46 Mathematics Grade 5 3. 960 ÷ 800 = 960 ÷ ÷ = ÷ = 4. 42 ÷ 7000 = 42 ÷ ÷ = ÷ = 5. 37 800 ÷ 2000 = 37 800 ÷ ÷ = ÷ = H Write your answers on the lines provided. 1. 2.3 kg + 34.05 kg = g 2. 305.25 ml – 259.75 ml = ml 3. 57.3 cm × 300 = m 4. 4907 g ÷ 700 = g 5. Add 713 g to 12.8 g = g 6. Multiply 1 hour 10 minutes by 20. Give your answer in hours and minutes. h min 7. Divide 165.06 l by 70. l 8. Subtract 0.24 m from 34 m. m 8 120 7 2 18 900 36 350 45.5 171.90 7.01 725.8 23 20 2.358 33.76 18.9 6 1.2 100 100 1000 1000 1000 1000 0.006 For Teachers Only
47 Chapter 4 Four operations with decimals I Find the sum of each of the following. 1. 2.097 + 0.487 = 2. 9.9 + 5.154 = 3. 7.322 + 7.426 = 4. 5.769 + 6.835 = 5. 10.975 + 18.574 + 21.405 = 6. 17.905 + 30.762 + 42.079 = 7. 8.986 + 23.9 + 40.257 = 8. 4.924 + 19.429 + 5.61 = 1 1 + 2.097 0.487 2.584 + 7.322 7.426 14.748 1 + 9.900 5.154 15.054 1 1 1 + 5.769 6.835 12.604 1 1 1 1 + 17.905 30.762 42.079 90.746 1 2 1 1 + 8.986 23.900 40.257 73.143 1 1 1 1 + 10.975 18.574 21.405 50.954 1 1 1 + 4.924 19.429 5.610 29.963 2.584 15.054 14.748 12.604 50.954 73.143 90.746 29.963 For Teachers Only
48 Mathematics Grade 5 J Find the difference of each of the following. 1. 0.832 – 0.664 = 2. 3.562 – 1.649 = 3. 6.295 – 5.71 = 4. 9.938 – 5.706 = 5. 12.51 – 9.694 = 6. 18.208 – 7.024 = 7. 15.789 – 9.28 = 8. 17.6 – 6.374 = – 9.938 5.706 4.232 0.168 0.585 4.232 1.913 2.816 6.509 11.184 11.226 – 0.832 0.664 0.168 7 2 12 12 – 3.562 1.649 1.913 2 15 5 12 – 6.295 5.710 0.585 5 12 – 12.510 9.694 2.816 1 4 0 10 11 14 10 – 18.208 7.024 11.184 1 10 – 15.789 9.280 6.509 15 – 17.600 6.374 11.226 5 9 10 For Teachers Only
49 Chapter 4 Four operations with decimals K Find the product of each of the following. 1. 12 × 10.4 = 2. 1.6 × 3.4 = 3. 1.9 × 2.4 = 4. 2.27 × 17.4 = 5. 37.5 × 9.41 = 6. 18.327 × 25 = × 10.4 1 2 208 1040 124.8 × 1.6 3.4 6 4 480 5.4 4 × 1.9 2.4 7 6 380 4.5 6 × 2.2 7 1 7.4 908 15890 2 2700 3 9.4 98 × 3 7.5 9.4 1 3 75 15000 337500 3 5 2.8 7 5 × 18.3 27 25 91635 366540 4 5 8.1 75 124.8 5.44 4.56 39.498 352.875 458.175 1 2 1 3 1 1 2 1 2 1 4 3 2 6 4 1 4 1 1 3 1 1 1 1 For Teachers Only
50 Mathematics Grade 5 1 7. 148.9 × 9 = 8. 12.1 × 15 = 9. 5.7 × 2.2 = 10. 5.319 × 46 = 11. 4.2 × 7.88 = 12. 66.4 × 3.1 = 4 8 8 × 148.9 9 1340.1 1 × 12.1 1 5 605 121 1 81.5 1 1 1 1 × 3 5.7 2.2 714 714 7 8.5 4 1 3 1 1 5 × 5.319 46 31914 21276 2 44.674 × 7.88 4.2 1576 3152 3 3.09 6 × 66.4 3.1 664 1992 2 0 5.84 1340.1 181.5 78.54 244.674 33.096 205.84 1 1 3 3 1 1 1 1 For Teachers Only
51 Chapter 4 Four operations with decimals L Find the quotient of each of the following. 1. 5.2 ÷ 5 = 2. 7.8 ÷ 3 = 3. 6.62 ÷ 4 = 4. 10.72 ÷ 4 = 1.04 5 5.20 5 20 0 2 0 2 0 0 1.6 55 4 6.6 20 4 2 6 2 4 2 2 2 0 20 20 0 2.6 3 7.8 6 1 8 1 8 0 2.68 4 10.72 8 2 7 2 4 32 32 0 1.04 1.04 2.6 2.68 For Teachers Only
52 Mathematics Grade 5 5. 23.082 ÷ 6 = 6. 445.04 ÷ 8 = 7. 1281.21 ÷ 7 = 8. 505.26 ÷ 9 = 3.8 4 7 6 2 3.0 8 2 1 8 5 0 4 8 2 8 2 4 4 2 4 2 0 5 5.6 3 8 4 4 5.0 4 4 0 4 5 4 0 5 0 4 8 2 4 2 4 0 3.847 183.03 55.63 56.14 1 8 3.0 3 7 1 2 8 1.2 1 7 5 8 5 6 2 1 2 1 2 1 2 1 0 5 6.1 4 9 5 0 5.2 6 4 5 5 5 5 4 1 2 9 3 6 3 6 0 For Teachers Only
53 Chapter 4 Four operations with decimals M Solve the following word problems. 1. A piece of string measures 43.2 cm. What is the total length of a dozen of such strings? 2. Lisa mixed 2.3 l of water with 4 similar bottles of orange syrup. The volume of the total mixture is 3700 ml. What was the volume of orange syrup in each bottle at first? 3. Alan had a roll of rope measuring 10 m. He cut out 5 equal pieces of rope each measuring 1.55 m from the original rope. What is the length of the remaining rope? 12 × 43.2 cm = 518.4 cm The total length of a dozen of such strings is 518.4 cm. 1l – 1000 ml 2.3 × 1000 = 2300 ml 3700 ml – 2300 ml = 1400 ml The total volume of 4 bottles of orange syrup is 1400 ml. 1400 ml ÷ 4 = 350 ml Each bottle of orange syrup is 350 ml. 5 × 1.55 m = 7.75 m 7.75 m of rope were cut. 10 m – 7.75 m = 2.25 m The length of the remaining rope was 2.25 m. 43.2 cm 43.2 cm 43.2 cm ? 43.2 cm 1 12 43.2 × 1 2 86 4 432 0 518.4 2300 ml 3700 ml ???? 350 4 1400 12 20 20 0 0 10 m 1.55 m 1.55 m 1.55 m 1.55 m 1.55 m ? – 10.00m 7.75m 2.25m × 1.55 5 m 7.75 m 2 2 9 910 For Teachers Only
