Comparing Fractions Worksheet
20 fresh comparison problems at your level. Generate, print, and check with the answer key.
Skill: comparing-fractions
Each click of Generate builds a brand-new set of 20 problems. Toggle the answer key any time; printing includes the key only when it is visible.
Comparing Fractions Worksheet
Answer Key
For the teacher or for self-checking after you finish.
/* ===== Fibo elementary core — skill: comparing-fractions — pure, node-testable ===== */ (function (root, factory) { 'use strict'; var api = factory(); if (typeof module === 'undefined') { root.FiboCore_comparing_fractions = api; } else { module.exports = api; } })(typeof self !== 'undefined' ? self : this, function () { 'use strict'; /* ---------------- seeded PRNG ---------------- */ function mulberry32(a){ return function(){ a |= 0; a = (a + 0x6D2B79F5) | 0; var t = Math.imul(a ^ (a >>> 15), 1 | a); t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t; return ((t ^ (t >>> 14)) >>> 0) / 4294967296; }; } function shuffle(arr, rand){ for (var i = arr.length - 1; i > 0; i--){ var j = Math.floor(rand() * (i + 1)); var t = arr[i]; arr[i] = arr[j]; arr[j] = t; } return arr; } var _rand = Math.random; function setSeed(s){ _rand = mulberry32(s >>> 0); } function ri(lo, hi){ return lo + Math.floor(_rand() * (hi - lo + 1)); } function rpick(arr){ return arr[Math.floor(_rand() * arr.length)]; } function rchance(p){ return _rand() < p; } function rshuffle(a){ for (var i = a.length - 1; i > 0; i--){ var j = Math.floor(_rand() * (i + 1)); var t = a[i]; a[i] = a[j]; a[j] = t; } return a; } /* ---------------- exact integer / rational math ---------------- */ function ggcd(a, b){ a = Math.abs(a); b = Math.abs(b); while (b){ var t = a % b; a = b; b = t; } return a || 1; } function gred(n, d){ if (d === 0) throw new Error('gred: zero denominator'); if (d < 0){ n = -n; d = -d; } if (n === 0) return { n: 0, d: 1 }; var g = ggcd(n, d); return { n: n / g, d: d / g }; } function sameFrac(a, b){ return a.n * b.d === b.n * a.d; } /* exact decimal as {v: integer digits, p: places} */ function decVal(d){ return d.v / Math.pow(10, d.p); } function decNorm(d){ var v = d.v, p = d.p; while (p > 0){ if (v % 10 !== 0) break; v = v / 10; p = p - 1; } return { v: v, p: p }; } function decAdd(a, b){ var p = Math.max(a.p, b.p); var va = a.v * Math.pow(10, p - a.p); var vb = b.v * Math.pow(10, p - b.p); return decNorm({ v: va + vb, p: p }); } function decSub(a, b){ var p = Math.max(a.p, b.p); var va = a.v * Math.pow(10, p - a.p); var vb = b.v * Math.pow(10, p - b.p); return decNorm({ v: va - vb, p: p }); } function decTextFromVP(v, p){ var neg = v < 0; var s = String(Math.abs(v)); while (s.length <= p) s = '0' + s; var out; if (p === 0) out = s; else out = s.slice(0, s.length - p) + '.' + s.slice(s.length - p); if (neg) out = '-' + out; return out; } function decText(v){ var r = Math.round(v * 1e6) / 1e6; var s = String(r); if (s.indexOf('.') < 0) return s; s = s.replace(/0+$/, '').replace(/\.