[ { "id": 22638, "action": "convert", "question": "Andy placed identical rectangular tiles in a large rectangular frame. What fraction of the frame is not covered by rectangular tiles? Express your answer as a fraction in the simplest form.", "answer0": "$$\\frac{2}{3}$$", "answer1": "$$\\frac{1}{3}$$", "answer2": "$$\\frac{1}{4}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct value 1/3 plus complement and common fraction distractors." }, { "id": 22649, "action": "convert", "question": "What is the mixed number represented by the letter A in the number line?", "answer0": "$$2\\frac{1}{4}$$", "answer1": "$$2\\frac{3}{4}$$", "answer2": "$$3\\frac{3}{4}$$", "answer3": "$$2\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct 2 3/4; distractors vary fractional part and whole-number part." }, { "id": 22651, "action": "skip", "question": "Arrange the fractions in decreasing order.
$$\\frac{7}{3}$$ , $$\\frac{11}{5}$$ , $$2\\frac{2}{5}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 22666, "action": "skip", "question": "Arrange these numbers from the greatest to the smallest.
$$\\frac{2}{5}$$ , 0.403 , 0.043", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different answers; cannot be one MCQ." }, { "id": 22685, "action": "convert", "question": "What is the mixed number represented by A?", "answer0": "$$2\\frac{5}{8}$$", "answer1": "$$2\\frac{3}{8}$$", "answer2": "$$3\\frac{5}{8}$$", "answer3": "$$2\\frac{1}{8}$$", "correct_answer": 0, "reason": "Correct 2 5/8; distractors vary fractional and whole-number parts." }, { "id": 22686, "action": "skip", "question": "Arrange the fractions in increasing order.
$$1\\frac{5}{9}$$ , $$\\frac{15}{7}$$ , $$1\\frac{2}{3}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 22687, "action": "convert", "question": "Subtract $$\\frac{3}{5}$$ from 7.", "answer0": "$$6\\frac{2}{5}$$", "answer1": "$$7\\frac{2}{5}$$", "answer2": "$$6\\frac{3}{5}$$", "answer3": "$$5\\frac{2}{5}$$", "correct_answer": 0, "reason": "Correct 6 2/5; distractors from wrong whole part and un-subtracted numerator." }, { "id": 22691, "action": "convert", "question": "Siti jogged $$\\frac{4}{5}$$ km. She jogged $$\\frac{3}{10}$$ km more than Tom. How far did Tom jog?", "answer0": "$$\\frac{11}{10}$$", "answer1": "$$\\frac{1}{2}$$", "answer2": "$$\\frac{2}{5}$$", "answer3": "$$\\frac{1}{5}$$", "correct_answer": 1, "reason": "Correct 1/2 (4/5−3/10); distractor 11/10 from adding instead of subtracting." }, { "id": 22695, "action": "skip", "question": "Jamie had 3 kg of flour. She used $$\\frac{3}{10}$$ kg of flour to bake a cake and $$\\frac{1}{4}$$ kg of flour to bake cookies.
a) What is the total mass of flour Jamie used?
b) What is the mass of flour left after baking the cake and cookies? (Express your answer as a mixed number.)", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 22706, "action": "skip", "question": "Arrange the following fractions in decreasing order.
$$\\frac{7}{4}$$, $$\\frac{4}{3}$$, $$1\\frac{5}{6}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 22708, "action": "convert", "question": "Find the missing fraction A on the number line. Express your answer as a mixed number in its simplest form.
The marked points in order are $$\\frac{4}{5}$$, 1, A, $$\\frac{6}{5}$$, $$\\frac{7}{5}$$, $$\\frac{8}{5}$$.", "answer0": "$$1\\frac{1}{10}$$", "answer1": "$$1\\frac{1}{5}$$", "answer2": "$$1\\frac{1}{2}$$", "answer3": "$$\\frac{11}{10}$$", "correct_answer": 0, "reason": "Correct 1 1/10; distractors include next mark value and improper form." }, { "id": 22733, "action": "convert", "question": "What fraction of the triangles shown are grey in colour?", "answer0": "$$\\frac{7}{12}$$", "answer1": "$$\\frac{5}{12}$$", "answer2": "$$\\frac{5}{7}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct 5/12; distractors include complement and ratio-style error." }, { "id": 22737, "action": "convert", "question": "Mary poured $$\\frac{1}{3}$$ $$l$$ of juice from a jug for Peter and $$\\frac{1}{9}$$ $$l$$ of juice for Tom. There was $$\\frac{7}{9}$$ $$l$$ of juice left in the jug. How much juice was in the jug at first? Express your answer as a mixed number in its simplest form.", "answer0": "$$1\\frac{2}{9}$$", "answer1": "$$1\\frac{1}{9}$$", "answer2": "$$\\frac{11}{9}$$", "answer3": "$$\\frac{1}{3}$$", "correct_answer": 0, "reason": "Correct 1 2/9; distractors include improper form and partial-sum errors." }, { "id": 22749, "action": "convert", "question": "Aini had 6 ten-dollar notes and 3 five-dollar notes. She spent $18.65 on food, $6.35 on a notebook and saved the rest of the money. What fraction of her money did she save? Give your answer in the simplest form.", "answer0": "$$\\frac{1}{3}$$", "answer1": "$$\\frac{2}{3}$$", "answer2": "$$\\frac{1}{2}$$", "answer3": "$$\\frac{3}{4}$$", "correct_answer": 1, "reason": "Correct 2/3 saved; distractor 1/3 is the fraction spent." }, { "id": 22775, "action": "convert", "question": "What is the value of $$\\frac{4}{5}+\\frac{9}{10}$$? Express your answer as a mixed number.", "answer0": "$$1\\frac{7}{10}$$", "answer1": "$$\\frac{17}{10}$$", "answer2": "$$1\\frac{3}{10}$$", "answer3": "$$1\\frac{1}{2}$$", "correct_answer": 0, "reason": "Correct 1 7/10; distractors include improper form and arithmetic slips." }, { "id": 22777, "action": "convert", "question": "Write $$3\\frac{3}{7}$$ as an improper fraction.", "answer0": "$$\\frac{24}{7}$$", "answer1": "$$\\frac{21}{7}$$", "answer2": "$$\\frac{9}{7}$$", "answer3": "$$\\frac{27}{7}$$", "correct_answer": 0, "reason": "Correct 24/7; distractors from forgetting to add numerator or wrong product." }, { "id": 22780, "action": "skip", "question": "Arrange these fractions in decreasing order.