54 Mathematics Grade 5 4. David cut 5 m of wire into 20 equal pieces. Find the length of each piece of wire in cm. 5. Tank A contains 27.3 l of water while Tank B contains 1 3 of the volume of water in Tank A. What is the total volume of water in both tanks? Give your answer in millimetres. 6. Mary used 4.41 kg of flour to make 7 cakes. How much flour does Mary need to make 11 cakes? Give your answer in grams. 5 m ? ? ? ? 1 20 5 m = 5 × 100 = 500 cm 500 cm ÷ 20 = 500 cm ÷ 2 ÷ 10 = 250 cm ÷ 10 = 25 cm Each piece of wire is 25 cm. 27.3 l ? ml Tank B ? Tank A 3 units 27 300 ml 1 unit 27 300 ml ÷ 3 = 9100 ml Tank B contains 9100 ml of water. 4 units 4 × 9100 ml = 36 400 ml The total volume of water in both 27.3 l tanks is 36 400 ml. = 27.3 × 1000 = 27 300 ml 4.41 kg ? ? ? ? ? ? ? 4.41 kg = 4.41 × 1000 = 4410 g 7 units 4410 g 1 unit 4410 g ÷ 7 =630 g 630 g of flour is needed to make 1 cake. ? g 11 units 11 × 630 g = 6930 g Mary needs 6930 g of flour to make 11 cakes. For Teachers Only
55 Chapter 4 Four operations with decimals 7. Robert lives 570 m from his school. He walks to school and returns home along the same route 5 days a week. How many kilometres does Robert travel in a week? 8. Mrs Lim bought 4 cartons of cans of raspberry juice for a party. Each carton contains 12 cans of raspberry juice. She emptied all the cans of drinks into a large container. The total volume of raspberry juice is 12.48 l. What is the volume of raspberry juice in each can at first? 9. A curtain tailor receives an order for making 48 similar curtains. Each curtain requires 330 cm of cloth. Each roll of cloth was 40 m long. (a) How many rolls of cloth were needed to make 48 similar curtains? (b) If the curtain tailor buys 4 rolls of cloth, how much cloth did the tailor have left? Give your answer in metres. (Assume there was no wastage.) 570 m = 570 ÷ 1000 = 0.57 km 2 × 0.57 km = 1.14 km Robert travels 1.14 km a day. 5 × 1.14 km = 5.70 km Robert travels 5.70 km in a week. 4 × 12 = 48 There are 48 cans of raspberry juice in total. 12.48 l = 12.48 × 1000 = 12 480 ml 12 480 ml ÷ 48 = 260 ml Each can contains 260 ml of raspberry juice. (a) 330 cm 330 cm ? 330 cm 330 cm 1 48 330 cm = 330 ÷ 100 = 3.3 m 48 × 3.3 m = 158.4 m 158.4 m of cloth is needed to make 48 curtains. 158.4 m ÷ 40 m = 3.96 The tailor needs to order 4 rolls of cloth. (b) 4 × 40 m = 160 m 160 m – 158.4 m = 1.6 m He had 1.6 m of cloth left. For Teachers Only
56 Mathematics Grade 5 Mastery Practice Circle the correct answers. 1. 77.087 + 57.54 = A 134.131 B 134.141 C 134.527 D 134.627 2. 85.487 – 51.008 = A 33.687 B 34.407 C 34.479 D 34.489 3 13.409 × 12 = A 160 908 B 16 090.8 C 1609.08 D 160.908 4. 54.3 × 300 = A 16 290 B 1629 C 162.90 D 16.290 5. 71.5 ÷ 20 = A 0.325 C 3.252 B 3.575 D 3.525 6. Convert 15 24 into a decimal. A 0.6 C 0.625 B 0.62 D 6.25 7. Convert 11 23 into the equivalent decimal, correct to 2 decimal places. A 0.45 C 0.47 B 0.46 D 0.48 8. Which of the following is the sum of 34.8 + 7.707 rounded off to the nearest hundredth? A 42.49 B 42.50 C 42.51 D 42.52 9. Jenny uses three ribbons to decorate her book. The ribbons are 3.12 cm, 4.5 cm and 5.19 cm long. Find the total length of ribbons. A 8.76 cm B 87.6 cm C 128.1 cm D 12.81 cm 10. There are 162.1 litres of water in a tank. If 32.09 litres of water is used, how much water is left? A 130.01 litres B 130 litres C 130.1 litres D 130.2 litres 11. A construction company bought 0.283 tonnes of gravel and 0.535 tonnes of sand. How many tonnes of material did the company buy altogether? For Teachers Only
57 Chapter 4 Four operations with decimals A 0.718 tonnes C 0.918 tonnes B 0.818 tonnes D 1.018 tonnes 12. A carpenter bought a piece of wood that was 1.88 metres long. He sawed 0.569 metres off. How long is the piece of wood now? A 1.341 metres B 1.331 metres C 1.321 metres D 1.311 metres 13. Kenneth’s car uses 148.50 litres of petrol a month. How many litres of petrol does his car use in a year? A 1780 litres B 1781 litres C 1782 litres D 1783 litres 14. James has a ball of string. He cuts out 25 pieces of string, each measuring 0.55 m. He then cuts another 12 pieces that measures 0.35 m each. If he still has 12.05 m of string left, how long is the ball of string? A 10 m B 20 m C 30 m D 40 m For Teachers Only