$/, ''); if (s === '-0') s = '0'; return s; } /* ---------------- formatting (HTML) ---------------- */ function fracHTML(n, d){ var r = gred(n, d); var sign = r.n < 0 ? '−' : ''; if (r.d === 1) return '' + sign + Math.abs(r.n) + ''; return sign + '' + Math.abs(r.n) + '' + r.d + ''; } function mixedHTML(w, n, d){ var r = gred(n, d); if (r.n === 0) return '' + w + ''; return '' + w + ' ' + fracHTML(r.n, r.d); } function intHTML(v){ return '' + v + ''; } function qrHTML(q, r){ if (r === 0) return '' + q + ''; return '' + q + ' R ' + r + ''; } function ansHTML(ans){ if (ans.kind === 'int') return intHTML(ans.v); if (ans.kind === 'frac') return fracHTML(ans.n, ans.d); if (ans.kind === 'mixed') return mixedHTML(ans.w, ans.n, ans.d); if (ans.kind === 'dec') return '' + decText(ans.v) + ''; if (ans.kind === 'qr') return qrHTML(ans.q, ans.r); if (ans.kind === 'cmp') return '' + (ans.c === '<' ? '<' : (ans.c === '>' ? '>' : '=')) + ''; if (ans.kind === 'yesno') return '' + (ans.v ? 'Yes' : 'No') + ''; if (ans.kind === 'parts') return '' + ans.parts.join(' + ') + ''; return '?'; } function ansText(ans){ if (ans.kind === 'int') return String(ans.v); if (ans.kind === 'frac'){ var r = gred(ans.n, ans.d); return r.d === 1 ? String(r.n) : r.n + '/' + r.d; } if (ans.kind === 'mixed'){ var g = gred(ans.n, ans.d); if (g.n === 0) return String(ans.w); var f = g.d === 1 ? String(ans.w + g.n) : ans.w + ' ' + g.n + '/' + g.d; return f; } if (ans.kind === 'dec') return decText(ans.v); if (ans.kind === 'qr') return ans.r === 0 ? String(ans.q) : ans.q + ' R ' + ans.r; if (ans.kind === 'cmp') return ans.c; if (ans.kind === 'yesno') return ans.v ? 'yes' : 'no'; if (ans.kind === 'parts') return ans.parts.join(' + '); return ''; } /* ---------------- input parsing ---------------- */ function parseIntInput(raw){ var t = String(raw).trim().replace(/,/g, ''); if (!/^[+-]?\d+$/.test(t)) return { ok: false }; return { ok: true, kind: 'int', v: parseInt(t, 10) }; } function parseFracInput(raw){ var t = String(raw).trim().replace(/\s+/g, ''); var m = t.match(/^([+-]?\d+)\/(\d+)$/); if (m){ var d = parseInt(m[2], 10); if (d === 0) return { ok: false }; var r = gred(parseInt(m[1], 10), d); return { ok: true, kind: 'frac', n: r.n, d: r.d }; } var iv = parseIntInput(raw); if (iv.ok) return { ok: true, kind: 'frac', n: iv.v, d: 1 }; return { ok: false }; } function parseMixedInput(raw){ var t = String(raw).trim().replace(/\s+/g, ' '); var m = t.match(/^(\d+)\s+(\d+)\/(\d+)$/); if (m){ var w = parseInt(m[1], 10), n = parseInt(m[2], 10), d = parseInt(m[3], 10); if (d === 0) return { ok: false }; if (n >= d) return { ok: false }; var r = gred(n, d); return { ok: true, kind: 'mixed', w: w, n: r.n, d: r.d }; } var f = parseFracInput(raw); if (f.ok) return f; return { ok: false }; } function parseDecInput(raw){ var t = String(raw).trim().replace(/,/g, '').replace(/^\$/, ''); if (!/^[+-]?(\d+(\.\d*)?|\.\d+)$/.test(t)) return { ok: false }; return { ok: true, kind: 'dec', v: parseFloat(t) }; } function parseCmpInput(raw){ var t = String(raw).trim().toLowerCase(); if (t === '<' || t === 'less' || t === 'less than' || t === 'smaller') return { ok: true, kind: 'cmp', v: -1 }; if (t === '>' || t === 'greater' || t === 'greater than' || t === 'bigger' || t === 'larger') return { ok: true, kind: 'cmp', v: 1 }; if (t === '=' || t === '==' || t === 'equal' || t === 'equals' || t === 'same') return { ok: true, kind: 'cmp', v: 0 }; return { ok: false }; } function parseYesNo(raw){ var t = String(raw).trim().toLowerCase(); if (t === 'yes' || t === 'y') return { ok: true, kind: 'yesno', v: true }; if (t === 'no' || t === 'n') return { ok: true, kind: 'yesno', v: false }; return { ok: false }; } function parseQRInput(raw){ var t = String(raw).trim().toLowerCase().replace(/remainder/g, 'r'); var parts = t.split(/[^0-9]+/); var nums = []; for (var i = 0; i < parts.length; i++){ if (parts[i] !