$$\\frac{1}{2}$$, $$\\frac{5}{6}$$, $$\\frac{5}{9}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 22792, "action": "convert", "question": "There were some candies in a bag. Ethan took $$\\frac{3}{8}$$ of the candies, Fedrick took $$\\frac{1}{3}$$ of the candies and Germaine took the rest. Ethan took 12 more candies than Germaine.
(a) What fraction of the candies did Germaine take?", "answer0": "$$\\frac{7}{24}$$", "answer1": "$$\\frac{17}{24}$$", "answer2": "$$\\frac{1}{3}$$", "answer3": "$$\\frac{5}{24}$$", "correct_answer": 0, "reason": "Part (a) single fraction 7/24; part (b) is a whole number, only fraction part converted." }, { "id": 22811, "action": "convert", "question": "$$\\frac{2}{3}$$ + $$\\frac{2}{9}$$ =", "answer0": "$$\\frac{8}{9}$$", "answer1": "$$\\frac{4}{9}$$", "answer2": "$$\\frac{4}{12}$$", "answer3": "$$\\frac{7}{9}$$", "correct_answer": 0, "reason": "Correct 8/9; distractors include add-across error and numerator slip." }, { "id": 22817, "action": "convert", "question": "The pie chart shows the favourite food of a group of children. $$\\frac{1}{2}$$ of the children chose nuggets as their favourite food.
(a) What fraction of the children chose cakes and burgers as their favourite food?", "answer0": "$$\\frac{1}{4}$$", "answer1": "$$\\frac{1}{2}$$", "answer2": "$$\\frac{3}{4}$$", "answer3": "$$\\frac{1}{3}$$", "correct_answer": 0, "reason": "Part (a) single fraction 1/4; part (b) is a whole number, only fraction part converted." }, { "id": 22826, "action": "convert", "question": "$$\\frac{4}{7}$$ kg of flour is needed to bake 6 buns. Melvin has 3 kg of flour and he baked 12 buns. How much flour does he have left?", "answer0": "$$1\\frac{6}{7}$$", "answer1": "$$\\frac{13}{7}$$", "answer2": "$$1\\frac{1}{7}$$", "answer3": "$$2\\frac{1}{7}$$", "correct_answer": 0, "reason": "Correct 1 6/7 (3 − 8/7); distractors include improper form and arithmetic slips." }, { "id": 22855, "action": "skip", "question": "Which two of the fractions below are smaller than $$\\frac{1}{2}$$ ?
$$\\frac{7}{12}$$ , $$\\frac{3}{7}$$ , $$\\frac{2}{5}$$ , $$\\frac{5}{10}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Select-two question with two different fraction answers; cannot be one MCQ." }, { "id": 22856, "action": "convert", "question": "What is the value of $$\\frac{5}{6}$$ − $$\\frac{2}{3}$$ ?", "answer0": "$$\\frac{1}{6}$$", "answer1": "$$\\frac{3}{6}$$", "answer2": "$$\\frac{1}{2}$$", "answer3": "$$\\frac{3}{3}$$", "correct_answer": 0, "reason": "Correct 1/6; distractors from subtract-across error." }, { "id": 22863, "action": "skip", "question": "Arrange these numbers in decreasing order.
$$\\frac{84}{100}$$ , 0.8 , 0.804 , $$\\frac{84}{10}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with four different answers; cannot be one MCQ." }, { "id": 22872, "action": "skip", "question": "Jenny has 2 kg of flour. She used $$\\frac{3}{8}$$ kg of the flour to bake a cake. She used $$\\frac{1}{4}$$ kg of the flour to bake some cookies.
