Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.1: Recall: Fractions, Equivalent Fractions and Simplest Form (answers)
Section A · Multiple choice 4 marks
1. The strip is divided into equal parts. What fraction of the strip is shaded?1 mark
(A) 28(B) 62(C) 86(D) 68
Answer: (D) 68There are 8 equal parts and 6 are shaded, so 68 of the strip is shaded.
2. Which fraction is equivalent to 23?1 mark
(A) 812(B) 45(C) 32(D) 26
Answer: (A) 812Multiply the top and bottom by 4: 23 = 2 × 43 × 4 = 812. (Adding 2 to the top and bottom does not give an equal fraction.)
3. What is 1824 in its simplest form?1 mark
(A) 912(B) 34(C) 68(D) 23
Answer: (B) 34The biggest number that goes into 18 and 24 is 6. 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 1824 = 34. (912 and 68 are equal but can be made simpler.)
4. 35 = □20. What number goes in the box?1 mark
(A) 8(B) 15(C) 12(D) 17
Answer: (C) 125 × 4 = 20, so multiply the top by 4 as well: 3 × 4 = 12.
Section B · Write your answer 11 marks
5. The strip is divided into equal parts. What fraction of the strip is shaded? Give your answer in its simplest form.1 mark
Answer: 254 out of 10 parts are shaded: 410. Divide the top and bottom by 2: 25.
6. 56 = □18. Find the missing number.1 mark
Answer: 156 × 3 = 18, so multiply the top by 3: 5 × 3 = 15.
7. Write 1230 in its simplest form.1 mark
Answer: 25Divide the top and bottom by 6: 12 ÷ 6 = 2 and 30 ÷ 6 = 5. So 1230 = 25.
8. Write 2436 in its simplest form.1 mark
Answer: 23Divide the top and bottom by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. So 2436 = 23.
9. The fraction wall shows 34 shaded. Use it to find the missing number: 34 = □12.1 mark
Answer: 9Each fourth is the same as 3 twelfths. So 3 fourths = 3 × 3 = 9 twelfths. 34 = 912.
10. A ribbon is cut into 12 equal pieces. 9 pieces are used. What fraction of the ribbon is not used? Give your answer in its simplest form.2 marks
Answer: 1412 − 9 = 3 pieces are not used. That is 312. Divide the top and bottom by 3: 14.
11. Find the missing numbers: 46 = □3 = 20□.2 marks
Answer: 2 and 306 ÷ 2 = 3, so divide the top by 2 as well: 4 ÷ 2 = 2. Then 23 = 2030 because 2 × 10 = 20 and 3 × 10 = 30.
12. A box has 36 sweets. 12 are red and 9 are green. The rest are yellow. What fraction of the sweets are yellow? Give your answer in its simplest form.2 marks
Answer: 512Yellow sweets: 36 − 12 − 9 = 15. Fraction: 1536. Divide the top and bottom by 3: 512.
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.2: Mixed Numbers (answers)
Section A · Multiple choice 4 marks
1. What mixed number does the picture show?1 mark
(A) 2 34(B) 2 14(C) 3 34(D) 2 35
Answer: (A) 2 342 whole bars are shaded and 3 out of 4 parts of the last bar. So the mixed number is 2 34.
2. Point A is shown on the number line. What mixed number does A stand for?1 mark
(A) 1 14(B) 1 34(C) 1 35(D) 2 14
Answer: (B) 1 34Each space from 1 to 2 is divided into 4 equal parts. A is 3 parts after 1, so A = 1 34.
3. Write 3 48 with the fraction part in its simplest form.1 mark
(A) 3 48(B) 3 24(C) 3 12(D) 4 12
Answer: (C) 3 12Divide the top and bottom of 48 by 4: 12. So 3 48 = 3 12.
4. Which of these is a mixed number?1 mark
(A) 23(B) 73(C) 5(D) 2 13
Answer: (D) 2 13A mixed number has a whole number part and a fraction part. 2 13 has 2 wholes and 13.
Section B · Write your answer 11 marks
5. What mixed number does the picture show? Give the fraction part in its simplest form.1 mark
Answer: 1 231 whole circle and 4 out of 6 parts of the next circle are shaded: 1 46. 46 = 23, so the answer is 1 23.
6. Point B is shown on the number line. What mixed number does B stand for? Give the fraction part in its simplest form.1 mark
Answer: 2 12B is 2 spaces after 2 and each space is one quarter: 2 24 = 2 12.