== '') nums.push(parseInt(parts[i], 10)); } if (nums.length === 1) return { ok: true, kind: 'qr', q: nums[0], r: 0 }; if (nums.length === 2) return { ok: true, kind: 'qr', q: nums[0], r: nums[1] }; return { ok: false }; } function parsePartsInput(raw){ var t = String(raw).trim().toLowerCase().replace(/plus|and/g, '+'); var chunks = t.split(/[^0-9]+/); var parts = []; for (var i = 0; i < chunks.length; i++){ if (chunks[i] !== '') parts.push(parseInt(chunks[i], 10)); } if (parts.length === 0) return { ok: false }; return { ok: true, kind: 'parts', parts: parts }; } function parseByKind(kind, raw){ if (kind === 'int') return parseIntInput(raw); if (kind === 'frac') return parseFracInput(raw); if (kind === 'mixed') return parseMixedInput(raw); if (kind === 'dec') return parseDecInput(raw); if (kind === 'cmp') return parseCmpInput(raw); if (kind === 'yesno') return parseYesNo(raw); if (kind === 'qr') return parseQRInput(raw); if (kind === 'parts') return parsePartsInput(raw); return { ok: false }; } function entryHintFor(kind){ if (kind === 'int') return 'Enter a whole number, e.g. 42.'; if (kind === 'frac') return 'Enter a fraction like 3/4 (a whole number is fine too).'; if (kind === 'mixed') return 'Enter a mixed number like 2 1/3, or an improper fraction like 7/3.'; if (kind === 'dec') return 'Enter a decimal like 0.75.'; if (kind === 'cmp') return 'Enter <, >, or = (you can also type "less", "greater", or "equal").'; if (kind === 'yesno') return 'Enter yes or no.'; if (kind === 'qr') return 'Enter the quotient and remainder like 7 R 2.'; if (kind === 'parts') return 'Enter the partial products separated by +, e.g. 120 + 30.'; return 'Type your answer.'; } /* ---------------- answer checking ---------------- */ function ratOf(ans){ if (ans.kind === 'int') return { n: ans.v, d: 1 }; if (ans.kind === 'frac') return { n: ans.n, d: ans.d }; if (ans.kind === 'mixed') return { n: ans.w * ans.d + ans.n, d: ans.d }; return null; } function checkAnswer(exp, parsed){ if (!parsed.ok) return false; if (exp.kind === 'int') return !(!(parsed.kind === 'int') || !(parsed.v === exp.v)); if (exp.kind === 'qr') return !(!(parsed.kind === 'qr') || !(parsed.q === exp.q) || !(parsed.r === exp.r)); if (exp.kind === 'cmp'){ if (parsed.kind !== 'cmp') return false; var ev = exp.c === '<' ? -1 : (exp.c === '>' ? 1 : 0); return parsed.v === ev; } if (exp.kind === 'yesno') return !(!(parsed.kind === 'yesno') || !(parsed.v === exp.v)); if (exp.kind === 'parts'){ if (parsed.kind !== 'parts') return false; if (parsed.parts.length !== exp.parts.length) return false; var a = exp.parts.slice().sort(function(x, y){ return x - y; }); var b = parsed.parts.slice().sort(function(x, y){ return x - y; }); for (var i = 0; i < a.length; i++) if (a[i] !== b[i]) return false; return true; } if (exp.kind === 'dec'){ if (parsed.kind !== 'dec') return false; var dd = parsed.v - exp.v; if (dd < 0) dd = -dd; return dd < 1e-9; } var e = ratOf(exp); if (!e) return false; if (parsed.kind === 'frac' || parsed.kind === 'int' || parsed.kind === 'mixed'){ return sameFrac(e, ratOf(parsed)); } if (parsed.kind === 'dec'){ var dv = parsed.v - e.n / e.d; if (dv < 0) dv = -dv; return dv < 1e-9; } return false; } /* ---------------- per-skill question templates ---------------- */ function _cSteps(items){ var h = '