(a) How much flour did she use to bake the cake and the cookies altogether?
(b) How much flour did she have left? Express your answer as a mixed number.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 22897, "action": "convert", "question": "$$\\frac{1}{4}$$ + $$\\frac{5}{8}$$ =", "answer0": "$$\\frac{6}{8}$$", "answer1": "$$\\frac{7}{8}$$", "answer2": "$$\\frac{6}{12}$$", "answer3": "$$\\frac{3}{8}$$", "correct_answer": 1, "reason": "Correct 7/8; distractors include un-converted and add-across errors." }, { "id": 22898, "action": "convert", "question": "Write $$\\frac{19}{5}$$ as a mixed number.", "answer0": "$$3\\frac{4}{5}$$", "answer1": "$$4\\frac{4}{5}$$", "answer2": "$$3\\frac{1}{5}$$", "answer3": "$$3\\frac{4}{19}$$", "correct_answer": 0, "reason": "Correct 3 4/5; distractors vary whole part and remainder." }, { "id": 22901, "action": "convert", "question": "Jerry bought a box containing 30 grapes. His brother ate 8 of them and his grandparents ate 16 of them. What fraction of the box of grapes had Jerry left? Give your answer in its simplest form.", "answer0": "$$\\frac{4}{5}$$", "answer1": "$$\\frac{1}{5}$$", "answer2": "$$\\frac{6}{30}$$", "answer3": "$$\\frac{1}{6}$$", "correct_answer": 1, "reason": "Correct 1/5 (6/30 simplified); distractors include complement and un-simplified form." }, { "id": 22942, "action": "convert", "question": "$$1 - \\frac{1}{8} - \\frac{1}{4}$$ =", "answer0": "$$\\frac{3}{8}$$", "answer1": "$$\\frac{5}{8}$$", "answer2": "$$\\frac{7}{8}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct 5/8; distractors from arithmetic and conversion slips." }, { "id": 22949, "action": "convert", "question": "Mrs Lee bought a papaya and a durian. The mass of the papaya was $$\\frac{9}{10}$$ kg. It was $$\\frac{1}{2}$$ kg lighter than the mass of the durian. What was the mass of the durian? Express your answer as a mixed number in its simplest form.", "answer0": "$$\\frac{2}{5}$$", "answer1": "$$1\\frac{2}{5}$$", "answer2": "$$1\\frac{1}{2}$$", "answer3": "$$\\frac{14}{10}$$", "correct_answer": 1, "reason": "Correct 1 2/5 (9/10+1/2); distractor 2/5 from subtracting instead of adding." }, { "id": 22951, "action": "skip", "question": "In the number line, (a) what is the mixed number represented by A? (b) what is the improper fraction represented by B?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 22958, "action": "convert", "question": "The pie chart shows the choices made by a group of children about their favourite snacks. Half of the group likes cookies and brownies. The number of children who like muffins is equal to the number of children who like brownies.
(a) What fraction of the students like cookies?", "answer0": "$$\\frac{1}{4}$$", "answer1": "$$\\frac{5}{12}$$", "answer2": "$$\\frac{1}{2}$$", "answer3": "$$\\frac{7}{12}$$", "correct_answer": 1, "reason": "Part (a) single fraction 5/12; part (b) is a whole number, only fraction part converted." }, { "id": 22976, "action": "convert", "question": "Write $$3\\frac{4}{5}$$ as an improper fraction.", "answer0": "$$\\frac{19}{5}$$", "answer1": "$$\\frac{12}{5}$$", "answer2": "$$\\frac{17}{5}$$", "answer3": "$$\\frac{23}{5}$$", "correct_answer": 0, "reason": "Correct 19/5; distractors from omitting numerator or wrong product." }, { "id": 22977, "action": "convert", "question": "What is the value of $$\\frac{5}{8} + \\frac{3}{4}$$? Express your answer as a mixed number.", "answer0": "$$1\\frac{3}{8}$$", "answer1": "$$\\frac{11}{8}$$", "answer2": "$$1\\frac{1}{8}$$", "answer3": "$$\\frac{8}{12}$$", "correct_answer": 0, "reason": "Correct 1 3/8; distractors include improper form and add-across error." }, { "id": 23017, "action": "skip", "question": "Arrange these fractions from the smallest to the greatest.