Mathematics Grade 5 58 A Choose the correct answer and write its number in the brackets provided. 1. Which of the following is not correct when each number is rounded off to the nearest thousand? (1) 472 039 → 472 000 (2) 613 974 → 614 074 (3) 803 500 → 804 000 (4) 999 990 → 1 000 000 ( ) 2. Arrange the following numbers in ascending order. 406 781, 401 687, 406 871, 407 618, 408 761 (1) 401 687, 407 618, 406 781, 406 871, 408 761 (2) 401 687, 406 781, 406 871, 407 618, 408 761 (3) 408 761, 407 618, 406 871, 406 781, 401 687 (4) 408 761, 407 618, 406 871, 401 687, 406 781 ( ) 3. Which of the following place value of digit 8 is not correct? (1) 140 800 → Hundreds (2) 8 201 493 → Millions (3) 823 594 → Ten thousands (4) 328 517 → Thousands ( ) 4. Seven million seventy thousand seven hundred and seventeen in numerals is . (1) 7 700 717 (2) 7 070 017 (3) 7 077 017 (4) 7 070 717 ( ) 5. Estimate the value of 714 × 52. (1) 35 000 (2) 42 000 (3) 40 000 (4) 48 000 ( ) General Revision 1 2 2 3 4 1 For Teachers Only
General Revision 1 59 6. Express 32—2 7 as a decimal. Round off your answer to 2 decimal places. (1) 32.27 (2) 32.28 (3) 32.29 (4) 32.72 ( ) 7. Find the value of 18—2 5 – 9—9 10. (1) 8—1 2 (2) 9—2 5 (3) 9—1 2 (4) 9—7 10 ( ) 8. Find the product of 4—2 3 and 135. (1) 360 (2) 630 (3) 540 (4) 542 ( ) 9. Mrs Ong has 27 m of ribbon. She cuts off —1 3 of it to tie up some presents. The remaining ribbon is shared equally among her 12 pupils. What is the length of ribbon received by each pupil? (1) —1 12 m (2) —1 6 m (3) —1 2 m (4) 1—1 2 m ( ) 10. Which of the following has the smallest value? (1) 4 5 (2) 2 3 (3) 0.702 (4) 0.72 ( ) 11. Convert 27.013 kg to grams. (1) 2713 g (2) 27 013 g (3) 27 130 g (4) 270 130 g ( ) 3 1 2 4 2 2 For Teachers Only
Mathematics Grade 5 60 B Write your answers on the lines provided. 1. Write 7 214 538 in words. 2. Complete the following number pattern. 9, 216, , 124 416, 2 985 984 3. Arrange the numbers in decreasing order. 3 995 688, 3 795 688, 3 895 886, 3 959 868 12. Which of the following is not true? (1) 91 cm = 0.091 m (2) 8 l 20 ml = 8.02 l (3) 0.08 kg = 80 kg (4) 453 m = 0.453 km ( ) 13. 23 ÷ 1000 = (1) 0.023 (2) 0.23 (3) 2.3 (4) 23 000 ( ) 14. Convert 9.35 to a fraction in its simplest form. (1) 9 3 20 (2) 9 7 20 (3) 9 3 5 (4) 9 7 10 ( ) 15. Which of the following is not equivalent to 43.6? (1) 43 600 ÷ 1000 (2) 4.36 × 10 (3) 0.436 × 100 (4) 4360 ÷ 10 ( ) 1 1 2 4 Seven million two hundred and fourteen thousand five hundred and thirty-eight 5184 3 995 688, 3 959 868, 3 895 886, 3 795 688 For Teachers Only
General Revision 1 61 4. 1 505 948 when rounded off becomes 1 506 000. It was rounded to the nearest . 5. What is the place value of digit 5 in 7 520 934? 6. Find the value of 12—4 5 + 2—1 3 . 7. Divide —3 5 by 6. 8. Multiply 859 by 94. 9. Express 6 5 11 as a decimal. Round off your answer to 2 decimal places. 6 5 11 = 6 + 5 11 6 + 0.45 = 6.45 Thousand Hundred thousands 80 746 6.45 12 4 5 ×3 ×3 + 2 1 3 ×5 ×5 = 12 12 15 + 2 5 15 = 14 17 15 = 15 2 15 3 5 ÷ 6 = 3 5 × 1 6 = 1 × 1 5 × 2 = 1 10 15 2 15 1 10 1 2 × 859 9 4 3436 77310 80746 5 8 2 3 For Teachers Only
Mathematics Grade 5 62 10. Convert 420 km 17 m to metres. 11. Express 25 kg 15 g as a decimal in kilograms. 12. Judy jogs 720 m every day. How many kilometres does she jog in a week? Express your answer in its simplest form or as a mixed number. 13. A grocer stacks up 115 identical boxes of cornflakes. If the thickness of each box is 3.5 cm, find the height of the stack of boxes of cornflakes. Give your answer in metres. 14. Pamela used 38 m of ribbon to tie 50 identical present boxes. How many centimetres of ribbon did she use for each present box? 420 km = 420 × 1000 = 420 000 m 420 km 17 m = 420 000 m + 17 m = 420 017 m 115 × 3.5 cm = 402.5 cm 402.5 cm = 402.5 ÷ 100 = 4.025 m The height of the stack is 4.025 m. 3800 cm ÷ 50 = 3800 cm ÷ 5 ÷ 10 = 760 cm ÷ 10 = 76 cm 15 g = 15 ÷ 1000 = 0.015 kg 25 kg 15 g = 25 kg + 0.015 kg = 25.015 kg 7 × 720 m = 5040 m 5040 m = 5040 ÷ 1000 = 5.04 km = 5 4 100 km = 5 1 25 km 420 017 m 25.015 kg 4.025 m 76 cm 5 1 25 km 3.5 cm 3.5 cm 3.5 cm ? m 3.5 cm 1 115 38 m = 38 × 100 ? ? ? ? = 3800 cm 38 m 1 50 × 11 5 3.5 575 3450 4 02.5 2 1 1 25 For Teachers Only