7. Write 5 69 with the fraction part in its simplest form.1 mark
Answer: 5 23Divide the top and bottom of 69 by 3: 23. So the answer is 5 23.
8. Write 6 + 1015 as a mixed number with the fraction part in its simplest form.1 mark
Answer: 6 236 + 1015 = 6 1015. Divide the top and bottom by 5: 23. The answer is 6 23.
9. Point Q is shown on the number line. What mixed number does Q stand for?1 mark
Answer: 3 35Q is 3 spaces after 3 and each space is one fifth, so Q = 3 35.
10. Mei ate the pizzas shown in the picture (shaded parts). How many pizzas did she eat? Give your answer as a mixed number in its simplest form.2 marks
Answer: 2 34She ate 2 whole pizzas and 6 out of 8 slices of another pizza: 2 68. 68 = 34, so she ate 2 34 pizzas.
11. A and B are shown on the number line. Write the mixed numbers for A and B.2 marks
Answer: A = 1 13, B = 2 23Each space is one third. A is 1 space after 1: 1 13. B is 2 spaces after 2: 2 23.
12. Lina bought 3 68 m of ribbon. Kim bought 3 12 m of ribbon. Write Lina's length with the fraction part in its simplest form. Who bought more ribbon?2 marks
Answer: Lina: 3 34 m; Lina bought more68 = 34, so Lina bought 3 34 m. 12 = 24 and 34 is more than 24. Lina bought more.
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.3: Improper Fractions (answers)
Section A · Multiple choice 4 marks
1. Which of these is an improper fraction?1 mark
(A) 49(B) 75(C) 13(D) 611
Answer: (B) 75An improper fraction has a numerator that is bigger than or equal to its denominator. 7 is bigger than 5, so 75 is improper.
2. Each bar is divided into 4 equal parts. What improper fraction is shaded?1 mark
(A) 78(B) 47(C) 74(D) 34
Answer: (C) 74Each bar has 4 parts, so each part is one quarter. 4 + 3 = 7 parts are shaded, so the fraction is 74.
3. Point A is shown on the number line. What improper fraction does A stand for?1 mark
(A) 53(B) 83(C) 13(D) 73
Answer: (D) 73Each space is one third. From 0 to 2 there are 6 thirds, and A is 1 more third, so A = 73.
Answer: 118Eleven eighths means 11 parts, each one eighth: 118.
10. Points P and Q are shown on the number line. Write an improper fraction for each point.2 marks
Answer: P = 54, Q = 114Each space is one quarter. P: 4 + 1 = 5 quarters = 54. Q: 8 + 3 = 11 quarters = 114.
11. Each pizza is cut into 6 equal slices. Tom eats 9 slices. What fraction of a pizza does he eat? Give your answer as an improper fraction in its simplest form.2 marks
Answer: 32Tom eats 96 of a pizza. Divide the top and bottom by 3: 32.
12. Mei pours 18 litre of juice into each cup. She fills 13 cups. How many litres of juice does she pour as an improper fraction? Is it more than 1 litre?2 marks
Answer: 138 litres: yes13 cups of one eighth is 13 eighths = 138 litres. 8 eighths is 1 litre and 13 is more than 8, so it is more than 1 litre.
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.4: Mixed Numbers and Improper Fractions (answers)
8. Write 3412 as a mixed number in its simplest form.1 mark
Answer: 2 5634 ÷ 12 = 2 remainder 10, so 3412 = 2 1012. Divide the top and bottom of 1012 by 2: 56. The answer is 2 56.
9. 5 23 = □3. Find the missing number.1 mark
Answer: 175 × 3 = 15. 15 + 2 = 17.
10. Write 4510 as a mixed number in its simplest form.2 marks
Answer: 4 1245 ÷ 10 = 4 remainder 5, so 4510 = 4 510. Divide the top and bottom of 510 by 5: 12. The answer is 4 12.
11. A recipe needs 2 34 cups of flour. Mrs Tan uses a scoop that holds 14 cup. How many scoops of flour does she need?2 marks
Answer: 11 scoops2 34 = 114 (2 × 4 = 8, 8 + 3 = 11). Each scoop is one quarter, so she needs 11 scoops.