$$\\frac{8}{11}$$ , $$\\frac{1}{2}$$ , $$\\frac{5}{11}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 23019, "action": "convert", "question": "Rectangle PQRS is made up of 8 unit squares. What fraction of rectangle PQRS is shaded?", "answer0": "$$\\frac{3}{8}$$", "answer1": "$$\\frac{5}{8}$$", "answer2": "$$\\frac{3}{5}$$", "answer3": "$$\\frac{1}{8}$$", "correct_answer": 0, "reason": "Correct 3/8; distractors include complement and ratio error." }, { "id": 23020, "action": "convert", "question": "Express 0.6 as a fraction.", "answer0": "$$\\frac{6}{10}$$", "answer1": "$$\\frac{6}{100}$$", "answer2": "$$\\frac{1}{6}$$", "answer3": "$$\\frac{60}{10}$$", "correct_answer": 0, "reason": "Correct 6/10; distractors from wrong place value." }, { "id": 23026, "action": "convert", "question": "Gladys jogged a distance of $$\\frac{2}{3}$$ km. She jogged $$\\frac{1}{5}$$ km more than the distance jogged by Ben. What was the total distance Gladys and Ben jogged? Give your answer as a mixed number.", "answer0": "$$1\\frac{2}{15}$$", "answer1": "$$\\frac{17}{15}$$", "answer2": "$$1\\frac{1}{15}$$", "answer3": "$$1\\frac{4}{15}$$", "correct_answer": 0, "reason": "Correct 1 2/15 (2/3 + 7/15); distractors include improper form and slips." }, { "id": 23034, "action": "convert", "question": "Farid baked some cookies. He gave away $$\\frac{3}{10}$$ of his cookies to his friends and gave away $$\\frac{1}{2}$$ of his cookies to his siblings. He had 50 cookies left.
(a) What fraction of Farid's cookies was left?", "answer0": "$$\\frac{2}{10}$$", "answer1": "$$\\frac{8}{10}$$", "answer2": "$$\\frac{1}{5}$$", "answer3": "$$\\frac{3}{10}$$", "correct_answer": 0, "reason": "Part (a) fraction 2/10; part (b) is a whole number, only fraction part converted." }, { "id": 23041, "action": "skip", "question": "a) In the number line, what is the value represented by A?
b) What is the missing number in the box? $$\\frac{3}{7} = \\frac{[?]}{14}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with a mixed number and a whole number; cannot be one MCQ." }, { "id": 23042, "action": "skip", "question": "a) Write $$\\frac{18}{5}$$ as a mixed number.
b) Write $$5\\frac{5}{9}$$ as an improper fraction.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 23043, "action": "skip", "question": "a) Arrange the following fractions in decreasing order.
$$\\frac{3}{4}$$ , $$\\frac{1}{3}$$ , $$\\frac{7}{12}$$
b) Find the value of $$3 - \\frac{5}{6}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Multi-part ordering plus computation with several different answers; cannot be one MCQ." }, { "id": 23050, "action": "convert", "question": "Mr Lee bought $$\\frac{1}{4}$$ kg of rice. He bought $$\\frac{2}{5}$$ kg more flour than rice. How many kilograms of rice and flour did Mr Lee buy altogether? Express your answer in its simplest form.", "answer0": "$$\\frac{9}{10}$$", "answer1": "$$\\frac{13}{20}$$", "answer2": "$$\\frac{3}{9}$$", "answer3": "$$\\frac{7}{10}$$", "correct_answer": 0, "reason": "Correct 9/10 (1/4 + 13/20); distractors from skipping the 'more than' step." }, { "id": 23095, "action": "convert", "question": "Express $$\\frac{10}{15}$$ in its simplest form.", "answer0": "$$\\frac{3}{2}$$", "answer1": "$$\\frac{2}{3}$$", "answer2": "$$\\frac{5}{15}$$", "answer3": "$$\\frac{1}{3}$$", "correct_answer": 1, "reason": "Correct 2/3; distractors include inverted and partly-reduced forms." }, { "id": 23096, "action": "convert", "question": "Write $$\\frac{15}{7}$$ as a mixed number.", "answer0": "$$2\\frac{1}{7}$$", "answer1": "$$1\\frac{1}{7}$$", "answer2": "$$2\\frac{2}{7}$$", "answer3": "$$2\\frac{1}{15}$$", "correct_answer": 0, "reason": "Correct 2 1/7; distractors vary whole part and remainder." }, { "id": 23101, "action": "convert", "question": "Express 0.4 as a fraction.", "answer0": "$$\\frac{4}{10}$$", "answer1": "$$\\frac{4}{100}$$", "answer2": "$$\\frac{1}{4}$$", "answer3": "$$\\frac{40}{10}$$", "correct_answer": 0, "reason": "Correct 4/10; distractors from wrong place value." }, { "id": 23114, "action": "convert", "question": "Mark bought some sweets. He gave his friends $$\\frac{1}{7}$$ of the sweets and gave his brother $$\\frac{3}{4}$$ of the sweets. All the remaining sweets were eaten by him. What fraction of the sweets did Mark eat?", "answer0": "$$\\frac{3}{28}$$", "answer1": "$$\\frac{25}{28}$$", "answer2": "$$\\frac{4}{11}$$", "answer3": "$$\\frac{1}{4}$$", "correct_answer": 0, "reason": "Correct 3/28 (1 − 1/7 − 3/4); distractors include complement and add-across error." }, { "id": 23143, "action": "skip", "question": "Arrange these fractions from the smallest to the greatest.
