 60-second math lesson by Selena Bui, Math Expert.
Why Map Scales Multiply Distance
Why does a map scale multiply distance? This 60-second concept video explains the WHY: a scale is just a proportion — one inch equals five miles means every inch stands for five miles. Watch a three-and-a-half-inch road become seventeen-and-a-half miles by multiplying by the scale factor, plus a bonus two-point-four-inch example giving twelve miles. The takeaway: the scale factor is the multiplier — measure, multiply, done. Perfect for scale drawings homework and test prep. A 60-second math lesson by Selena Bui, Math Expert.
Road Trip Word Problem: Map Scale
A story-form lesson on map scales and ratios. Two towns are 3.5 inches apart on a map with a scale of 1 inch = 5 miles — translating the story to math gives 3.5 × 5 = 17.5 miles. A second leg of 2.4 inches adds 12 miles, for a total road trip of 29.5 miles. The takeaway: measure the map, multiply by the scale. A 60-second math lesson by Selena Bui, Math Expert.
Recipe Word Problem: Scale for 12 Servings
A story-style ratio problem: a cookie recipe makes 8 servings with 2 cups of flour, but 12 guests are coming. Find the scale factor 12/8 = 1.5, multiply every ingredient (2 × 1.5 = 3 cups of flour), then verify with the proportion 2/8 = 3/12. Shows why scaling every ingredient by the same factor works. A 60-second math lesson by Selena Bui, Math Expert.
What 3x + 2 Means: Parts of an Expression
Every part of the expression 3x + 2 has a job: x is the variable (the unknown number), 3 is the coefficient (how many x's), and +2 is the constant (always there). Plugging in x = 5 gives 3 × 5 + 2 = 17, and x = 10 gives 3 × 10 + 2 = 32 — one expression, many answers. That's why a variable lets algebra describe so many situations. A 60-second math lesson by Selena Bui, Math Expert.
Evaluate 3x + 2 When x = 5
Evaluate the expression 3x + 2 when x = 5 in just 60 seconds. Step one: replace x with 5 to get 3(5) + 2. Step two: follow the order of operations — multiply first (3 × 5 = 15), then add (15 + 2 = 17). Bonus example with x = 10 and the method recap: replace, order, compute. A 60-second math lesson by Selena Bui, Math Expert.
Why Evaluating Means Plugging In
Learn why evaluating an expression means plugging in a value: the expression 2x + 5 is not a number — it's a rule waiting for input, where the variable x is the input slot. Evaluating at x = 4 gives 2 × 4 + 5 = 13, and one rule gives many outputs. The phone-plan story makes it real: $20 plus $0.10 per minute costs $30 for 100 minutes. A 60-second math lesson by Selena Bui, Math Expert.
Evaluate 2x + 5 at x = 4
Learn how to evaluate the expression 2x + 5 at x = 4 in just 60 seconds. Follow three steps: substitute to get 2(4) + 5, multiply 2 × 4 = 8, then add 8 + 5 = 13 — remembering to multiply before you add. Includes a bonus example: at x = 7, 2 × 7 + 5 = 19. A 60-second math lesson by Selena Bui, Math Expert.
The $20 Phone Plan: Evaluating 20 + 0.10m
A phone plan costs $20 plus $0.10 per minute — how much for 100 minutes? This 36-second story-style video shows how to translate a word problem into the expression C = 20 + 0.10m, plug in m = 100, and evaluate: 0.10×100 = 10, so 20 + 10 = $30. A bonus check (250 min → $45) reinforces the method. Teaches the one-mantra strategy: translate, plug, answer. A 60-second math lesson by Selena Bui, Math Expert.
What Are Like Terms?
Why can 3x + 5x combine into 8x, but 3x + 5 cannot? This 60-second concept lesson explains that like terms must share the same variable and the same power — like apples plus apples. Students see why a plain 5 can't join 3x, and why 4x² and 2x are different species that never combine. Ends with the one-sentence test: same variable, same power. A 60-second math lesson by Selena Bui, Math Expert.
Combine Like Terms: 4x² + 2x − x²
Combine Like Terms: 4x² + 2x − x². A 60-second how-to lesson: circle the like terms (4x² and −x²), combine their coefficients (4 − 1 = 3), and keep the 2x because it is not a like term — answer: 3x² + 2x. Bonus worked example: 5a + 3b − 2a = 3a + 3b. The method to remember: circle, combine, keep the rest. A 60-second math lesson by Selena Bui, Math Expert.
Trick Question: Simplify 2x + 3x² + x
Ninety percent of students get this one wrong: simplify 2x + 3x² + x. This 60-second challenge walks the trap slowly — circle the like terms first: 2x and x combine to 3x, while the 3x² stands alone, giving the answer 3x² + 3x in descending powers. A bonus trap, 5xy + 2x − 3xy, shows the xy terms combining to 2xy while the 2x stays apart. The payoff lesson: always check the powers first. A 60-second math lesson by Selena Bui, Math Expert.
Why 3(x + 4) = 3x + 12
Three times a group means three groups: 3(x + 4) is (x + 4) three times over, so x's and 4's just pile up — x + x + x = 3x, and 4 + 4 + 4 = 12. A garden visual makes it stick: 3 rows, each with x plants and 4 herbs, gives 3x + 12. The takeaway: multiply every piece inside by what's outside — that's distribution. A 60-second math lesson by Selena Bui, Math Expert.
Expand 3(x + 4) Step by Step
Learn how to distribute in 60 seconds! Expanding 3(x + 4) means the 3 multiplies every piece: 3 × x = 3x and 3 × 4 = 12, so the answer is 3x + 12. Includes a bonus example, 5(2y − 3) = 10y − 15 — don't forget to distribute the sign! A 60-second math lesson by Selena Bui, Math Expert.
Why Undo Works: x + 7 = 15
Why does solving an equation mean "undoing"? This 60-second lesson explains the idea behind x + 7 = 15: the +7 is done to x, so undo it with the inverse operation — subtract 7 from both sides to keep the scale balanced. That gives x = 8, verified by the check 8 + 7 = 15. The one-line takeaway: do the inverse to both sides, and that's solving. A 60-second math lesson by Selena Bui, Math Expert.
The Garden Rows Story: 3(x + 4)
A word-problem lesson on the distributive property: 3 garden rows, each holding x tomato plants and 4 herbs, translate into the expression 3(x + 4). Distributing the 3 gives 3 times x is 3x and 3 times 4 is 12, for 3x + 12 plants total. The takeaway method is story → expression → distribute. A 60-second math lesson by Selena Bui, Math Expert.
Solve x + 7 = 15
Learn how to solve one-step equations in under a minute. This lesson walks through x + 7 = 15 step by step: identify what's done to x, undo it by subtracting 7 from both sides, get x = 8, and always check the answer. Includes a bonus example: x − 9 = 4. The payoff is a reusable method — undo to both sides, then check. A 60-second math lesson by Selena Bui, Math Expert.
Why 2x + 3 = 11 Needs Two Undos
Discover why 2x + 3 = 11 needs two undos. In this 60-second concept lesson, learn to undo in reverse order: subtract 3 from both sides to get 2x = 8, then divide both sides by 2 to get x = 4. A movie-ticket story makes the idea stick, and plugging x = 4 back in confirms 2×4 + 3 = 11. The takeaway: reverse the order, undo twice — that's two-step. A 60-second math lesson by Selena Bui, Math Expert.