12. Each pizza is cut into 8 equal slices. A class eats 45 slices. (a) How many pizzas did they eat? Give your answer as a mixed number. (b) They ordered 6 pizzas. How much pizza is left? Give your answer as a fraction of one pizza.2 marks
Answer: (a) 5 58 pizzas (b) 38 of a pizza(a) 45 ÷ 8 = 5 remainder 5, so they ate 5 58 pizzas. (b) 6 pizzas have 6 × 8 = 48 slices. 48 − 45 = 3 slices are left, which is 38 of a pizza.
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.5: Recall: Comparing and Ordering Fractions (answers)
Section A · Multiple choice 4 marks
1. Which comparison is correct?1 mark
(A) 12 < 13(B) 25 > 35(C) 58 = 34(D) 34 > 23
Answer: (D) 34 > 2334 = 912 and 23 = 812. 9 twelfths is more than 8 twelfths, so 34 > 23.
2. Which is the smallest fraction?1 mark
(A) 12(B) 56(C) 23(D) 34
Answer: (A) 12Change them to twelfths: 56 = 1012, 12 = 612, 23 = 812, 34 = 912. 6 twelfths is the smallest, so 12 is the smallest.
3. Arrange the fractions from the smallest to the greatest: 38, 12, 141 mark
Answer: (B) 14, 38, 12In eighths: 38, 48 and 28. From smallest: 28, 38, 48, which is 14, 38, 12.
4. Which fraction is greater than 35?1 mark
(A) 12(B) 25(C) 710(D) 1120
Answer: (C) 71035 = 610. Only 710 is more than 610. (12 = 510, 25 = 410 and 1120 is less than 1220.)
Section B · Write your answer 11 marks
5. Write > or < in the box: 56 □ 791 mark
Answer: 56 > 79Change both to eighteenths: 56 = 1518 and 79 = 1418. 15 is more than 14, so 56 > 79.
6. Write >, < or = in the box: 45 □ 12151 mark
Answer: 45 = 1215Multiply the top and bottom of 45 by 3: 1215. They are equal.
7. Arrange the fractions from the smallest to the greatest: 12, 310, 251 mark
Answer: 310, 25, 12In tenths: 510, 310, 410. From smallest: 310, 410, 510. So the order is 310, 25, 12.
8. Arrange the fractions from the greatest to the smallest: 58, 34, 121 mark
Answer: 34, 58, 12In eighths: 58, 68 and 48. From greatest: 68, 58, 48, so the order is 34, 58, 12.
9. Strip A is 34 shaded and strip B is 56 shaded. The strips are the same length. Which fraction is greater?1 mark
Answer: 56In twelfths, 34 = 912 and 56 = 1012. 10 twelfths is more, so 56 is greater. (Strip B has more shaded.)
10. Arrange the fractions from the smallest to the greatest: 23, 512, 342 marks
Answer: 512, 23, 34Change all to twelfths: 23 = 812, 512, 34 = 912. From smallest: 512, 812, 912. So the order is 512, 23, 34.
11. Ali drank 35 of a bottle of water, Ben drank 710 of an identical bottle and Cara drank 12 of another identical bottle. Who drank the most? Who drank the least?2 marks
Answer: Ben drank the most; Cara drank the leastIn tenths: Ali 610, Ben 710, Cara 510. 7 tenths is the most (Ben) and 5 tenths is the least (Cara).
12. Ria read 58 of her book, Sam read 35 of his book and Tia read 710 of her book. All the books have the same number of pages. Arrange the children from the one who read the least to the one who read the most.2 marks
Answer: Sam, Ria, TiaChange to fortieths (8, 5 and 10 all go into 40): Ria 2540, Sam 2440, Tia 2840. From least: Sam (2440), Ria (2540), Tia (2840).
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Lesson 5.6: Comparing and Ordering Improper Fractions and Mixed Numbers (answers)
Answer: (C) 154, 3 12, 103154 = 3 34, 103 = 3 13. All have 3 wholes. Compare the fraction parts in twelfths: 912, 612, 412. The order is 154, 3 12, 103.
4. Which number is greater than 2 35?1 mark
(A) 125(B) 52(C) 73(D) 83
Answer: (D) 832 35 = 135. 83 = 2 23. Compare 35 and 23: 915 and 1015. So 83 is greater. The others, 125 = 2 25, 52 = 2 12 and 73 = 2 13, are all less than 2 35.