General Revision 1 63 C Write your answers on the lines provided. 1. Identify the like fractions. 7 11 , 11 7 , 3 11 , 3 8 , 8 3 2. Add. Express your answer in its simplest form if necessary. (a) 9 10 + 2 5 15. Anthony ate —2 7 of a cake. The remaining cake was shared equally between his 2 brothers, Eddie and Ian. What fraction of the cake did Ian eat? 16. Sandra has some uncooked rice. After cooking 4—1 3 kg of uncooked rice for dinner, she still has 5—1 2 kg of uncooked rice left. How much uncooked rice did Sandra have at first? 5 7 ÷ 2 = 5 7 × 1 2 = 5 14 4 1 3 + 5 1 2 = 4 1 3 ×2 ×2 + 5 1 2 ×3 ×3 = 4 2 6 + 5 3 6 = 9 5 6 Sandra has 9 5 6 kg of uncooked rice at first. 9 10 + 2 5 ×2 ×2 = 9 10 + 4 10 = 13 10 = 10 10 + 3 10 = 1 3 10 Remaining fraction of cake = 1 – 2 7 = 5 7 Ian received 5 14 of the cake. 5 14 9 5 6 kg 1 3 10 7 11 , 3 11 For Teachers Only
Mathematics Grade 5 64 (b) 14 2 3 + 2 3 7 (c) 17 5 6 + 21 1 9 3. Subtract. Express your answer in its simplest form if necessary. (a) 7 11 – 1 4 (b) 8 3 7 – 2 4 5 (c) 24 7 9 – 13 5 6 14 2 3 ×7 × 7 + 2 3 7 ×3 ×3 = 14 14 21 + 2 9 21 = 16 23 21 = 17 2 21 8 3 7 – 2 4 5 = 8 15 35 – 2 28 35 = 7 50 35 – 2 28 35 = 5 22 35 24 7 9 – 13 5 6 = 24 14 18 – 2 15 18 = 23 32 18 – 13 15 18 = 10 17 18 17 5 6 + 21 1 9 = 17 15 18 + 21 2 18 = 38 17 18 7 11 – 1 4 = 28 44 – 11 44 = 17 44 17 2 21 38 17 18 17 44 5 22 35 10 17 18 For Teachers Only
General Revision 1 65 D Find the value of the following. 1. 1 2 × 3 4 = 2. 2 5 × 6 7 = 3. 5 8 × 4 5 = 4. 4 5 × 12 7 = 5. 8 9 × 27 3 = 6. 20 3 × 7 6 = 4. Find the value of each product in its simplest form. (a) 10 9 × 9 5 (b) 3 5 × 20 7 (c) 3 1 8 × 18 10 9 × 9 5 = 2 × 1 1 × 1 = 2 1 = 2 3 5 × 20 7 = 3 × 4 1 × 7 = 12 7 = 1 5 7 2 1 5 7 56 1 4 1 4 = 25 8 × 18 = 225 4 = 56 1 4 4 9 1 × 3 2 × 4 = 3 8 5 8 × 4 5 = 1 2 8 9 × 27 3 = 8 20 9 × 7 6 = 70 9 = 7 7 9 2 × 6 5 × 7 = 12 35 4 × 12 5 × 7 = 48 35 = 1 13 35 1 3 3 1 10 2 1 1 For Teachers Only
Mathematics Grade 5 66 E Divide these fractions. Express your answer in its simplest form. 1. 7 12 ÷ 7 = 2. 3 8 ÷ 6 = 3. 8 9 ÷ 4 = 4. 5 11 ÷ 20 = 5. 6 10 ÷ 2 = 6. 4 5 ÷ 12 = F Solve the following word problems. 1. A factory produces 115 808 dozen of canned drinks in a week. How many cans of drinks does the factory produce in a week? 7 12 × 1 7 = 1 × 1 12 × 1 = 1 12 3 8 × 1 6 = 1 × 1 8 × 2 = 1 16 5 11 × 1 20 = 1 × 1 11 × 4 = 1 44 4 5 × 1 12 = 1 × 1 5 × 3 = 1 15 8 9 × 1 4 = 2 × 1 9 × 1 = 2 9 6 10 × 1 2 = 3 × 1 10 × 1 = 3 10 1 2 3 1 1 1 1 2 1 1 4 3 1 dozen = 12 cans 115 808 = 115 808 × 12 cans = 1 389 696 cans 1 week = 7 days 7 × 1 389 696 = 9 727 872 The factory produces 9 727 872 cans of drinks. For Teachers Only
General Revision 1 67 2. The total mass of 3 cartons of oranges is 25—3 4 kg. Carton A has a mass of 8—3 8 kg and Carton B has a mass of 3—1 4 kg more than Carton A. What is the difference in mass between the heaviest and the lightest cartons of oranges? 3. Alex has some screws. He uses —5 6 of them to fix a shelf and —1 4 of the remaining screws to fix a desk. He has 48 screws left. (a) How many more screws does he use to fix the shelf than the desk? (b) How many screws does he have at first? Carton A = 8 3 8 kg The heaviest carton is Carton B and the lightest carton is Carton C. 11 5 8 – 5 3 4 = 11 5 8 – 5 6 8 = 10 13 8 – 5 6 8 = 5 7 8 kg Carton C = 25 3 4 – 11 5 8 – 8 3 8 = 25 6 8 – 11 5 8 – 8 3 8 = 24 14 8 – 19 8 8 = 5 6 8 = 5 3 4 kg Carton B = 8 3 8 + 3 1 4 = 8 3 8 + 3 2 8 = 11 5 8 kg The difference of mass between the heaviest and lightest cartons of oranges is 5 7 8 kg. (a) L L L Desk 48 ? L : Left He uses 16 screws to fix the desk. Remaining screws = 48 + 16 = 64 S S S S S R S : Shelf R : Remaining ? 64 5 × 64 = 320 He uses 320 screws to fix the shelf. 320 – 16 = 304 He uses 304 more screws to fix the shelf than the desk. (b) 6 × 64 = 384 He has 384 screws at first. 3 units 48 1 unit 48 ÷ 3 = 16 For Teachers Only