Movie Tickets: 2x + 3 = 11
A 60-second word-problem lesson: two movie tickets plus a $3 booking fee cost $11, which translates to the equation 2x + 3 = 11. Undoing the operations backwards — subtracting 3 gives 2x = 8, then dividing by 2 gives x = 4 — reveals that one ticket costs $4. The check 2 × 4 + 3 = 11 confirms the answer. Teaches the story → equation → solve strategy for two-step equation word problems. A 60-second math lesson by Selena Bui, Math Expert.
Solve 2x + 3 = 11
Learn how to solve two-step equations in 60 seconds. This video works through 2x + 3 = 11 step by step: first undo the plus 3 by subtracting 3 from both sides to get 2x = 8, then undo the times 2 by dividing both sides by 2 to get x = 4. It shows how to check the answer by substituting back, and finishes with a bonus problem, 5x − 7 = 18, solved the same way (x = 5). A 60-second math lesson by Selena Bui, Math Expert.
Solve 3(x − 2) = 12
A 60-second worked example on solving multi-step equations. Walks through 3(x − 2) = 12 step by step: distribute to get 3x − 6 = 12, add 6 to both sides (3x = 18), divide by 3 (x = 6), and check with 3 × 4 = 12. Includes a bonus problem, 4(2x − 1) = 3(x + 5), solved by distributing both sides first. A 60-second math lesson by Selena Bui, Math Expert.
Trick: Solve 4(2x − 1) = 3(x + 5)
Trick question: can you solve 4(2x − 1) = 3(x + 5)? Most students get it wrong because they distribute only one side. This 60-second lesson walks through the trap slowly — distribute both sides to get 8x − 4 = 3x + 15, then solve step by step to x = 19/5, verified by checking that both sides equal 132/5. The twist: the answer is a fraction, and that's perfectly fine! A 60-second math lesson by Selena Bui, Math Expert.
Solve 5x + 2 = 3x + 10
Solve equations with variables on both sides in three steps: collect the x's first, then solve as usual. Works through 5x + 2 = 3x + 10 (subtract 3x → 2x + 2 = 10, subtract 2 → 2x = 8, divide by 2 → x = 4), checks both sides (22 = 22), and shows a bonus phone-plan example where two plans cost the same at 4 minutes. A 60-second math lesson by Selena Bui, Math Expert.
Two Phone Plans: When Are They Equal?
Two phone plans — Plan A charges five dollars a minute plus a two-dollar fee, Plan B charges three dollars a minute plus a ten-dollar fee. After how many minutes do they cost the same? This 60-second lesson translates the story into the equation 5x + 2 = 3x + 10, collects the x's on one side (2x = 8), solves x = 4 minutes, and checks both plans cost twenty-two dollars. Perfect pre-algebra practice for variables on both sides of the equation. A 60-second math lesson by Selena Bui, Math Expert.
Why the Sign Flips: −2x > 6
Why does the inequality sign flip when you multiply or divide by a negative? This 60-second concept video solves −2x > 6, showing that dividing by −2 flips the sign to x < −3. Test values (−2(−4) = 8 > 6 works; x = 0 fails) and the number line (3 > 2 but −3 < −2) reveal why: negatives reverse order. The takeaway: multiply or divide by a negative, flip the sign. A 60-second math lesson by Selena Bui, Math Expert.
Solve −2x > 6 Step by Step
Learn how to solve the inequality −2x > 6 step by step: divide both sides by −2 and flip the inequality sign to get x < −3. This 60-second lesson shows how to check the answer with a test value (x = −4 gives 8 > 6, correct) and teaches the key rule — dividing by a negative flips the sign. Part of Selena Bui's Math in 60 Seconds series.
Open or Closed? Graphing Inequalities
Why do some inequality graphs use filled circles and others use hollow ones? This 60-second lesson explains it with test values: x ≥ −2 includes −2, so the circle is closed (filled in) with the arrow pointing right; x < 5 excludes 5, so the circle is open (hollow). The one-line takeaway: ≥/≤ means closed, >/< means open — the equal sign fills the circle. A 60-second math lesson by Selena Bui, Math Expert.
Graph x < 5 on a Number Line
Graph the inequality x < 5 on a number line in 60 seconds: mark 5, draw an open (hollow) circle because 5 is not included, and shade the arrow to the left for "less than." Test the graph by plugging in x = 4 (works, since 4 < 5) and x = 5 (fails, since 5 < 5 is false), then compare with x ≥ −2, which uses a closed circle because −2 is included. A one-idea-per-video lesson by Selena Bui, Math Expert.
Plot (3, −2): X Comes Before Y
Why does the order matter in (3, −2)? This 60-second concept video explains the coordinate plane: the x axis goes across, the y axis goes up and down, and an ordered pair (x, y) always lists x first. Using the elevator trick — across first, then up or down — we plot (3, −2) in Quadrant IV and show that swapping to (−2, 3) lands in a totally different place, Quadrant II. A 60-second math lesson by Selena Bui, Math Expert.
Plot (−2, 3) on the Coordinate Plane
This 60-second lesson shows how to plot the point (−2, 3) on the coordinate plane step by step: start at the origin, move left 2 along the x-axis, then up 3 along the y-axis, and mark the point. The video teaches the quadrant check — x negative and y positive means left and up, so the point lands in Quadrant II — and contrasts it with (3, −2), which is Quadrant IV. Perfect for pre-algebra practice and homework review. A 60-second math lesson by Selena Bui, Math Expert.
3, 7, 11… What's the Pattern?
A 60-second concept lesson on arithmetic sequences: for 3, 7, 11, …, each term adds 4, and the nth-term formula a_n = 3 + (n−1)×4 is the shortcut that jumps straight to any term — the 50th is 3 + 49×4 = 199. Students learn why spotting the pattern beats adding step by step. By Selena Bui, Math Expert.
Find the 10th Term: 3, 7, 11…
Find the 10th term of the sequence 3, 7, 11… in 60 seconds. This typical lesson walks through the three steps: spot the pattern (each term adds 4), write the shortcut formula a_n = 3 + (n−1)×4, and plug in n = 10 to get 39 — then double-check the formula against the first two terms. A 60-second arithmetic sequences lesson by Selena Bui, Math Expert.
100th Term Challenge: 3, 7, 11…
A 60-second challenge lesson on arithmetic sequences: given 3, 7, 11, …, students spot the +4 pattern, write the nth-term formula a_n = 3 + (n−1)×4, and compute the 100th term as 3 + 99×4 = 399. The twist asks which term first passes 1000 — solving 3 + (n−1)×4 > 1000 gives n = 251, checked against a_250 = 999 and a_251 = 1003. By Selena Bui, Math Expert.
5 Less Than Twice a Number → 2x − 5
A 60-second lesson on translating the phrase "5 less than twice a number" into algebra. Work through it piece by piece: "a number" becomes x, "twice a number" becomes 2x, and "less than" flips the word order to give 2x − 5 — not the common trap 5 − 2x. Verify with the check: if the number is 10, 2 × 10 − 5 = 15, and 15 really is 5 less than 20. The one-line takeaway: translate, then flip. A 60-second math lesson by Selena Bui, Math Expert.