- ';
for (var i = 0; i < items.length; i++) h += '
- ' + items[i] + '
'; return h + '
'; } function _cWhy(steps, ansHTML){ return _cSteps(steps) + '
'; } function _ccmp(n1, d1, n2, d2){ var L = n1 * d2, R = n2 * d1; return L < R ? '<' : (L > R ? '>' : '='); } function _cftex(n, d){ return '' + n + '' + d + ''; } function _cgcd(a, b){ while (b){ var t = a % b; a = b; b = t; } return a; } function _llcm(a, b){ return a / _cgcd(a, b) * b; } var TEMPLATES = [ { id: 'C1', tag: 'Benchmarks', level: 0, enumerate: function(){ var out = []; var sets = [ { fr: [[7, 8], [8, 9], [5, 6], [9, 10]], target: 1 }, { fr: [[1, 9], [1, 8], [2, 9], [1, 7]], target: 0 }, { fr: [[4, 7], [3, 5], [5, 9], [5, 11]], target: 0.5 } ]; for (var bi = 0; bi < sets.length; bi++){ var s = sets[bi].fr, target = sets[bi].target; for (var i = 0; i < s.length; i++) for (var j = 0; j < s.length; j++) for (var k = 0; k < s.length; k++){ if (!(!(i !== j) || !(j !== k) || !(i !== k))){ var fr = [s[i], s[j], s[k]]; var win = fr[0], wd = Math.abs(fr[0][0] / fr[0][1] - target); for (var m = 1; m < 3; m++){ var dd = Math.abs(fr[m][0] / fr[m][1] - target); if (dd < wd){ wd = dd; win = fr[m]; } } out.push({ key: 'b' + bi + i + j + k, fr: fr, win: win, bi: bi }); } } } return out; }, make: function(p){ var names = ['closest to 1', 'closest to 0', 'closest to 1/2']; var w = p.win; var list = p.fr.map(function(f){ return _cftex(f[0], f[1]); }).join(', '); return { promptHTML: 'Which is ' + names[p.bi] + ': ' + list + '?', answer: { kind: 'frac', n: w[0], d: w[1] }, hintHTML: 'Ask how far each fraction is from ' + ['1', '0', '1/2'][p.bi] + '.', whyHTML: _cWhy([ 'Measure each fraction\'s distance from ' + ['1', '0', '1/2'][p.bi] + '.', 'The ' + names[p.bi] + ' is ' + _cftex(w[0], w[1]) + '.' ], '' + w[0] + '/' + w[1] + '') }; } }, { id: 'C2', tag: 'Same denominator', level: 0, enumerate: function(){ var out = []; for (var d = 4; d <= 12; d++) for (var n1 = 1; n1 < d; n1++) for (var n2 = 1; n2 < d; n2++) if (n1 !== n2) out.push({ key: 's' + n1 + 'f' + d + 'v' + n2, n1: n1, n2: n2, d: d }); return out; }, make: function(p){ var c = p.n1 < p.n2 ? '<' : '>'; return { promptHTML: 'Compare: ' + p.n1 + '/' + p.d + ' __ ' + p.n2 + '/' + p.d + '. Type <, >, or =.', answer: { kind: 'cmp', c: c }, hintHTML: 'Same denominator: the pieces are the same size. Compare the counts.', whyHTML: _cWhy([ 'Same denominator ' + p.d + ' → same-size pieces.', 'Compare numerators: ' + p.n1 + ' vs ' + p.n2 + ' → ' + p.n1 + '/' + p.d + ' ' + c + ' ' + p.n2 + '/' + p.d + '.' ], '' + c + '') }; } }, { id: 'C3', tag: 'Same numerator', level: 1, enumerate: function(){ var out = []; for (var n = 2; n <= 5; n++) for (var d1 = 3; d1 <= 10; d1++) for (var d2 = d1 + 1; d2 <= 12; d2++) out.push({ key: 'n' + n + 'f' + d1 + 'v' + d2, n: n, d1: d1, d2: d2 }); return out; }, make: function(p){ return { promptHTML: 'Compare: ' + p.n + '/' + p.d1 + ' __ ' + p.n + '/' + p.d2 + '. Type <, >, or =.', answer: { kind: 'cmp', c: '>' }, hintHTML: 'Same number of pieces — which pieces are bigger?', whyHTML: _cWhy([ 'Same numerator ' + p.n + ' → the same number of pieces.', p.d1 + 'ths are bigger pieces than ' + p.d2 + 'ths (smaller denominator = bigger pieces).', 'So ' + p.n + '/' + p.d1 + ' > ' + p.n + '/' + p.d2 + '.' ], '>') }; } }, { id: 'C4', tag: 'Unlike fractions', level: 1, enumerate: function(){ var out = []; for (var d1 = 2; d1 <= 6; d1++) for (var d2 = d1 + 1; d2 <= 8; d2++) for (var n1 = 1; n1 < d1; n1++) for (var n2 = 1; n2 < d2; n2++){ if (_ccmp(n1, d1, n2, d2) !== '=') out.push({ key: 'u' + n1 + 'f' + d1 + 'v' + n2 + 'f' + d2, n1: n1, d1: d1, n2: n2, d2: d2 }); } return out; }, make: function(p){ var c = _ccmp(p.n1, p.d1, p.n2, p.d2); var L = _llcm(p.d1, p.d2); return { promptHTML: 'Compare: ' + p.n1 + '/' + p.d1 + ' __ ' + p.n2 + '/' + p.d2 + '. Type <, >, or =.', answer: { kind: 'cmp', c: c }, hintHTML: 'Rename both with the LCD ' + L + ', then compare the new numerators.', whyHTML: _cWhy([ 'The LCD of ' + p.d1 + ' and ' + p.d2 + ' is ' + L + '.', p.n1 + '/' + p.d1 + ' = ' + (p.n1 * L / p.d1) + '/' + L + '; ' + p.n2 + '/' + p.d2 + ' = ' + (p.n2 * L / p.d2) + '/' + L + '.', (p.n1 * L / p.d1) + ' vs ' + (p.n2 * L / p.d2) + ' → ' + p.n1 + '/' + p.d1 + ' ' + c + ' ' + p.n2 + '/' + p.d2 + '.' ], '' + c + '') }; } }, { id: 'C5', tag: 'Greatest of three', level: 2, enumerate: function(){ var out = []; for (var d1 = 2; d1 <= 5; d1++) for (var d2 = d1 + 1; d2 <= 7; d2++) for (var d3 = d2 + 1; d3 <= 9; d3++) for (var n1 = 1; n1 < d1; n1++) for (var n2 = 1; n2 < d2; n2++) for (var n3 = 1; n3 < d3; n3++){ var c12 = _ccmp(n1, d1, n2, d2), c23 = _ccmp(n2, d2, n3, d3), c13 = _ccmp(n1, d1, n3, d3); if (!(c12 === '=' || c23 === '=' || c13 === '=')){ var win = c12 === '>' ? (c13 === '>' ? 0 : 2) : (c23 === '>' ? 1 : 2); var fr = [[n1, d1], [n2, d2], [n3, d3]]; out.push({ key: 'g' + n1 + 'f' + d1 + n2 + 'f' + d2 + n3 + 'f' + d3, fr: fr, win: win }); } } return out; }, make: function(p){ var w = p.fr[p.win]; var list = p.fr.map(function(f){ return _cftex(f[0], f[1]); }).join(', '); return { promptHTML: 'Which is the greatest: ' + list + '?', answer: { kind: 'frac', n: w[0], d: w[1] }, hintHTML: 'Compare two at a time; the winner faces the third.', whyHTML: _cWhy([ 'Compare the first two: ' + p.fr[0][0] + '/' + p.fr[0][1] + ' ' + _ccmp(p.fr[0][0], p.fr[0][1], p.fr[1][0], p.fr[1][1]) + ' ' + p.fr[1][0] + '/' + p.fr[1][1] + '.', 'The winner against the third: ' + w[0] + '/' + w[1] + ' is the greatest of the three.' ], '' + w[0] + '/' + w[1] + '') }; } }, { id: 'C6', tag: 'Against one-half', level: 1, enumerate: function(){ var out = []; for (var d = 3; d <= 12; d++) for (var n = 1; n < d; n++) if (n * 2 !== d) out.push({ key: 'h' + n + 'f' + d, n: n, d: d }); return out; }, make: function(p){ var c = p.n * 2 < p.d ? '<' : '>'; return { promptHTML: 'Is ' + p.n + '/' + p.d + ' above or below one-half? Type <, >, or = between ' + p.n + '/' + p.d + ' and 1/2.', answer: { kind: 'cmp', c: c }, hintHTML: 'Half of ' + p.d + ' is ' + (p.d / 2) + '. Is ' + p.n + ' more or less than that?', whyHTML: _cWhy([ 'One-half of ' + p.d + ' is ' + (p.d / 2) + '.', p.n + ' is ' + (c === '<' ? 'less' : 'more') + ' than ' + (p.d / 2) + ', so ' + p.n + '/' + p.d + ' ' + c + ' 1/2.' ], '' + c + '') }; } } ];