Mathematics Grade 5 68 4. 9.66 kg of flour is needed to make 7 similar cakes. How much flour is needed to make 25 such cakes? 5. Mary buys 4 bottles of grapefruit juice. Each bottle contains 1.89 l of juice. She drinks 0.9 l of grapefruit juice every day. How many millilitres of grapefruit juice does she have left after a week? 6. James bought 3 cartons of cans of mango juice. There are 6 cans of mango juice in each carton. Each can contained 295 ml of juice. How many litres of mango juice did James buy? 9.66 kg ÷ 7 = 1.38 kg 1.38 kg of flour is needed for each cake. 25 × 1.38 kg = 34.5 kg 34.5 kg of flour is needed to make 25 such cakes. ? 1.89 l 1.89 l 1.89 l 1.89 l 4 × 1.89 l = 7.56 l 4 bottles of grapefruit juice contain 7.56 l of juice. 0.9 l 0.9 l 0.9 l 0.9 l 0.9 l 0.9 l ? 0.9 l 7 × 0.9 l = 6.3 l Mary drinks 6.3 l of grapefruit juice in a week. 7.56 l – 6.3 l = 1.26 l 1.26 l = 1.26 × 1000 = 1260 m l Mary has 1260 m l of grapefruit juice left. 3 × 6 = 18 3 cartons of mango juice contain 18 cans. 295 ml ? 295 ml 1 18 295 ml 295 ml 18 × 295 ml = 5310 ml 5310 ml = 5310 ÷ 1000 = 5.31 l James bought 5.31 l of mango juice. For Teachers Only
General Revision 1 69 7. One full lap of a race track is 3 km. (a) What is the total distance of a 35.5-lap race? (b) How many laps make up a distance of 46.5 km? 8. Lucy bought 16 packs of nuggets and Jane bought 3 8 as much nuggets as Lucy. If a pack of nuggets has a mass of 810 g, (a) How many kilograms of nuggets did Lucy buy? (b) How many kilograms of nuggets did both of them buy? 9. Jack cut 4.2 m of string into 30 equal pieces. What is the length of each piece of string? Give your answer in centimetres. (a) 35.5 × 3 km = 106.5 km The total distance of a 35.5-lap race is 106.5 km. (b) 46.5 km ÷ 3 km = 15.5 15.5 laps make up 46.5 km. (a) 16 × 810 g = 12 960 g 12 960 g = 12 960 ÷ 1000 = 12.96 kg Lucy bought 12.96 kg of nuggets. (b) 3 8 × 12.96 kg = 4.86 kg Jane bought 4.86 kg of nuggets. 12.96 kg + 4.8 kg = 17.82 kg Both of them bought 17.82 kg of nuggets. 4.2 m ? cm ? cm ? cm ? cm 1 30 4.2 m = 4.2 × 100 = 420 cm 420 cm ÷ 30 = 420 cm ÷ 3 ÷ 10 = 140 cm ÷ 10 = 14 cm Each piece strings is 14 cm. For Teachers Only
Mathematics Grade 5 70 Chapter 5 Percentage The atmosphere is a mixture of gases surrounding the Earth. The composition of the atmosphere is shown in the table below. Gases Volume As a fraction As a decimal As a percentage Nitrogen 78 100 0.78 78% Oxygen 21 100 0.21 21% Other gases 1 100 0.01 1% 78 out of 100 parts of the gases are nitrogen. 21 100 of the gases is oxygen. 1% of the gases is made up of other gases. We read "%" as per cent. It means "out of a hundred ". For Teachers Only
Chapter 5 Percentage 71 A Find the value of each of the following. 1. 3% of 500 = 2. 6% of 80 = 3. 10% of 9 = 4. 35% of 65 = 5. 85% of 880 = 6. 100% of 1000 = 7. 70% of 380 = 8. 20% of 450 = 9. 76% of 8000 = 10. 40% of 10 050 = 11. 63% of 5000 = 12. 99% of 35 000 = Exercises 35 100 × 65 = 0.35 × 65 = 22.75 1000 3 100 × 500 = 15 6 100 × 80 = 0.6 × 8 = 4.8 10 100 × 9 = 0.1 × 9 = 0.9 85 100 × 880 = 8.5 × 88 = 748 70 100 × 380 = 7 × 38 = 266 76 100 × 8000 = 76 × 80 = 6080 63 100 × 5000 = 63 × 50 = 3150 99 100 × 35 000 = 99 × 305 = 34 650 40 100 × 10 050 = 4 × 1005 = 4020 20 100 × 450 = 2 × 45 = 90 For Teachers Only
72 Mathematics Grade 5 B Fill in each blank with the correct answer. 1. There are 50 apples in a crate. 30 of them are green apples and the rest are red apples. (a) % of the apples are green. (b) % of the apples are red. 2. There are 150 children in the Speech and Drama Club. 96 of them are girls and the rest are boys. (a) % of the members are girls. (b) % of the members are boys. C Express each fraction as a percentage. 1. 1 2 = 1 2 × 100% 2. 3 4 = × % = % = % 3. 3 25 = × % 4. 9 20 = × % = % = % 5. 17 50 = × % 6. 7 10 = × % = % = % 60 40 64 36 50 3 9 3 17 7 100 100 100 100 100 25 20 4 50 10 12 45 75 34 70 For Teachers Only
73 Chapter 5 Percentage D Express each fraction as a percentage. 1. 58 200 = × % 2. 267 300 = × % = % = % 3. 280 400 = × % 4. 75 500 = × % = % = % E Express each fraction as a percentage. Round off your answer to the nearest whole number. 1. 75 140 = 75 140 × 100% 2. 36 245 = × % = % = % % % 3. 250 405 = × % 4. 490 578 = × % = % = % % % 29 7 3 89 100 100 100 100 100 10 20 100 29 70 53.57 250 490 36 250 100 100 61.73 84.78 14.69 54 405 578 245 62 85 15 15 89 For Teachers Only