3 More Than a Number = x + 3
A 60-second word-problem lesson: Mia has some apples and gets 3 more. Translate the story — "some" becomes x and "three more" becomes x + 3 — then check it with 5 (5 + 3 = 8). It also covers the classic twist: "five less than twice a number" flips the order to 2x − 5 (check: 2(10) − 5 = 15). Story, translate, check — that's word problems. A 60-second math lesson by Selena Bui, Math Expert.
Slope = Rise Over Run
How steep is a line? Slope answers that! This 60-second concept video explains why slope works: slope is rise over run — how much up, for each step across. Using the points (2, 3) and (5, 9): rise = 9 − 3 = 6, run = 5 − 2 = 3, so slope = 6/3 = 2. A slope of 2 means every 1 step right climbs 2 up, and we check it on the graph: from (2, 3), one right and two up lands on (3, 5), right on the line. Slope is the line's rate of change — how fast y changes with x. A 60-second math lesson by Selena Bui, Math Expert.
Find the Slope: (2,3) and (5,9)
Learn the 3-step method for finding slope between two points. Using the points (2,3) and (5,9), this 60-second lesson shows how to find the rise (9 − 3 = 6), the run (5 − 2 = 3), and divide (6 ÷ 3 = 2) — then check the answer by moving right 1 and up 2 from (2,3) to land on (3,5). Rise, run, divide — that's the method. A 60-second math lesson by Selena Bui, Math Expert.
Read the Slope from a Graph
No equation, just a graph! This 60-second lesson shows how to read the slope of a line from its graph. Pick two points where the line crosses grid corners — (0,1) and (2,7) — count the rise (7 − 1 = 6) and the run (2 − 0 = 2), then divide: 6/2 = 3. The check: a slope of 3 means 1 right and 3 up, so from (0,1) you land on (1,4), right on the line! A 60-second math lesson by Selena Bui, Math Expert.
y = 2x + 1: What m and b Mean
This 60-second lesson explains what m and b mean in slope-intercept form y = mx + b, using the example y = 2x + 1. Learners discover that m is steepness (how fast y changes) and b is the starting value (where the line starts when x is zero), through a savings story: start with $1 and save $2 a week, so after 3 weeks you have $7 and after 5 weeks $11 — and the graph starts at the y-intercept (0, 1). Perfect for Algebra 1 students building intuition before graphing lines. A 60-second math lesson by Selena Bui, Math Expert.
Graph y = 2x + 1 in 3 Steps
Graph the line y = 2x + 1 in three steps: start at the y-intercept b = 1 and plot (0, 1), use the slope m = 2 by going right 1 and up 2 to plot (1, 3), then draw the line through the points. Check your graph with x = 2: 2 times 2 plus 1 is 5, so (2, 5) is on the line. A 60-second lesson by Selena Bui, Math Expert.
The Savings Story: y = 2x + 1
Mia starts with $1 and saves $2 every week — after how many weeks does she have $11? This 60-second video translates the story into the slope-intercept equation y = 2x + 1 (m = 2 per week, b = 1 starting), solves 2x + 1 = 11 → 2x = 10 → x = 5 weeks, and verifies with 2 × 5 + 1 = 11. The payoff: story, equation, solve — that's word problems. A 60-second math lesson by Selena Bui, Math Expert.
Graph y = −x + 4 with Intercepts
Graph the line y = −x + 4 in 60 seconds using the intercepts method. First find the y-intercept: set x = 0 to get y = 4 and plot (0,4). Then find the x-intercept: set y = 0 to get x = 4 and plot (4,0). Draw the line through both points, and verify with a third point: x = 2 gives y = −2 + 4 = 2, so (2,2) is on the line. A 60-second math lesson by Selena Bui, Math Expert.
y = 3 vs x = −2: Which Is Which?
In this 60-second lesson, Selena Bui answers the classic confusion: which is flat, y = 3 or x = −2? The line y = 3 is horizontal because every point on it has y = 3, so its slope is 0 — there is no rise. The line x = −2 is a vertical wall because every point on it has x = −2, so its slope is undefined — the run is 0 and you cannot divide by zero. Quick checks confirm (5,3) is on y = 3 and (−2,7) is on x = −2. Takeaway: flat line means slope zero, wall means undefined. A 60-second math lesson by Selena Bui, Math Expert.
Slope of y = 3 and x = −2
Learn how to find the slopes of horizontal and vertical lines step by step! Pick two points on y = 3, like (0,3) and (4,3): slope = (3−3)/(4−0) = 0, a flat line. On x = −2, points like (−2,1) and (−2,5) give slope = (5−1)/(−2−(−2)) = 4 ÷ 0, which is undefined — a wall. Always check: any point on y = 3 has y = 3, and any point on x = −2 has x = −2. A 60-second math lesson by Selena Bui, Math Expert.
Two Lines, One Meeting Point
Why does solving a system by graphing work? This 60-second lesson graphs y = x + 1 and y = −x + 3, which cross at (1, 2). Checking the point — 2 = 1 + 1 and 2 = −1 + 3 — shows it lies on BOTH lines, which is exactly why the intersection solves the system. A 60-second math lesson by Selena Bui, Math Expert.
Solve by Graphing: y = x + 1 and y = −x + 3
Learn how to solve a system of linear equations by graphing: graph y = x + 1 and y = −x + 3, find their intersection point, and check that it satisfies both equations. The lines cross at (1, 2), and plugging it in confirms 2 = 1 + 1 and 2 = −1 + 3. Graph, cross, check — that's the method. A 60-second math lesson by Selena Bui, Math Expert.
Solve by Substitution: y = 2x, x + y = 9
Learn to solve the system y = 2x and x + y = 9 by substitution in 60 seconds. Since y is already isolated, substitute 2x into the second equation: x + 2x = 9 gives 3x = 9, so x = 3; back-substituting gives y = 2 × 3 = 6. The check confirms it: 3 + 6 = 9 and 6 = 2 × 3, so the solution is (3, 6). The method in one line: swap, solve, plug back. A 60-second math lesson by Selena Bui, Math Expert.
The Concert Tickets Story
A 60-second word problem lesson: nine concert tickets where the VIP tickets are twice the regular ones. Translate the story into the equation x + 2x = 9, solve for x = 3 regular tickets and 2x = 6 VIP tickets, then check that 3 + 6 = 9. Demonstrates the story-equation-solve translation trick that makes word problems easy. A 60-second math lesson by Selena Bui, Math Expert.
Solve by Elimination: 2x + 3y = 12, 3x − 3y = 3
Learn to solve the system 2x + 3y = 12 and 3x − 3y = 3 by elimination in 60 seconds. Since +3y and −3y are opposites, adding the two equations cancels the y terms, giving 5x = 15 and x = 3. Back-substituting gives y = 2, and checking both equations confirms the solution (3, 2). The method: add to cancel, solve, plug back. A 60-second math lesson by Selena Bui, Math Expert.
Elimination Challenge: When Multiplying Comes First
In this challenge video, the elimination method hits a twist: the system 2x + 3y = 12 and 3x + 2y = 13 has nothing to cancel directly. The trick is to multiply first — times 2 and times 3 — so the y-terms match at 6y, subtract to find x = 3, back-substitute for y = 2, and verify with 9 + 4 = 13. If nothing cancels, make it cancel. A 60-second math lesson by Selena Bui, Math Expert.