Section B · Write your answer 11 marks
5. Write > or < in the box: 175 □ 3 151 mark
Answer: 175 > 3 15175 = 3 25. Same wholes, and 2 fifths is more than 1 fifth, so 175 > 3 15.
6. Write > or < in the box: 4 23 □ 1331 mark
Answer: 4 23 > 133133 = 4 13. Same wholes, and 2 thirds is more than 1 third, so 4 23 > 133.
7. Arrange the numbers from the smallest to the greatest: 73, 2 12, 1161 mark
Answer: 116, 73, 2 12116 = 1 56 is the only one less than 2. 73 = 2 13 and 2 12: 13 < 12. So the order is 116, 73, 2 12.
8. Which is smaller, 196 or 3 13?1 mark
Answer: 196196 = 3 16. Same wholes, and 16 < 13 (13 = 26). So 196 is smaller.
9. Which is the greatest? 4 12, 174, 133, 4 251 mark
Answer: 4 12Change to mixed numbers: 4 12, 4 14, 4 13, 4 25. All have 4 wholes. Compare the fractions in sixtieths: 3060, 1560, 2060 and 2460. The greatest is 3060, so 4 12 is the greatest.
10. Arrange the numbers from the greatest to the smallest: 3 34, 144, 1132 marks
Answer: 3 34, 113, 144144 = 3 24 = 3 12 and 113 = 3 23. Compare 34, 23 and 12 in twelfths: 912, 812, 612. The order is 3 34, 113, 144.
11. Ann has 2 38 m of ribbon, Ben has 218 m of ribbon and Cara has 52 m of ribbon. Who has the longest ribbon? Who has the shortest ribbon?2 marks
Answer: Ben has the longest; Ann has the shortest218 = 2 58 and 52 = 2 12 = 2 48. Ann 2 38, Cara 2 48, Ben 2 58. Ben has the longest and Ann has the shortest.
12. Three jugs hold 2 23 litres, 176 litres and 52 litres of water. (a) Arrange the amounts from the least to the greatest. (b) What is the difference between the greatest and the least amounts?2 marks
Answer: (a) 52, 2 23, 176 (b) 13 litre(a) In sixths: 2 23 = 166, 176, 52 = 156. The order is 156, 166, 176, which is 52, 2 23, 176. (b) 176 − 156 = 26 = 13 litre.
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Primary 4 Mathematics · Chapter 5 · Answers and explanations
Chapter 5 Revision Paper: Fractions (I) (answers)
Section A · Multiple choice 10 marks
1. The strip is divided into equal parts. What fraction of the strip is shaded? Give your answer in its simplest form.1 mark
(A) 25(B) 53(C) 35(D) 310
Answer: (C) 356 out of 10 equal parts are shaded: 610. Divide the top and bottom by 2: 35. (25 is the part not shaded.)
2. Which fraction is equivalent to 38?1 mark
(A) 611(B) 316(C) 1116(D) 924
Answer: (D) 924Multiply the top and bottom by 3: 3 × 38 × 3 = 924. (Adding the same number to the top and bottom, or changing only one of them, does not keep the value.)
3. Which of these fractions is in its simplest form?1 mark
(A) 712(B) 69(C) 1015(D) 814
Answer: (A) 712A fraction is in simplest form when no number except 1 divides both the top and bottom. 7 and 12 share no such number. 69 = 23, 1015 = 23 and 814 = 47 can all be made simpler.
4. Point P is shown on the number line. What mixed number does P stand for?1 mark
(A) 2 35(B) 3 25(C) 3 35(D) 2 25
Answer: (B) 3 25Each space from 3 to 4 is divided into 5 equal parts. P is 2 parts after 3, so P = 3 25.
Answer: (D) 4 5629 ÷ 6 = 4 remainder 5. So there are 4 wholes and 56 left over: 296 = 4 56.
7. Each circle is divided into equal parts. What improper fraction does the picture show?1 mark
(A) 114(B) 1112(C) 113(D) 84
Answer: (A) 114Each circle has 4 equal parts. 4 + 4 + 3 = 11 parts are shaded, so the picture shows 114.
8. Which fraction is greater than 23 but smaller than 56?1 mark
(A) 712(B) 34(C) 1112(D) 58
Answer: (B) 34Change to twelfths: 23 = 812 and 56 = 1012. The fraction between them is 912 = 34. (712 is less than 812; 1112 is more than 1012; 58 = 1524 is less than 1624 = 23.)