74 Mathematics Grade 5 F Find the value of each of following. 1. 30% of 900 = 2. 8% of 50 = 3. 50% of Rp 125.000,00 = Rp 4. 25% of 1600 g = g 5. 60% of 25 kg = kg 6. 95% of 4000 km = km 7. 32% of 250 minutes = minutes 8. 12% of 8 l = ml G Answer the following questions. 1. A restaurant served 120 burgers last night. If 70% of them were chicken burgers, how many chicken burgers did the restaurant serve? 2. During lunchtime, a cafe served 275 drinks in all. If 40% of them were milk tea, how many cups of milk tea did the cafe serve? 270 4 62.500,00 400 15 3800 80 960 70 100 × 120 = 7 × 12 = 84 40 100 × 275 = 0.4 × 275 = 110 The restaurant served 84 chicken burgers. The cafe served 110 cups of milk tea . For Teachers Only
75 Chapter 5 Percentage 3. A can of mixed fruits weighs 480 grams. It contains 384 grams of lychee. What percentage of the can of mixed fruits is lychee? 4. A college has 1750 students. 980 students are female. What is the percentage of the students are male? 5. In a test, Adi answered 36 out of 40 questions correctly. What percentage of questions did he answer wrongly? 6. Joanne's daily allowance is Rp 35.000,00. She spends some of the money and keeps 15% of it as savings. How much money does she save? 7. Alicia baked some vanilla muffins and some chocolate muffins. 9 20 of the muffins are vanilla muffins. What percentage of the muffins are chocolate muffins? 384 480 × 100% = 80% 80% of the can of mixed fruits is lychee. 48 60 4 5 980 1750 × 100% = 56% 100% – 56% = 44% 1750 – 980 = 800 800 students are male. 800 1750 × 100% = 44% or 44% of the students are male. 14 25 160 350 36 40 × 100% = 90% 100% – 90% = 10% 40 – 36 = 4 4 40 × 100% = 10% or He answered 10% of the questions wrongly. 9 1 15 100 × Rp 35.000,00 = Rp 5.250,00 She saves Rp 5.250,00. 9 20 × 100% = 45% 100% – 45% = 55% 20 – 9 = 11 11 20 × 100% = 55% or 55% of the muffins are chocolate muffins. 1 5 1 5 For Teachers Only
76 Mathematics Grade 5 H Solve the following word problems. 1. 35% of the audiences who went to a cultural show were children. The rest of the audiences were adult. There were 420 children altogether. How many audiences were there at the cultural show? 2. A milk supplier donated 140 l of milk for under previleged children. Home A received 35% of it and Home B received 25%. How much of the milk was not donated? Give your answer in litres. 3. Last year, Sam deposited Rp 300.000,00 in his bank account. The annual interest rate is 3.5% per year. How much money will he have in the account after 1 year? 100 – 35% – 25% = 40% 40% of the milk was not donated. 40% 40 100 × 140 = 56 l 56 l of the milk was not donated. 100 – 35% = 65% 65% of the audiences were adult. 35% 420 children 1% = 1 35 × 420 = 12 65% of adult 65 × 12 = 780 adult 420 + 780 = 1200 There were 1200 audiences at the cultural show. 5 60 12 5 2 28 1 Interest = 3.5% of Rp 300.000,00 = 3.5 100 × Rp 300.000,00 = Rp 10.500,00 He will get Rp 10.500,00 interest. Amount of money in the account after 1 year Rp 300.000,000 + Rp 10.500,00 = Rp 310.500,00 He will have Rp 310.500,00 in the account after 1 year. 420 Children 35% ? ?% Home A 35% 25% ? Home B 140 l I I : Interest 100% 3.5% Rp 300.000,00 For Teachers Only
77 Chapter 5 Percentage 4. The usual price for a T-shirt is Rp 120.000,00. At a sale, James bought the T-shirt at a 15% discount. (a) How much was the discount given to James? (b) How much did he pay for the T-shirt? 5. Jimmy, Amy and Billy shared a jug of chocolate milk. Jimmy drank 20% of it while Amy drank 55% of the chocolate milk. (a) What percentage of the chocolate milk did Billy drink? (b) If Jimmy drank 400 ml of the chocolate milk, what was the total volume of chocolate milk shared by Jimmy, Amy and Billy? Rp 120.000,00 – Rp 18.000,00 = Rp 102.000,00 He paid Rp 102.000,00 for the T-shirt. 100% – 20% – 55% = 65% Billy drank 65% of the chocolate milk. 20% 400 ml 1% 400 ml ÷ 20 = 20 ml 100% 100 × 20 ml = 2000 ml The total volume of chocolate milk shared by Jimmy, Ammy and Billy was 2000 ml. 15 100 × Rp 120.000,00 = Rp 18.000,00 The discount given to James was Rp 18.000,00. For Teachers Only
78 Mathematics Grade 5 6. Arif went to a restaurant with his brother for lunch. The food that they ordered costed Rp 250.000,00. In addition, they also paid 10% VAT. (a) How much was the VAT? (b) What was the total cost of the food? 7. The usual price of a backpack was Rp 140.000,00. At a sale, Amos bought the backpack at a 20% discount. (a) How much was the discount? (b) How much did Amos pay for the backpack? Rp 250.000,00 + Rp 25.000,00 = Rp 275.000,00 The total cost of the food was Rp 275.000,00. Rp 140.000,00 + Rp 28.000,00 = Rp 168.000,00 Amos paid Rp 168.000,00 for the backpack. 10 100 × Rp 250.000,00 = Rp 25.000,00 The VAT was Rp 25.000,00. 20 100 × Rp 140.000,00 = Rp 28.000,00 The discount was Rp 28.000,00. 1 51 28.000,00 For Teachers Only