Special Systems: No Solution vs Infinite Solutions
This 60-second lesson explains the WHY behind the two special cases of systems of equations. Learners see that y = 2x + 1 and y = 2x + 3 share the same slope (m = 2) with different intercepts, so the lines are parallel and never meet — no solution. They also see that 2x + 2y = 8 is just double x + y = 4, so both equations describe the same line — infinite solutions. The payoff is a one-line rule for spotting special systems without solving: same slope, different line means none; one equation a multiple of the other means infinite. A 60-second math lesson by Selena Bui, Math Expert.
Special System Challenge: Spot the Trick
This 60-second challenge asks learners to spot the trick in a system before solving: 3x + 2y = 7 and 6x + 4y = 14. The reveal shows the second equation is exactly double the first, so both equations describe the same line and there are infinite solutions. A bonus challenge shows y = x + 5 and y = x − 2 share the same slope with different intercepts, so the lines are parallel and there is no solution. The payoff is the one-line rule: spot the special case, no solving needed. A 60-second math lesson by Selena Bui, Math Expert.
What Is a Function? The Input-Output Machine
A 60-second concept lesson on what a function really is: an input-output machine where each input gets exactly one output. Uses f(x) = 2x + 1 with input 3 giving output 7, plus the vertical line test as a visual check. A 60-second math lesson by Selena Bui, Math Expert.
Evaluating Functions: f(4) Step by Step
Learn how to evaluate a function step by step: for f(x) = 3x − 2, swap x for 4 to get f(4) = 3(4) − 2, then simplify 12 − 2 = 10. A bonus example covers g(x) = x² + 1, giving g(2) = 5. The payoff: swap x for the number, then simplify — the same two steps every time. A 60-second math lesson by Selena Bui, Math Expert.
Function Notation: f(x) Is Not f Times x!
How do you read function notation? This 60-second how-to video clears up the most common mix-up: f(x) does NOT mean f times x — it means the function named f, with input x. Watch the worked example f(x) = 2x + 1: finding f(3) means replacing x with 3, so f(3) = 2(3) + 1 = 7. A bonus shows the same input-swap idea converting 20°C to 68°F. A 60-second math lesson by Selena Bui, Math Expert.
Temperature Story: C to F with Function Notation
How do you turn a word problem into math? This 60-second story video converts 25°C to Fahrenheit using function notation: translate the story into F(C) = 9/5 × C + 32, swap in the input 25, and simplify — F(25) = 9/5 × 25 + 32 = 45 + 32 = 77°F. A backwards check (9 × 25 = 225, 225 ÷ 5 = 45) confirms the answer. The takeaway: story → equation → solve. A 60-second math lesson by Selena Bui, Math Expert.
Domain and Range: What Goes In, What Comes Out
Why do domain and range matter? This 60-second concept video gives the intuition: the domain is the x-values you're allowed to put in, the range is the y-values you get out. Using f(x) = √x as the example, it shows why the domain is x ≥ 0 (you can't square-root a negative) and the range is y ≥ 0 (square roots are never negative), plus how to read both off any graph — domain is the left-to-right span, range is the bottom-to-top span. A 60-second math lesson by Selena Bui, Math Expert.
Find Domain and Range: f(x) = 1/x
Find the domain and range of f(x) = 1/x in 60 seconds. Step 1: the domain — 1/0 is undefined, so x cannot be 0, giving all real numbers except 0. Step 2: the range — y = 1/x solves to x = 1/y, which fails when y = 0, so y cannot be 0 either. The payoff: the fraction trick — whatever makes the bottom zero is out of the domain. A 60-second math lesson by Selena Bui, Math Expert.
Polynomials: Terms and Degree
This 60-second lesson explains what makes a polynomial: it is a sum of terms, where each term is a number times a whole-number power of x. Using the example 4x³ − 2x + 7, the video identifies the three terms (4x³, −2x, +7) and shows the degree is 3, the highest exponent. It also covers the naming rules: degree 1 is linear, 2 is quadratic, 3 is cubic. A 60-second math lesson by Selena Bui, Math Expert.
Name That Polynomial: Terms, Degree, Name
How do you name a polynomial? This 60-second how-to video walks through classifying polynomials step by step: count the terms for the -nomial name (one term = monomial, two = binomial, three = trinomial) and take the highest power for the degree (degree 1 = linear, degree 2 = quadratic, degree 4 = quartic). Three worked examples — 5x²−3x+1 as a quadratic trinomial, 2x⁴+1 as a quartic binomial, and 7x as a linear monomial — end with a one-line method recap: count the terms for the name, highest power for the degree. A 60-second math lesson by Selena Bui, Math Expert.
Add and Subtract Polynomials: (3x² + 2x) + (x² − 5x)
How do you add and subtract polynomials? This 60-second typical lesson walks through the steps: drop the parentheses — plus signs, nothing changes — then group like terms and combine, so (3x² + 2x) + (x² − 5x) = 4x² − 3x. It also covers the classic twist: subtraction flips every sign, giving (3x² + 2x) − (x² − 5x) = 2x² + 7x. The one-line payoff: match the exponents, combine, and watch the minus sign. A 60-second math lesson by Selena Bui, Math Expert.
Multiply Binomials with FOIL: (x + 3)(x − 2)
Learn how to multiply binomials step by step with FOIL. This 60-second lesson works through (x + 3)(x − 2): First, Outer, Inner, Last — x·x = x², x·(−2) = −2x, 3·x = 3x, 3·(−2) = −6 — then combines like terms for the answer x² + x − 6. Includes a bonus challenge: (2x − 1)² = 4x² − 4x + 1. A 60-second math lesson by Selena Bui, Math Expert.
Special Products Challenge: (x + 4)(x − 4)
FOIL (x + 4)(x − 4) — but watch the middle: the −4x and +4x cancel, leaving x² − 16, a difference of squares. Bonus twist: (x + 5)² gives x² + 10x + 25, where the middle term doubles instead of vanishing — a perfect square trinomial. Learn to spot the patterns (a+b)(a−b) = a² − b² and (a+b)² = a² + 2ab + b² and skip the FOIL. A 60-second math lesson by Selena Bui, Math Expert.
GCF First: Factor 6x² + 9x
Learn to factor 6x² + 9x by pulling out the GCF first. The greatest common factor is 3x — 6 and 9 share 3, and x² and x share x. Dividing each term gives 3x(2x + 3), and distributing back confirms the answer. A step-by-step 60-second algebra lesson by Selena Bui, Math Expert.
The Garden Plot Story
A word-problem lesson in 60 seconds: a garden plot has area 6x² + 9x square feet with one side measuring 3x feet. Students translate the story into Area = length × width, factor out the GCF (3x), and find the other side is (2x + 3) feet — then verify by distributing. Story, equation, solve — that's word problems. A 60-second math lesson by Selena Bui, Math Expert.
Difference of Squares: Why the Middle Cancels
Why does the middle term vanish in the difference of squares? FOILing (x+3)(x−3) gives x² − 3x + 3x − 9, and the middle terms −3x + 3x cancel to zero because their signs are opposite. That leaves x² − 9, revealing the pattern a² − b² = (a+b)(a−b). The one-line payoff: see a minus between two squares — split it. A 60-second math lesson by Selena Bui, Math Expert.