/* ---------------- practice session ---------------- */ function PracticeSession(seed){ this._rand = mulberry32(seed >>> 0); this.pools = {}; this.seen = {}; this.score = 0; this.streak = 0; this.problemNum = 0; this.current = null; this.wrongCount = 0; this.revealed = false; this._done = false; } PracticeSession.prototype._draw = function (){ var guard, t, pool, p, key, prob; for (guard = 0; guard < 200; guard++){ t = TEMPLATES[Math.floor(this._rand() * TEMPLATES.length)]; pool = this.pools[t.id]; if (!pool || pool.length === 0){ pool = shuffle(t.enumerate().slice(), this._rand); this.pools[t.id] = pool; } p = pool.pop(); key = t.id + '|' + p.key; if (this.seen[key]) continue; this.seen[key] = 1; prob = t.make(p); prob.templateId = t.id; prob.tag = t.tag; prob.key = key; prob.params = p; prob.answerDisplayHTML = ansHTML(prob.answer); prob.accept = [ansText(prob.answer)]; return prob; } this.pools = {}; this.seen = {}; t = TEMPLATES[0]; p = t.enumerate()[0]; prob = t.make(p); prob.templateId = t.id; prob.tag = t.tag; prob.key = t.id + '|' + p.key; prob.params = p; prob.answerDisplayHTML = ansHTML(prob.answer); prob.accept = [ansText(prob.answer)]; return prob; }; PracticeSession.prototype.next = function (){ this.current = this._draw(); this.wrongCount = 0; this.revealed = false; this._done = false; this.problemNum++; return this.current; }; PracticeSession.prototype.submit = function (raw){ var pr = this.current; if (!pr) return { status: 'none' }; if (this._done) return { status: 'already' }; var parsed = parseByKind(pr.answer.kind, raw); if (!parsed.ok) return { status: 'invalid', entryHint: entryHintFor(pr.answer.kind) }; var ok = checkAnswer(pr.answer, parsed); if (ok){ this._done = true; var firstTry = !(!(this.wrongCount === 0) || this.revealed); if (!this.revealed){ this.streak++; if (firstTry) this.score++; } return { status: 'correct', firstTry: firstTry, score: this.score, streak: this.streak, answerHTML: pr.answerDisplayHTML }; } this.wrongCount++; this.streak = 0; if (this.wrongCount === 1) return { status: 'hint', hintHTML: pr.hintHTML, streak: 0 }; this.revealed = true; return { status: 'why', whyHTML: pr.whyHTML, streak: 0 }; }; PracticeSession.prototype.reveal = function (){ if (!this.current) return null; this.revealed = true; return this.current.whyHTML; }; /* ---------------- game API (wraps the same templates) ---------------- */ var _gameKind = 'int'; function difficultyFor(qi){ if (qi < 5) return 0; if (qi < 12) return 1; return 2; } function genQuestion(rng, asked, qIndex){ var diff = difficultyFor(qIndex); var elig = []; var i, t; for (i = 0; i < TEMPLATES.length; i++){ if (TEMPLATES[i].level <= diff) elig.push(TEMPLATES[i]); } if (elig.length === 0) elig = TEMPLATES; for (var tries = 0; tries < 80; tries++){ t = elig[Math.floor(rng() * elig.length)]; var pool = t.enumerate(); var p = pool[Math.floor(rng() * pool.length)]; var key = t.id + '|' + p.key; if (asked[key]) continue; asked[key] = 