79 Chapter 5 Percentage 7. What is 60% of 365 days? A 22 days C 305 days B 219 days D 425 days 8. What is the percentage of 60 out of 48? A 0.8% B 1.25% C 80% D 125% 9. What is 50 millilitres out of 2 litres expressed as a percentage? A 2.5% B 5% C 25% D 2500% 10. Which of the following gives the smallest value? A 8% of 700 B 15% of 550 C 25% of 210 D 40% of 125 11. Which of the following is true? A 50% of 100 = 10 B 3% of 27 = 550 C 25% of 12 cm = 3 cm D 80% of 20 = 4 Circle the correct answer. 1. The figure shows 10 equal squares. What percentage of the whole figure is shaded? A 4% C 24% B 20% D 40% 2. 14 out of 56 is A 25% C 40% B 28% D 75% 3. Express 48 ———600 as a percentage. A 2% C 8% B 4% D 48% 4. How much is 34% of 1500? A 5.1 C 510 B 51 D 5100 5. Express 28% as a fraction in its lowest terms? A 2 5 C 7 25 B 4 7 D 3 4 6. Express 45% of 9. A 0.405 C 4.05 B 0.45 D 4.5 Mastery Practice For Teachers Only
80 Mathematics Grade 5 12. On a certain day, there were a total of 60 flights that took off from an airport. If 15% of them were not on time, what is the number of flights that were not on time? A 9 C 25 B 15 D 45 13. 48% of the pupils in a school wear glasses. The number of pupils who wear glasses is 420. How many pupils do not wear glasses? A 380 C 435 B 400 D 455 14. A clothing store is having a 40% off sale. How much would a shopper have to pay for a Rp 135.000, 00 shirt? A Rp 54.000,00 B Rp 81.000,00 C Rp 131.000,00 D Rp 189.000,00 15. A teacher asked four pupils to write a percentage of a number that gives the value of 25. The following are written by the four pupils. Jimmy – 40% of 150 Lee – 50% of 210 Agnes – 25% of 100 June – 70% of 220 Who is correct? A Jimmy C Agnes B Lee D June 16. A trader has 240 chickens. He sells 75% of his chickens. How many chickens are left? A 60 C 180 B 120 D 190 For Teachers Only
Chapter 6 Ratio 81 Ratio Diameter of the Earth = 12 742 km Diameter of the Moon = 3474 km 13 000 3000 km Diameter of the Earth : Diameter of the Moon 13 000 : 3000 13 : 3 4.33 : 1 4 : 1 (Simplest form) ÷ 1000 ÷ 3 ÷ 1000 ÷ 3 The size of the earth is about four times of the size of the moon. The ratio of the size of the earth to the size of the moon is 4 : 1. The ratio of the size of the moon to the size of the earth is 1 : 4. Ratio can be used to show comparison between two or more quantities in the same unit. Ratio can be expressed in the form a : b, p : q : r and more. Chapter 6 For Teachers Only
Mathematics Grade 5 82 A Fill in each blank with its simplest ratio. 1. (a) The ratio of the number of photographs to the number of cameras is : . (b) The ratio of the number of cameras to the number of photographs is : . 2. (a) The ratio of the number of yo-yos to the number of skateboards is : . (b) The ratio of the number of skateboards to the number of yo-yos is : . 3. (a) The ratio of the number of tickets to the number of coins is : . (b) The ratio of the number of coins to the number of tickets is : . Exercises 8 5 3 3 1 4 5 8 1 4 3 3 For Teachers Only
83 Chapter 6 Ratio 4. (a) The ratio of the length of pencil to the length of straw is : . (b) The ratio of the length of straw to the length of screwdriver is : . (c) The ratio of the length of pencil to the length of straw to the length of screwdriver is : : . 5. (a) The ratio of the mass of carrots to the mass of pumpkins is : . (b) The ratio of the mass of pumpkins to the mass of watermelons is : . (c) The ratio of the mass of carrots to the mass of pumpkins to the mass of watermelon is : : . 0 1 2 3 4 5 6 7 8 9 10 cm 11 12 13 14 15 Screwdriver Pencil Straw 0 10kg 1kg 2kg 3kg 4kg 5kg 6kg 7kg 8kg 9kg 0 10kg 1kg 2kg 3kg 4kg 5kg 6kg 7kg 8kg 9kg 0 10kg 1kg 2kg 3kg 4kg 5kg 6kg 7kg 8kg 9kg 2 6 4 3 7 6 7 1 2 2 3 1 2 3 For Teachers Only