$$\\frac{4}{7}$$ , $$\\frac{1}{2}$$ , $$\\frac{6}{7}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 23144, "action": "convert", "question": "Write $$4\\frac{2}{3}$$ as an improper fraction.", "answer0": "$$\\frac{14}{3}$$", "answer1": "$$\\frac{12}{3}$$", "answer2": "$$\\frac{8}{3}$$", "answer3": "$$\\frac{11}{3}$$", "correct_answer": 0, "reason": "Correct 14/3; distractors from omitting numerator or wrong product." }, { "id": 23145, "action": "convert", "question": "$$\\frac{3}{4}$$ + $$\\frac{1}{8}$$ =", "answer0": "$$\\frac{7}{8}$$", "answer1": "$$\\frac{4}{12}$$", "answer2": "$$\\frac{5}{8}$$", "answer3": "$$\\frac{4}{8}$$", "correct_answer": 0, "reason": "Correct 7/8; distractors include add-across and conversion slips." }, { "id": 23149, "action": "convert", "question": "Express 0.39 as a fraction.", "answer0": "$$\\frac{39}{100}$$", "answer1": "$$\\frac{39}{10}$$", "answer2": "$$\\frac{39}{1000}$$", "answer3": "$$\\frac{3}{9}$$", "correct_answer": 0, "reason": "Correct 39/100; distractors from wrong place value." }, { "id": 23158, "action": "skip", "question": "Jane receives the same amount of pocket money every month from January to April. The bar graph shows the amount spent: Jan $34, Feb $28, Mar $48, Apr $40. The pie chart shows Jane's spending and savings for Jan to Apr (savings is a quarter / right angle shown). (a) What is the amount of pocket money Jane received for the months of Jan to Apr? (b) Jane spent the same amount in May and April. Express the pocket money Jane saved from Jan to May as a fraction of the pocket money she received from Jan to May. Write your answer in the simplest form.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question; part (a) is a dollar amount, only part (b) is a fraction; cannot be one MCQ." }, { "id": 23182, "action": "convert", "question": "Write $$3\\frac{4}{5}$$ as an improper fraction.", "answer0": "$$\\frac{12}{5}$$", "answer1": "$$\\frac{17}{5}$$", "answer2": "$$\\frac{19}{5}$$", "answer3": "$$\\frac{23}{5}$$", "correct_answer": 2, "reason": "Correct 19/5; distractors from omitting numerator or wrong product." }, { "id": 23183, "action": "convert", "question": "$$\\frac{1}{4} + \\frac{5}{8}$$ =", "answer0": "$$\\frac{6}{8}$$", "answer1": "$$\\frac{6}{12}$$", "answer2": "$$\\frac{7}{8}$$", "answer3": "$$\\frac{3}{8}$$", "correct_answer": 2, "reason": "Correct 7/8; distractors include un-converted and add-across errors." }, { "id": 23184, "action": "convert", "question": "$$1 - \\frac{1}{10} - \\frac{1}{5}$$ =", "answer0": "$$\\frac{7}{10}$$", "answer1": "$$\\frac{8}{10}$$", "answer2": "$$\\frac{9}{10}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 0, "reason": "Correct 7/10; distractors from incomplete subtraction." }, { "id": 23224, "action": "convert", "question": "Write $$\\frac{20}{9}$$ as a mixed number.", "answer0": "$$2\\frac{2}{9}$$", "answer1": "$$2\\frac{1}{9}$$", "answer2": "$$1\\frac{2}{9}$$", "answer3": "$$2\\frac{2}{20}$$", "correct_answer": 0, "reason": "Correct 2 2/9; distractors vary whole part and remainder." }, { "id": 23231, "action": "skip", "question": "Which two of the fractions below are in the simplest form?
$$\\frac{2}{5}$$ , $$\\frac{3}{6}$$ , $$\\frac{5}{7}$$ , $$\\frac{6}{8}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Select-two question with two different fraction answers; cannot be one MCQ." }, { "id": 23232, "action": "convert", "question": "Find the value of $$1 - \\frac{1}{3} - \\frac{2}{9}$$.", "answer0": "$$\\frac{5}{9}$$", "answer1": "$$\\frac{4}{9}$$", "answer2": "$$\\frac{6}{9}$$", "answer3": "$$\\frac{1}{3}$$", "correct_answer": 1, "reason": "Correct 4/9; distractors from arithmetic slips." }, { "id": 23234, "action": "skip", "question": "Arrange the following numbers from the smallest to the greatest.
$$0.801$$ , $$0.081$$ , $$\\frac{4}{5}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different answers; cannot be one MCQ." }, { "id": 23259, "action": "skip", "question": "Which two of the fractions below are smaller than $$\\frac{1}{2}$$?