Factor the Difference of Squares: x² − 25
How do you factor a difference of squares? Spot the pattern: a minus between two squares — x² and 25 = 5². Take the square roots (x and 5), then write (x+5)(x−5). Verify with FOIL: x² − 5x + 5x − 25 — the middle cancels — back to x² − 25. Bonus example: 4x² − 9 = (2x+3)(2x−3), since (2x)² = 4x² and 3² = 9. The one-line trick: root, root, plus-and-minus. A 60-second math lesson by Selena Bui, Math Expert.
Perfect Square Trinomial: x² + 10x + 25
Learn to factor a perfect square trinomial in 60 seconds! Factor x² + 10x + 25 step by step: spot the squares (x² = (x)² and 25 = 5²), check the middle term (2·x·5 = 10x ✓), then write (x + 5)². Bonus example: 4x² − 12x + 9 = (2x − 3)². Remember the pattern: square, square, twice-the-product. A 60-second math lesson by Selena Bui, Math Expert.
Spot the Perfect Square Trinomial Challenge
A 60-second algebra challenge: is 4x² − 12x + 9 a perfect square trinomial? The three-check test (first term a square, last term a square, middle matches twice-the-product) gives (2x − 3)². Then the twist: x² + 6x + 8 is NOT a perfect square trinomial because 8 is not a perfect square, so factor it the normal way as (x + 2)(x + 4). The payoff: the middle is the judge — always verify 2ab. A 60-second math lesson by Selena Bui, Math Expert.
Factor 2x² + 7x + 3 (a > 1)
Learn how to factor a trinomial when a is bigger than 1 in 60 seconds. This video works through 2x²+7x+3 step by step: multiply a·c to get 6, find the pair 1 and 6 that multiply to 6 and add to 7, split the middle term, then factor by grouping to get (2x+1)(x+3). A bonus example, 3x²−5x−2 = (3x+1)(x−2), shows how to handle signs. The payoff: multiply a·c, find the pair, split and group. A 60-second math lesson by Selena Bui, Math Expert.
Factor 2x² + 7x + 3 Challenge (a > 1)
Factor 2x²+7x+3 in 30 seconds using the a·c method: a·c = 6, the pair 1 and 6, split and group to get (2x+1)(x+3). Then the twist — 3x²−5x−2: here a·c = −6, the sign trap, so the pair must have different signs: −6 and +1, giving (3x+1)(x−2). The payoff rule: when a·c is negative, the pair splits across the minus. A 60-second math lesson by Selena Bui, Math Expert.
Factor by Grouping: ax + ay + bx + by
Factor by grouping, the how-to method for four-term polynomials. In 60 seconds: group 3x + 6 + 4xy + 8y into pairs, factor each pair to 3(x + 2) + 4y(x + 2), then pull out the common bracket (x + 2) to get (x + 2)(3 + 4y) — always double-check by distributing. Bonus example: 2xy + 10x + 3y + 15 becomes (y + 5)(2x + 3). A 60-second math lesson by Selena Bui, Math Expert.
The Zero Product Property — Why Factoring Solves Equations
The zero product property is the key that unlocks solving equations: if a times b equals zero, then a is zero or b is zero, because zero times anything is zero. That's why we factor first — factoring turns an equation into a product equal to zero, and each factor gives a solution, as in (x+3)(x−4) = 0 giving x = −3 or x = 4. Beware the classic trap: the property only works when the product equals zero, so for (x+3)(x−4) = 5 you must move everything to zero first. A 60-second math lesson by Selena Bui, Math Expert.
Solve (x+3)(x−4) = 0 with the Zero Product Property
The zero product property is the fastest way to solve a factored equation: split (x+3)(x−4) = 0 into x + 3 = 0 and x − 4 = 0, solve each to get x = −3 or x = 4, then check both answers by plugging them back in. If the equation isn't factored yet, factor first: x² − x − 12 = 0 becomes (x−4)(x+3) = 0, giving x = 4 or x = −3. Remember the key rule: the equation must equal zero BEFORE you split — for (x+3)(x−4) = 5, move the 5 first. A 60-second math lesson by Selena Bui, Math Expert.
Solve x² + 7x + 12 = 0 by Factoring
Learn how to solve x²+7x+12=0 by factoring in 60 seconds. Step 1: make sure the equation equals zero. Step 2: factor — find two numbers that multiply to 12 and add to 7 (3 and 4), giving (x+3)(x+4) = 0. Step 3: split with the zero product property — x = −3 or x = −4 — and check: 9−21+12 = 0. Includes a bonus rectangle word problem: area 40, length 3 more than width, so x(x+3) = 40 gives width 5 and length 8. Payoff: factor first, then zero product. A 60-second math lesson by Selena Bui, Math Expert.
The Garden Problem: Solve x² + 7x + 12 = 0 in Real Life
Maya's garden is 3 meters longer than it is wide, and its area is 40 square meters — how wide is it? This 60-second lesson translates the words into an equation: with width x, the area gives x(x + 3) = 40, or x² + 3x − 40 = 0. Factoring with 8 and −5 gives (x + 8)(x − 5) = 0, so x = 5 (rejecting the negative width): the garden is 5 m by 8 m, verified by 5 × 8 = 40 and 8 − 5 = 3. It uses the same factoring pattern as x²+7x+12 = 0 — words to equation, factor, solve. A 60-second math lesson by Selena Bui, Math Expert.
The Quadratic Formula — Why It Works
The quadratic formula is the universal backup when factoring fails on messy numbers: completing the square once on ax²+bx+c = 0 produces x = (−b ± √(b²−4ac)) / 2a, a formula that always works. For 2x²+4x−6 = 0, identifying a = 2, b = 4, c = −6 and plugging in gives x = (−4 ± √(16+48))/4 = (−4 ± 8)/4, so x = 1 or x = −3 — both check out. Bonus insight: the discriminant b²−4ac tells you how many real solutions exist — positive means two, zero means one, and negative means no real solution. A 60-second math lesson by Selena Bui, Math Expert.
Use the Quadratic Formula: 3x² + 2x − 5 = 0
Learn to use the quadratic formula in 60 seconds with a worked example. For 3x²+2x−5=0, identify a=3, b=2, c=−5, plug into x=(−b±√(b²−4ac))/2a, and simplify: the discriminant is 64, so the two answers are x=1 and x=−5/3. A bonus example, x²−4x+3=0, shows the same steps give x=3 and x=1. A 60-second math lesson by Selena Bui, Math Expert.
Quadratic Formula Challenge: Negative Discriminant!
Can the quadratic formula say NO? This 60-second challenge solves x² + 2x + 5 = 0 with the quadratic formula: a = 1, b = 2, c = 5 gives x = (−2 ± √(4−20)) / 2. The discriminant is 4 − 20 = −16 — negative — so there is no real solution, and the discriminant warns you before you compute. Bonus quick-fire: x² − 6x + 9 = 0 has discriminant 0, so one solution: x = 3 (a double root). A 60-second math lesson by Selena Bui, Math Expert.
Graphing Parabolas: Why y = x² Opens Up
Why does the graph of y = x squared look like a U? This 60-second lesson shows that squaring any number gives a non-negative result, so the lowest point of the graph is the vertex at the origin — a minimum — and the parabola opens upward. Flipping the sign to y = negative x squared reverses every value, putting the vertex at the top as a maximum so the parabola opens downward. A plotted table of values and coordinate graphs make the direction rule stick: squaring sets the direction, and the vertex is the extreme point. A 60-second math lesson by Selena Bui, Math Expert.
