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\\div \\frac{3}{4}$\n\nGive your answer as a mixed number in its simplest form.","markscheme":"- Inverts and multiplies, e.g. $\\frac{7}{8} \\times \\frac{4}{3}$ M1\n- Final answer $1\\frac{1}{6}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Inverts the second fraction and multiplies, e.g. $\\frac{7}{8} \\times \\frac{4}{3}$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer as a mixed number $1\\frac{1}{6}$.","code":"A"}],"finalAnswers":["1 1/6"],"generatedAt":"2026-05-06T15:44:07.141Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]},{"id":"f369be6d-8205-49c6-9624-c150d82698db","label":"b","content":"Work out $1\\frac{5}{6} \\times \\frac{2}{9}$","markscheme":"- Converts to improper fraction, e.g. $\\frac{11}{6} \\times \\frac{2}{9}$ M1\n- Final answer $\\frac{11}{27}$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Converts mixed number to improper fraction, e.g. $\\frac{11}{6} \\times \\frac{2}{9}$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\frac{11}{27}$.","code":"A"}],"finalAnswers":["11/27"],"generatedAt":"2026-05-06T15:44:07.141Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"convert_then_multiply","label":"Convert then multiply","steps":[{"type":"text","order":0,"title":"Convert the mixed number","content":"A mixed number contains a whole number and a fraction. Convert $1\\frac{5}{6}$ to an improper fraction by multiplying the whole number by the denominator, then adding the numerator:\n\n$$1\\times6+5=11$$\n\nKeep the denominator $6$, so $1\\frac{5}{6}=\\frac{11}{6}$. This conversion earns the first mark.","highlights":[{"text":"Work out $1\\frac{5}{6} \\times \\frac{2}{9}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=improper}{\\color{@sky}{11}}}{\\color{@sky}{6}}\\times\\frac{2}{9}"},{"latex":"\\frac{\\htmlData{anchor=product}{\\color{@orange}{22}}}{\\color{@orange}{54}}"},{"latex":"\\frac{\\htmlData{anchor=answer}{\\color{@green}{11}}}{\\color{@green}{27}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"improper"},{"color":"orange","style":"text-color-with-background","anchor":"product"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"product","from":"improper","color":"sky","label":"multiply","style":"solid"},{"to":"answer","from":"product","color":"green","label":"divide by 2","style":"solid"}]},"order":1,"title":"Multiply and simplify","description":"Now multiply numerators together and denominators together, then simplify the fraction. The result is already in simplest form, so this earns the final answer mark."}]}],"generatedAt":"2026-07-21T03:22:30.579Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"3de4fab5-fe21-4c32-9a26-1597f7ffde6b","revisionId":"b1c2cce5-b465-4e09-bda4-63e003e3c946","questionNumber":"13","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Fractions","calculatorUse":null,"isCalculation":true,"parts":[{"id":"3dc9de6b-f4b3-4c05-a906-dc25dad16b15","label":"0","content":"Work out $1\\frac{3}{5} \\div \\frac{3}{4}$","markscheme":"- Converts to improper fraction and multiplies by reciprocal, e.g. $\\frac{8}{5} \\times \\frac{4}{3}$ M1\n- Final answer $\\frac{32}{15}$ or $2\\frac{2}{15}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Converts mixed number to improper fraction and multiplies by reciprocal, e.g. $\\frac{8}{5} \\times \\frac{4}{3}$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\frac{32}{15}$ or $2\\frac{2}{15}$.","code":"A"}],"finalAnswers":["32/15","2 2/15"],"generatedAt":"2026-05-06T15:44:07.141Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"reciprocal_method","label":"Multiply by the reciprocal","steps":[{"type":"text","order":0,"title":"Convert the mixed number","content":"First convert $1\\frac{3}{5}$ to an improper fraction. Multiply the whole number by the denominator, then add the numerator: $(1\\times5)+3=8$. So $1\\frac{3}{5}=\\frac{8}{5}$.","highlights":[{"text":"Work out $1\\frac{3}{5} \\div \\frac{3}{4}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=improper}{\\frac{8}{5}}\\div\\htmlData{anchor=divisor}{\\color{@sky}{\\frac{3}{4}}}"},{"latex":"\\frac{8}{5}\\times\\htmlData{anchor=reciprocal}{\\color{@sky}{\\frac{4}{3}}}"}],"highlights":[{"color":"amber","style":"text-color-with-background","anchor":"improper"},{"color":"sky","style":"text-color-with-background","anchor":"reciprocal"}],"connections":[{"to":"reciprocal","from":"divisor","color":"sky","label":"use reciprocal","style":"solid"}]},"order":1,"title":"Multiply by the reciprocal","description":"Dividing by a fraction means multiplying by its reciprocal: turn the second fraction upside down. Examiner note (M1): converting to eight fifths and multiplying by the reciprocal gives eight fifths multiplied by four thirds."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=product}{\\frac{8}{5}\\times\\frac{4}{3}}"},{"latex":"\\htmlData{anchor=result}{\\boxed{\\frac{32}{15}}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"result"}],"connections":[{"to":"result","from":"product","color":"green","label":"multiply top and bottom","style":"solid"}]},"order":2,"title":"Multiply the fractions","description":"Multiply the numerators together and multiply the denominators together. Examiner note (A1): thirty-two fifteenths earns the accuracy mark."}]}],"generatedAt":"2026-07-21T04:06:07.877Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":67},"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"0e46151b-227c-46e1-a3f3-907e0a964da7","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"48c71fdc-924c-4a11-b8cd-eb38f0e91ec6","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"ea6a61c1-5d8d-4cb5-a0f2-c865119f56db","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"30050684-d8c4-41cc-a12f-76f9e9a7532c","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"e77c48ce-d11f-48e5-8729-b4c618951058","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"33dae1d1-25d4-4cb7-8022-d9b3eb21117f","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"5f60042b-0941-45ef-a915-deb13be7db84","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"5bfb14f1-bea0-4004-9cb5-9c234ad4c013","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f6332863-1ad8-40e3-915f-008acde620fe","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"52c0eb29-a7b3-4a9a-ae8b-3c83623920f9","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"39f8557b-be11-4cea-aedc-bb2eb718a84c","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"87bcdce0-09da-4a80-96fb-85d83f58e286","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"3de4fab5-fe21-4c32-9a26-1597f7ffde6b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d2312790-ebe1-4ad1-ac17-55cd464e7720","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"Fractions","topicId":"19dcdc31-6db7-41c8-b7c7-337ce087dc7f","topicSidebar":"$L3a","topicSlug":"grade-3-3-1-fractions","topicTitle":"Fractions"}]}],"$L3b","$L3c"]}]