$$\\frac{2}{3}$$ , $$\\frac{4}{9}$$ , $$\\frac{5}{11}$$ , $$\\frac{6}{12}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Select-two question with two different fraction answers; cannot be one MCQ." }, { "id": 23260, "action": "convert", "question": "What is the value of $$\\frac{5}{6} + \\frac{7}{12}$$? Express your answer as a mixed number.", "answer0": "$$1\\frac{5}{12}$$", "answer1": "$$\\frac{17}{12}$$", "answer2": "$$1\\frac{1}{12}$$", "answer3": "$$1\\frac{7}{12}$$", "correct_answer": 0, "reason": "Correct 1 5/12; distractors include improper form and slips." }, { "id": 23283, "action": "convert", "question": "In March there were 312 students choosing a favourite sport, with 40 choosing tennis. In April, 8 new students chose badminton as their favourite sport. The number of students who chose tennis remained unchanged. What fraction of the students chose tennis as their favourite sport in April? Give your answer in the simplest form.", "answer0": "$$\\frac{1}{8}$$", "answer1": "$$\\frac{5}{39}$$", "answer2": "$$\\frac{1}{7}$$", "answer3": "$$\\frac{40}{312}$$", "correct_answer": 0, "reason": "Correct 1/8 (40/320); distractors include March fraction and un-simplified forms." }, { "id": 23284, "action": "convert", "question": "Mr Lee had red, yellow and purple files. $$\\frac{1}{4}$$ of the files were red and $$\\frac{3}{5}$$ of the files were yellow. The rest of the files were purple. What fraction of the files were purple?", "answer0": "$$\\frac{3}{20}$$", "answer1": "$$\\frac{17}{20}$$", "answer2": "$$\\frac{4}{9}$$", "answer3": "$$\\frac{7}{20}$$", "correct_answer": 0, "reason": "Correct 3/20 (1 − 1/4 − 3/5); distractors include complement and add-across error." }, { "id": 23308, "action": "convert", "question": "In a class of 40, the pupils participated in different Co-Curricular Activities. Each pupil only participated in 1 Co-Curricular Activity. The pie chart shows their participation. What fraction of the pupils in the class participated in Choir?", "answer0": "$$\\frac{1}{4}$$", "answer1": "$$\\frac{1}{8}$$", "answer2": "$$\\frac{1}{5}$$", "answer3": "$$\\frac{1}{10}$$", "correct_answer": 1, "reason": "Correct 1/8; distractors are nearby unit fractions of the class." }, { "id": 23342, "action": "skip", "question": "(a) What is the mixed number represented by A on the number line shown? Express your answer in the simplest form.
(b) Name a fraction greater than $$\\frac{2}{5}$$ but smaller than $$\\frac{4}{7}$$.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; part (b) is open-ended. Cannot be one MCQ." }, { "id": 23378, "action": "convert", "question": "Write $$4\\frac{2}{3}$$ as an improper fraction.", "answer0": "$$\\frac{12}{3}$$", "answer1": "$$\\frac{8}{3}$$", "answer2": "$$\\frac{14}{3}$$", "answer3": "$$\\frac{11}{3}$$", "correct_answer": 2, "reason": "Correct 14/3; distractors from omitting numerator or wrong product." }, { "id": 23384, "action": "convert", "question": "Find the value of $$1 - \\frac{1}{4} - \\frac{5}{12}$$
Express your answer in the simplest form.", "answer0": "$$\\frac{1}{3}$$", "answer1": "$$\\frac{4}{12}$$", "answer2": "$$\\frac{5}{12}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 0, "reason": "Correct 1/3 (4/12 simplified); distractors include un-simplified form." }, { "id": 23385, "action": "skip", "question": "Which two of the fractions are equivalent?
$$\\frac{8}{12}$$, $$\\frac{3}{9}$$, $$\\frac{4}{6}$$, $$\\frac{6}{8}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Select-two question with two different fraction answers; cannot be one MCQ." }, { "id": 23399, "action": "convert", "question": "What is the value of $$\\frac{3}{5} + \\frac{5}{8}$$? Express your answer as a mixed number.", "answer0": "$$1\\frac{9}{40}$$", "answer1": "$$\\frac{49}{40}$$", "answer2": "$$1\\frac{8}{13}$$", "answer3": "$$1\\frac{1}{40}$$", "correct_answer": 0, "reason": "Correct 1 9/40; distractors include improper form and add-across error." }, { "id": 23402, "action": "convert", "question": "$$\\frac{3}{8}$$ of counters in a container are red and the rest are blue.
(a) What fraction of the counters are blue?", "answer0": "$$\\frac{5}{8}$$", "answer1": "$$\\frac{3}{8}$$", "answer2": "$$\\frac{1}{2}$$", "answer3": "$$\\frac{5}{16}$$", "correct_answer": 0, "reason": "Part (a) fraction 5/8; part (b) is a whole number, only fraction part converted." }, { "id": 23411, "action": "skip", "question": "Arrange the following in increasing order.