Graph y = x² Step by Step (Table of Values)
Learn how to graph y = x squared step by step in 60 seconds. Build the table of values (x = negative 2 through 2 gives y = 4, 1, 0, 1, 4), plot the points, and connect them with a smooth U-curve, then label the vertex at (0, 0) and the axis of symmetry x = 0. Bonus: y = negative x squared uses the same steps but opens upside down, with the vertex as the maximum. A 60-second math lesson by Selena Bui, Math Expert.
Square Roots: Why √49 = 7 and √2 Never Ends
Learn what square roots really mean in 60 seconds. √49 = 7 because 7² = 49 — the square root UNDOES the square. Perfect squares give clean answers, from √1 = 1 all the way to √100 = 10. But √2 is different: it sits between 1 and 2, and its decimal 1.41421356… never ends and never repeats — it's irrational. A 60-second math lesson by Selena Bui, Math Expert.
Simplify √12 and √50 (Pull Out the Perfect Squares)
Learn how to simplify square roots in 60 seconds. To simplify the square root of 12, factor 12 into a perfect square times the rest (12 = 4 × 3), split the root into root 4 times root 3, and simplify to 2√3 — then check that (2√3)² = 4 × 3 = 12. Bonus examples: √50 = 5√2 and √18 = 3√2, plus the classic trap: √12 is not √9 + √3, because roots never split across addition. A 60-second math lesson by Selena Bui, Math Expert.
Simplify Radicals: √50 = 5√2
Learn how to simplify radicals in 60 seconds. To simplify the square root of 50, factor 50 into the biggest perfect square times the rest (50 = 25 × 2), split the root into root 25 times root 2, and simplify to 5√2 — then check that (5√2)² = 25 × 2 = 50. Bonus examples: √72 = 6√2 and √98 = 7√2, plus the classic trap: 9 does not divide 50, so always pull out the biggest perfect square.
Radical Challenge: Simplify √72 in 30 Seconds!
Take the radical challenge: simplify the square root of 72 in 30 seconds by splitting 72 into the biggest perfect square (72 = 36 × 2 → 6√2, and check (6√2)² = 72). Then the twist: the square root of 300 hides two perfect squares, 25 and 100 — always take the BIGGEST (300 = 100 × 3 → 10√3). Watch the trap: 2√12 is NOT finished, because 12 still hides a 4 — simplified means NO perfect square left inside, so √48 = √(16 × 3) = 4√3. Go all the way — biggest square, one step. A 60-second math lesson by Selena Bui, Math Expert.
Add Radicals Like Terms: 2√3 + 5√3 = 7√3
Why does 2√3 + 5√3 = 7√3? This 60-second concept video explains the WHY: radicals add like terms because the radical part is the same — just like 2x + 5x = 7x, the √3 is a thing being counted. Watch the key move of simplifying first: √12 + √27 becomes 2√3 + 3√3 = 5√3, confirmed by the decimal check (3.464 + 5.196 = 8.660 = 5√3). Plus the can't-combine trap: 2√3 + 5√2 stays as-is, like 2x + 5y. A 60-second math lesson by Selena Bui, Math Expert.
Combine √12 + √27 Step by Step
Learn how to combine radicals step by step: simplify √12 = 2√3 and √27 = 3√3, then add the front numbers to get 5√3 — verified with decimals (3.464 + 5.196 = 8.660). Includes a subtraction bonus (4√2 − √8 = 2√2) and the classic trap: different radicals like 2√3 + 5√2 canNOT combine. A 60-second math lesson by Selena Bui, Math Expert.
Multiply Radicals: √2 · √8 = 4
Learn HOW to multiply radicals in 60 seconds with a worked example: √2 · √8 = √(2·8) = √16 = 4 — verified with decimals, since 1.414 × 2.828 ≈ 4.000. With coefficients, multiply the fronts and the insides separately: 2√3 · 3√5 = 6√15. Watch the trap: multiplying radicals is NOT adding the insides (√2·√8 ≠ √10). The method recap: combine under one root, then simplify. A 60-second math lesson by Selena Bui, Math Expert.
Pythagoras: Why a² + b² = c²
Why does a²+b²=c²? This 60-second concept lesson explains the WHY behind the Pythagorean theorem: the squares built on the two legs of a right triangle have areas a² and b², and together they exactly fill the square built on the hypotenuse (c²) — area conservation, not just a rule. It verifies the idea on the 3-4-5 triangle (9+16=25=5²) and solves a real ladder problem: a 10-foot ladder with its base 6 feet from the wall reaches 8 feet up. A 60-second math lesson by Selena Bui, Math Expert.
Find the Missing Side: 6-8-? Triangle
Learn how to use the Pythagorean theorem step by step in 60 seconds. Label the legs a=6 and b=8, then solve for the hypotenuse: 6²+8²=c² gives 36+64=100, so c=10. Bonus: find a missing leg with hypotenuse 13 and leg 5 — a²=169−25=144, so a=12. Remember: the hypotenuse always stands alone, c²=a²+b² — square, add or subtract, root. A 60-second math lesson by Selena Bui, Math Expert.
The Ladder Problem: 10 ft Ladder, 6 ft Out
A 10-foot ladder leans against a wall, 6 feet from the base — how high does it reach? This 60-second word-problem video turns the story into a right triangle (the ladder is the hypotenuse), solves a² = 10² − 6² = 64 for 8 feet, and double-checks with 8² + 6² = 10². Shows how painters, firefighters, and roofers use the Pythagorean theorem every day. A 60-second math lesson by Selena Bui, Math Expert.
Complementary vs Supplementary Angles
Complementary vs supplementary angles — what’s the difference? This 60-second concept video explains the WHY: complementary angles add to 90 degrees because together they make a corner, like the corner of a book — C is for corner! Thirty-five plus fifty-five is ninety, so the complement of 35° is 55°. Supplementary angles add to 180 degrees because together they make a straight line, like a flat road — S is for straight! One hundred ten plus seventy is one eighty, so the supplement of 110° is 70°. Memory hook: C = Corner = 90°, S = Straight = 180°. A 60-second math lesson by Selena Bui, Math Expert.
Find Complements and Supplements Fast
Find complements and supplements in 60 seconds. Step one: spot the word — complementary means subtract from 90 and supplementary means subtract from 180. Worked examples: the complement of 28 degrees is 62 degrees, and the supplement of 132 degrees is 48 degrees. Trap: never mix the targets — 90 is the corner, 180 is the straight line. A 60-second math lesson by Selena Bui, Math Expert.
Vertical Angles Are Equal: Solve 2x = 60
This 60-second lesson teaches how to solve vertical-angles equations: spot the X formed by two crossing lines, set the opposite (vertical) angles equal, and solve. Worked example: vertical angles 2x and 60 degrees give 2x = 60, so x = 30, and the adjacent angle is 180 − 60 = 120 degrees. A harder example solves 3x + 10 = 130 to get x = 40, plus the trap to avoid: adjacent angles are supplementary, not equal. The payoff rule: opposite angles are equal, adjacent angles sum to 180 degrees. A 60-second math lesson by Selena Bui, Math Expert.
Why Every Triangle Adds to 180°
Why do the angles of every triangle add to 180 degrees? Tear off the three corners of a paper triangle and line them up — they form a straight line, which is exactly 180°. The proof uses a line through one vertex parallel to the opposite side: the corner angles swap onto the straight line (alternate interior angles) and lay flat. Two worked examples: given 50° and 60°, the missing angle is 70° (180 − 110); in a right triangle with 90° and 40°, the missing angle is 50° (180 − 130). Three angles — always 180°. A 60-second math lesson by Selena Bui, Math Expert.
