Division Facts & Remainders
Divide within 100, make sense of remainders, and use fact families to check every answer with multiplication.
1 What division really means
Division splits a total into equal groups. 13 ÷ 4 asks: how many full groups of 4 fit into 13?
The four names
In 13 ÷ 4 = 3 R 1: 13 is the dividend (the total), 4 is the divisor (group size), 3 is the quotient (full groups), and 1 is the remainder (what is left over).
Remainders are real answers
3 × 4 = 12, and 13 − 12 = 1 is left over. So 13 ÷ 4 = 3 R 1 — never just 3. The remainder must always be smaller than the divisor; if it is not, you can make another group.
What the remainder means depends on the story
Round up: 27 students, vans hold 6 → 4 full vans plus 3 students need a 5th van. Drop it: 27 stickers, 6 per page → 4 full pages, 3 stickers do not fill a page. Share it: 13 cookies among 4 friends → each gets 3, 1 cookie is left to share.
2 See it: groups and leftovers
13 dots sorted into groups of 4. Count the full groups, then the leftovers.
3 Worked examples
Divide, then always check: quotient × divisor + remainder = dividend.
- Thinking: which number times 7 gives 56? 7 × 8 = 56.
- So 56 ÷ 7 = 8 with nothing left over.
- Check: 8 × 7 = 56. Correct.
- Thinking: 4 × 3 = 12 fits; 4 × 4 = 16 is too big.
- 12 out of 13 are used, leaving 13 − 12 = 1.
- Check: 3 × 4 + 1 = 13. The remainder 1 is smaller than 4. Correct.
- Thinking: 27 ÷ 6 = 4 R 3. Four vans are full and 3 students still need a ride.
- Leftover students cannot be dropped — they need a van too.
- So we round up: 4 + 1 = 5 vans.
- Check: 4 vans hold 24 < 27; 5 vans hold 30 ≥ 27. Correct.
- Thinking: 5 × 9 = 45 fits; 5 × 10 = 50 is too big.
- 47 − 45 = 2 left over, so 47 ÷ 5 = 9 R 2.
- Check: quotient × divisor + remainder = 9 × 5 + 2 = 47. Correct.
4 Common mistakes
Two traps catch almost everyone.
5 Key vocabulary
- Dividend
- The total being split (13 in 13 ÷ 4).
- Divisor
- The size of each group, or the number of groups (4 in 13 ÷ 4).
- Quotient
- The number of full groups (3 in 13 ÷ 4 = 3 R 1).
- Remainder
- What is left over. Always smaller than the divisor.
- Fact family
- Related facts like 7 × 8 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7.
- Multiple
- The result of multiplying: 12, 16, 20 are multiples of 4.
6 Quick check
Try these, then reveal the answers.
Key points to remember
- 13 ÷ 4 = 3 R 1: the remainder is part of the answer.
- The remainder is always smaller than the divisor.
- Check every division: quotient × divisor + remainder = dividend.
- In stories, decide what the remainder means: round up, drop it, or share it.
- Fact families link division and multiplication: 56 ÷ 7 = 8 because 7 × 8 = 56.