$$4\\frac{3}{4}$$ , 4.90, $$4\\frac{7}{10}$$ , 4.65", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with four different answers; cannot be one MCQ." }, { "id": 23421, "action": "convert", "question": "What is the mixed number represented by the letter A on the number line?", "answer0": "$$3\\frac{4}{5}$$", "answer1": "$$3\\frac{1}{5}$$", "answer2": "$$4\\frac{4}{5}$$", "answer3": "$$3\\frac{4}{10}$$", "correct_answer": 0, "reason": "Correct 3 4/5; distractors vary fractional and whole-number parts." }, { "id": 23422, "action": "convert", "question": "Find the value of $$\\frac{1}{3} + \\frac{1}{9}$$.", "answer0": "$$\\frac{4}{9}$$", "answer1": "$$\\frac{2}{12}$$", "answer2": "$$\\frac{2}{9}$$", "answer3": "$$\\frac{3}{9}$$", "correct_answer": 0, "reason": "Correct 4/9; distractors from add-across and conversion slips." }, { "id": 23427, "action": "skip", "question": "Mrs Goh had some tea. She poured $$\\frac{2}{5}$$ $$\\ell$$ of it into a jug. She then poured the remaining amount of tea into 2 equal cups. Each cup contained $$\\frac{3}{10}$$ $$\\ell$$ less amount of tea than the amount of tea in the jug. (a) How much tea did she pour into each cup? (b) How much tea did she make? Express your answer in its simplest form.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 23431, "action": "skip", "question": "Arrange the following fractions from the smallest to the greatest.
$$\\frac{1}{3}$$ $$\\frac{1}{10}$$ $$\\frac{1}{6}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 23433, "action": "convert", "question": "$$\\frac{1}{2} - \\frac{3}{8} =$$", "answer0": "$$\\frac{1}{8}$$", "answer1": "$$\\frac{2}{6}$$", "answer2": "$$\\frac{2}{8}$$", "answer3": "$$\\frac{1}{4}$$", "correct_answer": 0, "reason": "Correct 1/8; distractors include subtract-across and conversion slips." }, { "id": 23451, "action": "skip", "question": "(a) Express $$\\frac{22}{4}$$ as a mixed number in its simplest form.
(b) $$\\frac{2}{9}$$ of 63 =", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question; part (a) is a mixed number, part (b) a whole number. Cannot be one MCQ." }, { "id": 23452, "action": "convert", "question": "Mdm Siti had 5 $$l$$ of orange juice. She drank $$\\frac{3}{8}$$ $$l$$ of orange juice. How much orange juice did she have left?", "answer0": "$$4\\frac{5}{8}$$", "answer1": "$$5\\frac{3}{8}$$", "answer2": "$$4\\frac{3}{8}$$", "answer3": "$$5\\frac{5}{8}$$", "correct_answer": 0, "reason": "Correct 4 5/8 (5 − 3/8); distractors include adding instead and wrong whole part." }, { "id": 23456, "action": "convert", "question": "Alice jogs $$\\frac{3}{4}$$ $$km$$ at a park. She walks $$\\frac{5}{12}$$ $$km$$ less than the distance she jogs. What is the total distance she jogs and walks?", "answer0": "$$1\\frac{1}{12}$$", "answer1": "$$\\frac{13}{12}$$", "answer2": "$$\\frac{1}{3}$$", "answer3": "$$1\\frac{1}{6}$$", "correct_answer": 0, "reason": "Correct 1 1/12 (3/4 + 1/3); distractors include improper form and walk-only value." }, { "id": 23463, "action": "skip", "question": "Bag A weighs $$\\frac{1}{4}$$ kg. Bag B weighs $$\\frac{3}{5}$$ kg. Bag C weighs $$\\frac{5}{8}$$ kg.
(a) Which 2 bags, when added together, will be heavier than 1 kg?
(b) Muthu puts a laptop into Bag B. The total mass of Bag B and the laptop is 3 kg. What is the mass of the laptop, in kg?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Multi-part question; part (a) selects bag letters, only part (b) is a fraction. Cannot be one MCQ." }, { "id": 23464, "action": "convert", "question": "Ali drank $$\\frac{7}{10}$$ $$\\ell$$ of water. He drank $$\\frac{1}{5}$$ $$\\ell$$ of water more than Harry. How much water did Ali and Harry drink in total? Give your answer as a mixed number.", "answer0": "$$1\\frac{2}{10}$$", "answer1": "$$\\frac{12}{10}$$", "answer2": "$$1\\frac{1}{10}$$", "answer3": "$$1\\frac{4}{10}$$", "correct_answer": 0, "reason": "Correct 1 2/10 (7/10 + 5/10); distractors include improper form and slips." }, { "id": 23465, "action": "skip", "question": "Jim had 3 pieces of rope. Rope A is the longest. Its length is $$\\frac{9}{10}$$ m. The difference between the lengths of Rope A and Rope B is $$\\frac{3}{4}$$ m.
(a) What is the length of Rope B, in m? Give your answer in its simplest form.