Find the Missing Angle: 50° and 60°
A 60-second lesson on finding a missing triangle angle: add the two known angles (50° + 60° = 110°) and subtract from 180° to get 70°, then check by adding all three back. Also covers the algebra version with angles x, 2x, 3x solving to 30°, 60°, 90°. A one-line method: add, subtract from 180°, check. A 60-second math lesson by Selena Bui, Math Expert.
Name That Triangle: 6 Types
Why do triangles have six different names? This 60-second lesson shows that triangles are classified two ways: by SIDES (scalene — all sides different; isosceles — two equal legs; equilateral — all equal) and by ANGLES (acute — all under 90 degrees; right — one exactly 90 degrees; obtuse — one over 90 degrees). The payoff: one triangle can wear TWO labels — an isosceles right triangle has 45-45-90 degree angles that sum to 180, and an equilateral triangle is always 60-60-60. Sides plus angles equals six names for one triangle. A 60-second math lesson by Selena Bui, Math Expert.
Classify the Triangle in 5 Seconds
Learn to classify any triangle in 60 seconds with the angle-first method. Step one: check the biggest angle — over 90° is obtuse, exactly 90° is right, under 90° is acute. Step two: check the sides. Three worked examples: 100°, 50°, 30° with sides 5, 7, 9 becomes obtuse scalene; 60°, 60°, 60° becomes acute equilateral; sides 8, 8, 5 with angles 80°, 80°, 20° becomes acute isosceles. The trap to avoid: always check angles first — it’s the faster filter. A 60-second math lesson by Selena Bui, Math Expert.
Area of a Parallelogram: 8 × 5
Find the area of a parallelogram with base 8 cm and height 5 cm: A = base × height = 8 × 5 = 40 square centimeters. Learn the classic trap — the height must be perpendicular to the base, not the slanted side (8 × 6 = 48 is wrong!). A garden word problem puts the formula to work: a parallelogram bed with base 8 m and height 5 m needs 40 square meters of soil, costing $120 at $3 per square meter. A 60-second math lesson by Selena Bui, Math Expert.
The Garden Bed: How Much Soil?
A 60-second word problem: Selena’s community garden bed is a parallelogram with base 8 m and height 5 m. Translate the story to math: area = base × height = 8 × 5 = 40 m² of soil, and at $3 per square meter the cost is 40 × 3 = $120. The trap: the slanted side is 6 m, but area uses the height — 8 × 6 = 48 is wrong. A 60-second math lesson by Selena Bui, Math Expert.
Why Triangle Area Is Half
Why does the triangle area formula have a half in it? This 60-second lesson shows that two copies of the same triangle fit together into a parallelogram with area base times height — so one triangle is exactly half of that box, giving A = one-half times b times h. It works through base 10, height 6 to get 30, then reverses the formula to find height 8 from area 48 and base 12. A 60-second math lesson by Selena Bui, Math Expert.
Triangle Area: Base 10, Height 6
How to find the area of a triangle in 60 seconds. With base 10 and height 6, first “box it” (10 × 6 = 60), then “halve it” — half of 60 is 30. The video also works the reverse problem (area 36, base 9 → height 8) and warns against the classic trap of forgetting the half, plus a speed tip: halve the even number first to keep the numbers whole. A 60-second math lesson by Selena Bui, Math Expert.
Circles: Circumference vs Area
Why does a circle have two pi formulas? This 60-second lesson explains that circumference (C = 2πr) measures the ROUND TRIP — the fence around the circle — while area (A = πr²) measures the FILL — the grass inside. It works through radius 3 (C ≈ 18.8, A ≈ 28.3) and a 12-inch pizza check (r = 6 → A ≈ 113 in²), and warns about the classic trap: circumference uses r once, but area squares it. A 60-second math lesson by Selena Bui, Math Expert.
Circle Math: r = 3 Step by Step
How do you find the circumference and area of a circle? This 60-second lesson works it step by step with radius 3 and pi about 3.14: C = 2πr = 2 × 3.14 × 3 = 18.84 and A = πr² = 3.14 × 9 = 28.26, with the warning that r squared is 9, not 6. It then reverses the formula — given C = 31.4, solving 31.4 = 6.28r gives r = 5 — and checks the answer back. The takeaway: double for the fence, square for the grass. A 60-second math lesson by Selena Bui, Math Expert.
The Pizza Deal: Which Size Wins?
A classic circle-area word problem: is a 12-inch pizza for $10 or two 8-inch pizzas for $5 each the better deal? This 60-second lesson translates the story into area-per-dollar math — the 12-inch pizza (r = 6, A ≈ 113 in²) gives 11.31 in² per dollar, while the two 8-inch pizzas (r = 4, A ≈ 50 in² each, 100 in² total) give 10.05 in² per dollar, so the 12-inch wins. Viewers learn the key trap: diameter is not the radius — always halve it first — and the payoff rule: price per square inch decides. A 60-second math lesson by Selena Bui, Math Expert.
Volume of a Box: 4 × 3 × 2
Learn how to find prism volume in 60 seconds. A prism’s volume is base AREA × height: for a box 4 × 3 × 2, the base area is 4 × 3 = 12, so the volume is 12 × 2 = 24 cubic inches — enough foam for the gift box. A triangular prism (triangle base 6, height 4, length 5) has base area ½ × 6 × 4 = 12, giving 12 × 5 = 60. Remember the trap: find the base AREA first — don’t just multiply three numbers. A 60-second math lesson by Selena Bui, Math Expert.
The Moving Box: How Much Fits?
A 60-second word problem: a 10 ft × 6 ft × 5 ft moving truck box — how many 1-ft³ boxes fit inside? Students translate the story into V = base area × height, compute 10 × 6 = 60 and 60 × 5 = 300 ft³, check the answer, then apply it to a 5 × 2 × 3 ft fish tank holding 30 ft³ of water. The lesson lands on one rule: volume tells you capacity, which is why movers, warehouses, and shipping companies charge by volume. A 60-second math lesson by Selena Bui, Math Expert.
Cylinder Volume: r = 2, h = 5
Find the volume of a cylinder in 60 seconds! Using a soup can with radius 2 and height 5, Selena walks through V = πr²h: the base area is π × 4 ≈ 12.57, and times the height 5 that gives ≈ 62.83 cubic inches. She also reverses it (V = 100π, r = 5 → h = 4) and flags the classic trap: r² means r × r, not 2r. A 60-second math lesson by Selena Bui, Math Expert.
Surface Area: Unfold the Box
Surface area is the OUTSIDE of a solid — unfold the box into its NET, lay every face flat, then add them all. Cube with side 3: 6 faces, each 3 × 3 = 9, so SA = 6 × 9 = 54 square units. Rectangular box 4 × 3 × 2: 2(4×3) + 2(4×2) + 2(3×2) = 24 + 16 + 12 = 52. The trap: surface area counts the outside only — that’s not volume! A 60-second math lesson by Selena Bui, Math Expert.