9. Arrange the numbers in order, starting with the smallest.1 mark
Answer: (C) 52, 2 58, 2 3452 = 2 12 = 2 48; 2 34 = 2 68. All have 2 wholes, so compare the eighths: 4, 5, 6. Order: 52, 2 58, 2 34.
10. Which is the greatest?1 mark
(A) 3 34(B) 113(C) 72(D) 195
Answer: (D) 195Change each to a mixed number: 195 = 3 45, 113 = 3 23, 72 = 3 12. Compare the fractions: 12 < 23 < 34 < 45 (use 60ths: 30, 40, 45, 48). The greatest is 195.
Section B · Short answers 4 marks
11. Write 2842 in its simplest form.1 mark
Answer: 23Divide the top and bottom by 14: 28 ÷ 14 = 2 and 42 ÷ 14 = 3. So 2842 = 23.
12. Express 3812 as a mixed number in its simplest form.1 mark
Answer: 3 1638 ÷ 12 = 3 remainder 2, so 3812 = 3 212. Divide the top and bottom of 212 by 2: 16. The answer is 3 16.
13. 59 = 20□. What is the missing number?1 mark
Answer: 365 × 4 = 20, so multiply the bottom by 4 as well: 9 × 4 = 36.
14. Arrange 34, 45 and 710 in order, starting with the smallest.1 mark
Answer: 710, 34, 45Change to twentieths: 34 = 1520, 45 = 1620, 710 = 1420. Since 14 < 15 < 16, the order is 710, 34, 45.
Section C · Show your working 16 marks
15. There are 36 pupils in a club. 15 of them are girls. What fraction of the pupils in the club are boys? Give your answer in its simplest form.2 marks
Answer: 712Boys: 36 − 15 = 21. Fraction of boys: 2136. Divide the top and bottom by 3: 712.
16. A rope is 6 410 m long. (a) Write its length as a mixed number with the fraction in its simplest form. (b) Express your answer in (a) as an improper fraction.2 marks
Answer: (a) 6 25 m (b) 325 m(a) Divide the top and bottom of 410 by 2: 25, so the length is 6 25 m. (b) 6 × 5 + 2 = 32, so 6 25 = 325 m.
17. P and Q are marked on the number line. (a) Write P as a mixed number in its simplest form. (b) Write Q as an improper fraction.2 marks
Answer: (a) 3 23 (b) 296Each space from 3 to 4 is divided into 6 equal parts. (a) P is 4 parts after 3: 3 46 = 3 23. (b) Q is 5 parts after 4: 4 56 = 4 × 6 + 56 = 296.
18. Ravi's rope is 176 m long. Sam's rope is 2 34 m long. Tim's rope is 83 m long. Arrange the three pupils in order, starting with the one with the longest rope.2 marks
Answer: Ravi, Sam, TimChange all to twelfths: 176 = 3412; 2 34 = 114 = 3312; 83 = 3212. Since 34 > 33 > 32, the order is Ravi, Sam, Tim.
19. A cake was cut into 20 equal slices. 5 slices were eaten on Monday and 3 slices on Tuesday. What fraction of the cake was left? Give your answer in its simplest form.2 marks
Answer: 35Slices left: 20 − 5 − 3 = 12. Fraction left: 1220. Divide the top and bottom by 4: 35.
20. Hana has a ribbon 3 35 m long. She cuts it into pieces that are each 15 m long. How many pieces does she get?2 marks
Answer: 181 m = 55 m, so 3 m = 15 fifths. Add the other 3 fifths: 15 + 3 = 18. 3 35 = 185, so she gets 18 pieces.
21. A tank has 476 litres of water. Mia pours the water into jugs that each hold 1 litre when full. (a) How many jugs are completely filled? (b) How much water is left over? Give your answer as a fraction of a litre.2 marks
Answer: (a) 7 jugs (b) 56 litre47 ÷ 6 = 7 remainder 5, so 476 = 7 56. (a) 7 jugs are completely filled. (b) 56 litre is left over.
22. Find a fraction with denominator 18 that is greater than 12 and smaller than 23, and is in its simplest form.2 marks
Answer: 111812 = 918 and 23 = 1218. The fractions between them are 1018 and 1118. But 1018 = 59 is not in simplest form (10 and 18 are both divisible by 2). So the answer is 1118.
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