(b) Rope B is the shortest. The difference between the lengths of Rope B and Rope C is $$\\frac{1}{2}$$ m. What is the length of Rope C, in m?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 23471, "action": "skip", "question": "Arrange the following from the greatest to the smallest.
$$1\\frac{1}{9}$$, $$\\frac{4}{5}$$, $$\\frac{7}{6}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 23474, "action": "convert", "question": "What is the value of $$\\frac{5}{6}+\\frac{2}{3}$$? Express your answer as a mixed number.", "answer0": "$$1\\frac{1}{6}$$", "answer1": "$$1\\frac{1}{2}$$", "answer2": "$$\\frac{9}{6}$$", "answer3": "$$1\\frac{1}{3}$$", "correct_answer": 1, "reason": "Correct 1 1/2 (9/6); distractors include un-simplified and arithmetic slips." }, { "id": 23484, "action": "convert", "question": "Find the value of $$\\frac{11}{12} - \\frac{2}{3}$$ in its simplest form.", "answer0": "$$\\frac{1}{4}$$", "answer1": "$$\\frac{3}{12}$$", "answer2": "$$\\frac{9}{9}$$", "answer3": "$$\\frac{1}{3}$$", "correct_answer": 0, "reason": "Correct 1/4 (3/12 simplified); distractors include un-simplified and subtract-across errors." }, { "id": 23487, "action": "convert", "question": "The letter A represents a mixed number. Give your answer in its simplest form.", "answer0": "$$1\\frac{2}{3}$$", "answer1": "$$1\\frac{1}{3}$$", "answer2": "$$2\\frac{1}{3}$$", "answer3": "$$1\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct 1 1/3; distractors vary fractional and whole-number parts." }, { "id": 23488, "action": "skip", "question": "Arrange the following fractions in increasing order.
$$\\frac{4}{5}$$ , $$\\frac{2}{3}$$ , $$\\frac{5}{3}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Ordering question with three different fraction answers; cannot be one MCQ." }, { "id": 23501, "action": "skip", "question": "(a) Write $$\\frac{15}{7}$$ as a mixed number.
(b) Express 0.75 as a fraction in its simplest form.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Two-part question with two different fraction answers; cannot be one MCQ." }, { "id": 23502, "action": "skip", "question": "(a) Arrange the following in decreasing order. $$\\frac{13}{5}$$, $$2\\frac{3}{4}$$, $$\\frac{7}{8}$$
(b) What is the missing number in the box? $$\\frac{15}{24} = \\frac{[?]}{8}$$", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "reason": "Multi-part ordering plus equivalent-fraction with several different answers; cannot be one MCQ." }, { "id": 23510, "action": "convert", "question": "There are some beads in a box. $$\\frac{7}{9}$$ of them are red beads and the rest are blue beads. There are 130 more red beads than blue beads.
(a) What fraction of the beads are blue?", "answer0": "$$\\frac{2}{9}$$", "answer1": "$$\\frac{7}{9}$$", "answer2": "$$\\frac{1}{9}$$", "answer3": "$$\\frac{5}{9}$$", "correct_answer": 0, "reason": "Part (a) fraction 2/9; part (b) is a whole number, only fraction part converted." }, { "id": 23519, "action": "convert", "question": "What fraction of the set of shapes is shaded? Give your answer as a fraction in the simplest form.", "answer0": "$$\\frac{2}{3}$$", "answer1": "$$\\frac{1}{3}$$", "answer2": "$$\\frac{1}{4}$$", "answer3": "$$\\frac{1}{2}$$", "correct_answer": 1, "reason": "Correct 1/3; distractors include complement and common fraction errors." }, { "id": 23520, "action": "convert", "question": "Find the sum of $$\\frac{1}{4}$$ and $$\\frac{1}{6}$$.", "answer0": "$$\\frac{5}{12}$$", "answer1": "$$\\frac{2}{10}$$", "answer2": "$$\\frac{2}{12}$$", "answer3": "$$\\frac{7}{12}$$", "correct_answer": 0, "reason": "Correct 5/12; distractors include add-across and conversion slips." }, { "id": 23523, "action": "convert", "question": "Express the number represented by the letter A on the number line as an improper fraction.", "answer0": "$$\\frac{22}{5}$$", "answer1": "$$\\frac{17}{5}$$", "answer2": "$$\\frac{22}{10}$$", "answer3": "$$\\frac{21}{5}$$", "correct_answer": 0, "reason": "Correct 22/5; distractors vary numerator and denominator." }, { "id": 23524, "action": "convert", "question": "Hanz ran a distance of $$\\frac{5}{7}$$ km. The distance Sam ran was $$\\frac{1}{2}$$ km shorter than Hanz. What was the total distance that Hanz and Sam ran?", "answer0": "$$\\frac{13}{14}$$", "answer1": "$$\\frac{6}{9}$$", "answer2": "$$\\frac{3}{14}$$", "answer3": "$$\\frac{11}{14}$$", "correct_answer": 0, "reason": "Correct 13/14 (5/7 + 3/14); distractor 3/14 is Sam's distance only." }, { "id": 23526, "action": "convert", "question": "Mrs Lim used $$\\frac{3}{4}$$ kg of flour to bake some cupcakes. She used $$\\frac{1}{3}$$ kg of flour more than Mdm Siti. How much flour did they use altogether? Express your answer as a mixed number in its simplest form.", "answer0": "$$1\\frac{1}{6}$$", "answer1": "$$\\frac{7}{6}$$", "answer2": "$$1\\frac{1}{12}$$", "answer3": "$$1\\frac{5}{12}$$", "correct_answer": 0, "reason": "Correct 1 1/6 (3/4 + 5/12); distractors include improper form and slips." } ]