Surface Area: Cube s = 3
Learn how to compute surface area in 60 seconds: a cube with side 3 gives SA = 6 × 3² = 54; a 5 × 4 × 2 rectangular box gives SA = 2(5×4) + 2(5×2) + 2(4×2) = 76; and a cylinder with radius 3 and height 7 gives SA = 2πr² + 2πrh = 60π ≈ 188.5. The one rule to remember: count all six faces — or think in three pairs. A 60-second math lesson by Selena Bui, Math Expert.
Mean: The Fair-Share Average
What does the average really mean? This 60-second lesson builds the intuition that the mean is the fair share — pool all the values, then share them equally. Two worked demos show how one number tells the whole story: candy shares (8, 6, 4, 2 → mean 5) and test scores (90, 80, 70, 60 → mean 75, rising to 80 with a fifth score of 100). It also flags the classic trap that the mean is not the most common value (that’s the mode), and closes with the one-line rule: total divided by count. A 60-second math lesson by Selena Bui, Math Expert.
Find the Mean: 88, 92, 76
Learn how to find the mean in 60 seconds: add all the values and divide by how many. Working through quiz scores 88, 92, and 76, we get 256 divided by 3 = 85.33, plus a missing-score problem where a mean of 90 over 4 quizzes with 88, 92, and 95 means you need 85. The key trap to avoid: always divide by the count, not the last number. A 60-second math lesson by Selena Bui, Math Expert.
Bake Sale: Find the Average Price
A bake sale word problem about the mean: four cupcakes sold at $2.50, $3.00, $1.50, and $3.00, for a $10.00 total and an average price of $2.50. Then a twist — when one cupcake sells for $5.00 instead of $1.50, the new total is $13.50 and the mean jumps to about $3.38. Shows why averages respond to every sale. A 60-second math lesson by Selena Bui, Math Expert.
Median vs Mode: Which Average to Use
Learn why the mean can lie: with salaries of 30k, 32k, 35k, 38k and a 200k boss, the average is 67k — but nobody earns that. This 60-second lesson shows why the median (35k, the middle value) resists outliers and why the mode (9, the most frequent shoe size) reveals what’s popular. Remember: median = middle, mode = most. A 60-second math lesson by Selena Bui, Math Expert.
Median of 3, 7, 8, 12, 21 & Mode of 4, 6, 6, 9
Learn how to find the median and mode in 60 seconds! Sort the data set 12, 3, 8, 21, 7 to 3, 7, 8, 12, 21 — with an odd count of five, the middle value is the median: 8. For an even count, like 2, 5, 9, 11, average the middle two: (5 + 9) / 2 = 7. The mode is simply the value that appears most often — in 4, 6, 6, 9, that is 6. Remember the trap: always sort first, never take the middle of an unsorted list! A 60-second math lesson by Selena Bui, Math Expert.
Range of 5, 12, 3, 21, 9
Learn to find the range of a data set in 60 seconds. Three steps: find the max, find the min, subtract — biggest minus smallest. Worked examples: 5, 12, 3, 21, 9 gives range 18, and 40, 45, 38, 50, 42 gives range 12. Plus the classic trap: range measures the spread (big range = scattered, small range = clustered), not the middle. A 60-second math lesson by Selena Bui, Math Expert.
Bar vs Line: How to Read Graphs
Learn to read graphs in 60 seconds. Bars compare values: daily sales Monday 5, Tuesday 7, Wednesday 4, Thursday 9, Friday 6, so the tallest bar — Thursday at 9 — wins. Lines show trends: temperatures 68, 70, 72, 75, 78 slope upward, a warming trend. Watch the trap: always read the axes first, because a y-axis starting at 100 makes tiny changes look huge. Rule: axes first, picture second. A 60-second math lesson by Selena Bui, Math Expert.
Read the Graph: Sales Quiz
Learn to read graphs in 60 seconds with three steps: read the title, read the axes, then answer the question. Bar graph example — Weekly Ice Cream Sales: Monday 12, Tuesday 8, Wednesday 15, Thursday 10, Friday 20 — Friday sold the most (20!), which is 8 more than Monday (20 − 12 = 8). Line graph example — Plant Height: weeks 1–4 measure 5, 9, 12, 18 — tallest is week 4 at 18, and the growth from week 3 to week 4 is 18 − 12 = 6. Trap to avoid: never guess from bar height alone — always read the numbers. Rule: Title — Axes — Question. A 60-second math lesson by Selena Bui, Math Expert.
Probability: Favorable Over Total
Why is probability just a fraction? This 60-second concept lesson explains that probability equals favorable outcomes over total outcomes: a die roll gives 1/6, a marble bag with 3 red of 10 marbles gives 3/10, and a coin flip gives 1/2. The key trap: count ALL outcomes, not just the ones you want. A 60-second math lesson by Selena Bui, Math Expert.
P(Spade): 52-Card Deck
How do you compute a probability step by step? This 60-second lesson works three probabilities from a standard 52-card deck: P(spade) = 13/52 = 1/4, P(face card) = 12/52 = 3/13, and P(red king) = 2/52 = 1/26. The method is three steps — count favorable, count total, divide — with the trap of counting suits carefully so red and black never get mixed up. A 60-second math lesson by Selena Bui, Math Expert.
The Candy Jar: P(Red)
Learn basic probability in 60 seconds with a candy jar story. A jar holds six red, four blue, and five green candies — fifteen total — so the probability of grabbing a red is six over fifteen, or two-fifths. Then the twist: you eat one red candy, so now it is five red out of fourteen total — the probability changed! The takeaway: eating changed both the favorable count and the total, so always count again after every change. A 60-second math lesson by Selena Bui, Math Expert.
Two Marbles, With Replacement
A story-style probability problem: a bag holds 5 red and 3 blue marbles. Drawing a red marble then a blue one WITH replacement gives P = 5/8 × 3/8 = 15/64 (verified: 5 × 3 = 15, 8 × 8 = 64). The twist shows WITHOUT replacement the total drops by one: 5/8 × 3/7 = 15/56 (5 × 3 = 15, 8 × 7 = 56). The payoff: replacement keeps the fractions the same. A 60-second math lesson by Selena Bui, Math Expert.
Challenge: P(Ace Then King)
A 60-second challenge on compound probability without replacement. After a marble warm-up (5/10 × 5/9 = 5/18), the twist: drawing an ace then a king from a 52-card deck gives 4/52 × 4/51 = 16/2652 = 4/663. The key insight: the second fraction’s total drops by one — never reuse the first total. A 60-second math lesson by Selena Bui, Math Expert.
60 Rolls: Expect 10 Sixes
A story problem: roll a fair die 60 times — how many sixes should you expect? Selena shows that expected count equals trials times probability: 60 × 1/6 = 10, and doubling to 120 rolls gives 20 sixes. She also runs a fairness check (expected 10, got 25 = probably loaded) and warns that expected is a long-run average, not a guarantee. A 60-second math lesson by Selena Bui, Math Expert.
Unit Rate: 120 mi / 2 h = 60 mph
Learn unit rates in 60 seconds: 120 miles in 2 hours — how fast? Write the rate (120 miles / 2 hours), divide (120 ÷ 2 = 60), attach the units — 60 miles per hour! Two more, same steps: $24 for 6 pizzas gives $4 per pizza, and 150 words in 3 minutes gives 50 words per minute. A rate compares two different units — a unit rate makes the second one 1. A 60-second math lesson by Selena Bui, Math Expert.
Selena Bui · Math Expert
New lessons are added to the bank regularly — check back soon.