1; var prob = t.make(p); _gameKind = prob.answer.kind; return { typeLabel: t.tag, prompt: prob.promptHTML, correct: prob.answer, why: prob.whyHTML, answerDisplayHTML: ansHTML(prob.answer) }; } t = elig[0]; var p0 = t.enumerate()[0]; var pr0 = t.make(p0); _gameKind = pr0.answer.kind; return { typeLabel: t.tag, prompt: pr0.promptHTML, correct: pr0.answer, why: pr0.whyHTML, answerDisplayHTML: ansHTML(pr0.answer) }; } function gameParseAnswer(raw){ return parseByKind(_gameKind, raw); } function gameAnswerEquals(correct, parsed){ return checkAnswer(correct, parsed); } function gameAnswerText(correct){ return ansText(correct); } function gameAnswerHintText(){ return entryHintFor(_gameKind); } function newGameState(){ return { score: 0, streak: 0, bestStreak: 0, lives: 3, timeLeft: 60, qIndex: 0, answered: 0, correct: 0, over: false, overReason: '' }; } function tickTimer(s){ if (s.timeLeft > 0) s.timeLeft--; if (s.timeLeft <= 0){ s.over = true; s.overReason = 'time'; return true; } return false; } function scoreStep(s, ok){ s.answered++; if (ok){ s.correct++; s.streak++; if (s.streak > s.bestStreak) s.bestStreak = s.streak; var pts = 10; if (s.streak >= 4) pts += 2 * (s.streak - 3); s.score += pts; return { points: pts, gameOver: false }; } s.streak = 0; s.lives--; var over = s.lives <= 0; if (over){ s.over = true; s.overReason = 'lives'; } return { points: 0, gameOver: over }; } function accuracyPct(s){ if (s.answered === 0) return 0; return Math.round(s.correct / s.answered * 100); } /* ---------------- worksheet generation ---------------- */ function _wgcd5(a, b){ while (b){ var t = a % b; a = b; b = t; } return a; } function _wlcm(a, b){ return a / _wgcd5(a, b) * b; } function _wcmp(n1, d1, n2, d2){ var L = n1 * d2, R = n2 * d1; return L < R ? '<' : (L > R ? '>' : '='); } function wgSameDen(){ var d = ri(4, 12), n1 = ri(1, d - 1), n2 = ri(1, d - 1); if (n1 === n2) n2 = (n2 % (d - 1)) + 1; var c = n1 < n2 ? '<' : '>'; return { kind: 'sden', params: { n1: n1, n2: n2, d: d }, stemHTML: 'Compare: ' + n1 + '/' + d + ' __ ' + n2 + '/' + d + '. Type <, >, or =.', answerHTML: '' + c + '', answer: { kind: 'cmp', c: c } }; } function wgSameNum(){ var n = ri(2, 5), d1 = ri(3, 10), d2 = d1 + ri(1, 4); return { kind: 'snum', params: { n: n, d1: d1, d2: d2 }, stemHTML: 'Compare: ' + n + '/' + d1 + ' __ ' + n + '/' + d2 + '. Type <, >, or =.', answerHTML: '>', answer: { kind: 'cmp', c: '>' } }; } function wgUnlike(){ var d1 = ri(2, 6), d2 = d1 + ri(1, 3); var n1 = ri(1, d1 - 1), n2 = ri(1, d2 - 1); var c = _wcmp(n1, d1, n2, d2); if (c === '='){ n1 = n1 % (d1 - 1) + 1; c = _wcmp(n1, d1, n2, d2); } return { kind: 'unlike', params: { n1: n1, d1: d1, n2: n2, d2: d2 }, stemHTML: 'Compare: ' + n1 + '/' + d1 + ' __ ' + n2 + '/' + d2 + '. Type <, >, or =.', answerHTML: '' + c + '', answer: { kind: 'cmp', c: c } }; } function wgHalf(){ var d = ri(3, 12), n = ri(1, d - 1); if (n * 2 === d) n = n - 1; var c = n * 2 < d ? '<' : '>'; return { kind: 'half', params: { n: n, d: d }, stemHTML: 'Compare: ' + n + '/' + d + ' __ 1/2. Type <, >, or =.', answerHTML: '' + c + '', answer: { kind: 'cmp', c: c } }; } var WSGENS = { easy: [wgSameDen, wgSameDen, wgSameNum], medium: [wgSameDen, wgSameNum, wgUnlike, wgHalf], hard: [wgUnlike, wgHalf, wgSameNum, wgUnlike] };
function generateSet(seed, diff){ setSeed(seed); var gens = WSGENS[diff] || WSGENS.medium; var probs = [], seen = {}, guard = 0; while (!(!(probs.length < 20) || !(guard < 600))){ guard++; var g = gens[Math.floor(_rand() * gens.length)]; var pr = g(); if (seen[pr.stemHTML]) continue; seen[pr.stemHTML] = 1; probs.push(pr); } return probs; } /* ---------------- expose ---------------- */ var API = { PracticeSession: PracticeSession, TEMPLATES: TEMPLATES, WSGENS: WSGENS, generateSet: generateSet, genQuestion: genQuestion, difficultyFor: difficultyFor, parseAnswer: gameParseAnswer, parseByKind: parseByKind, parsePartsInput: parsePartsInput, parseQRInput: parseQRInput, answerEquals: gameAnswerEquals, answerText: gameAnswerText, answerHintText: gameAnswerHintText, newGameState: newGameState, scoreStep: scoreStep, tickTimer: tickTimer, accuracyPct: accuracyPct, mulberry32: mulberry32, setSeed: setSeed, ggcd: ggcd, gred: gred, sameFrac: sameFrac, decVal: decVal, decNorm: decNorm, decAdd: decAdd, decSub: decSub, decText: decText, decTextFromVP: decTextFromVP, fracHTML: fracHTML, mixedHTML: mixedHTML, ansHTML: ansHTML, ansText: ansText, checkAnswer: checkAnswer }; return API; });
'use strict'; /* Worksheet DOM wiring (generic). Pure generation lives in the core. */ (function(){ var CORE = window.FiboCore_comparing_fractions; var current = { problems: [], difficulty: 'medium', keyVisible: false, genCount: 0 }; var el = {}; function renderProblems(){ el.problems.innerHTML = current.problems.map(function(p, i){ return '
'; }).join(''); el.probCount.textContent = current.problems.length + ' problems · ' + current.difficulty.charAt(0).toUpperCase() + current.difficulty.slice(1); } function renderKey(){ el.keyGrid.innerHTML = current.problems.map(function(p, i){ return '
'; }).join(''); } function newSet(seed){ var s = (seed === undefined) ? ((Date.now() + (current.genCount * 7919)) >>> 0) : (seed >>> 0); current.genCount++; current.problems = CORE.generateSet(s, current.difficulty); renderProblems(); if (current.keyVisible) renderKey(); } function setKeyVisible(v){ current.keyVisible = v; el.keySection.hidden = !v; el.btnKey.setAttribute('aria-pressed', v ? 'true' : 'false'); el.btnKey.textContent = v ? 'Hide Answer Key' : 'Show Answer Key'; if (v) renderKey(); } function init(){ el.diffSel = document.getElementById('diffSel'); el.btnGen = document.getElementById('btnGen'); el.btnKey = document.getElementById('btnKey'); el.btnPrint = document.getElementById('btnPrint'); el.problems = document.getElementById('problems'); el.probCount = document.getElementById('probCount'); el.keySection= document.getElementById('keySection'); el.keyGrid = document.getElementById('keyGrid'); current.difficulty = el.diffSel.value; el.diffSel.addEventListener('change', function(){ current.difficulty = el.diffSel.value; newSet(); }); el.btnGen.addEventListener('click', function(){ newSet(); }); el.btnKey.addEventListener('click', function(){ setKeyVisible(!current.keyVisible); }); el.btnPrint.addEventListener('click', function(){ window.print(); }); newSet(); } if (document.readyState === 'loading'){ document.addEventListener('DOMContentLoaded', init); } else { init(); } })();