84 Mathematics Grade 5 6. (a) The ratio of the volume of water to the volume of oil is : . (b) The ratio of the volume of oil to the volume of milk is : . (c) The ratio of the volume of water to the volume of oil to the volume of milk is : : . B Write each ratio in its simplest form. 1. 12 : 36 = : 2. 20 : 15 = : 3. 63 : 90 = : 4. 65 : 25 = : 5. 49 : 14 = : 6. 40 : 16 = : 7. 10 : 45 : 60 = : : 8. 300 : 600 : 150 = : : 9. 115 : 30 : 65 = : : C Complete the equivalent ratios. 1. 3 : 7 = 15 : 2. 8 : 3 = : 36 3. 4 : = 24 : 30 4. : 3 = 56 : 24 5. 5 : 3 : 1 = 25 : : 5 6. 8 : 2 : 5 = : 8 : 20 7. : 7 : = 12 : 21 : 30 8. : : 9 = 48 : 24 : 108 10 l Water Oil Milk 5 l 10 l 5 l 10 l 6 l 2 l 3 l 5 l 3 2 1 3 6 1 4 7 13 7 5 2 2 23 35 96 7 32 5 15 4 10 4 2 3 3 10 5 2 2 9 4 6 12 1 13 2 3 For Teachers Only
85 Chapter 6 Ratio D Write your answer on the lines provided. 1. What is the ratio of the distance from Tom’s house to the school to the distance from Tom’s house to the park? School Tom’s house Park 5 km 15 km 2. There are 44 tourists on a tour bus. The number of children on the bus is 12. (a) What is the ratio of the number of children to the total number of tourists on the tour bus? (b) What is the ratio of the number of adults to the number of children on the tour bus? 3. There are 51 boys in Class 5A. The ratio of the number of girls to the number of boys is 1 : 3. What is the ratio of the number of boys to the total number of pupils in Class 5A? Children : Tourist 12 : 44 ÷ 4 ÷ 4 = 3 : 11 1 : 3 3 : 11 8 : 3 3 : 4 Distance from Tom’s house to school : Distance from Tom’s house to the park Number of adults = 44 – 12 = 32 Number of girls = 1 3 × 51 = 17 Total number of pupils = 51 + 17 = 68 1 17 Boys : Pupils 51 : 12 ÷ 17 = 3 : 4 Adult : Children 32 : 12 ÷ 4 ÷ 4 = 8 : 3 ÷ 17 5 : 15 ÷ 5 ÷ 5 = 1 : 3 For Teachers Only
86 Mathematics Grade 5 4. A mini market has 121 cartons of milk in stock. There are 77 big cartons of milk and the rest are in small cartons. What is the ratio of the number of big cartons of milk to the number of small carton of milk? 5. Ben is 12 years old and his father is 36 years older. What is the ratio of Ben’s age to his father’s age? 6. The ratio of the length to the breadth of a rectangle is 5 : 3. If the length is 15 m, what is the ratio of the length to the perimeter of the rectangle? 7. Johari has 100 coins. Josef has 25 fewer coins than Johari. What is the ratio of the number of coins that Johari has to the total number of coins they both have? Number of small cartons of milk = 121 – 77 = 44 Ben's father's age = 12 + 36 = 48 years old Perimeter = 2 × (15 + 9) = 48 cm Josef's coin = 100 – 25 = 75 Total number of coins = 100 + 75 = 175 Numbers of big cartons : Numbers of small cartons 77 : 44 ÷ 11 ÷ 11 = 7 : 4 Ben : Father 5 : 48 ÷ 12 ÷ 12 = 1 : 4 Length : Breadth 5 : 48 × 3 × 3 = 15 : 9 Length : Perimeter 15 : 48 ÷ 3 ÷ 3 = 5 : 16 7 : 4 1 : 4 5 : 16 4 : 7 100 : 175 ÷ 25 ÷ 25 = 4 : 7 For Teachers Only
87 Chapter 6 Ratio 8. The table shows the number of medals won by a school at a sports meet. Types of Medals Quantity Gold 36 Silver 48 Bronze 24 (a) What is the ratio of the number of gold medals to the total number of medals? (b) What is the ratio of the number of silver medals to the number of bronze medals? E Solve the following word problems. 1. In a bakery, the number of raisin buns sold to the number of red bean buns sold was 5 : 6. If 60 raisin buns were sold, how many red bean buns were sold? Total number of medals = 36 + 48 + 24 = 108 Gold : Totals of medals 36 : 108 ÷ 36 ÷ 36 = 1 : 3 Silver medals : Bronze medals 48 : 24 ÷ 24 ÷ 24 = 2 : 1 1 : 3 2 : 1 5 units 60 buns 1 unit 60 ÷ 5 = 12 6 units 6 × 12 = 72 72 red bean buns were sold Raisin Red bean 60 For Teachers Only
88 Mathematics Grade 5 2. The ratio of the number of oranges to the number of apples in a shop is 7 : 2. If there are 85 more oranges than apples, how many fruits are there in the shop? 3. The ratio of the number of boys to the number of girls in a choir team is 5 : 3. If there are 25 boys, how many pupils are there in the choir team? 4. Desmond, Sean and Alan share some candies in the ratio 3 : 7 : 5. Alan gets 55 candies. (a) How many candies does Sean get than Desmond? (b) What is the total number of candies shared by Desmond, Sean and Alan? Total number of fruits = 7 units + 2 units = 9 units 9 × 17 = 153 There are 153 fruits in the shop. Total number of pupils = 5 units + 3 units = 8 units 8 × 5 = 40 There are 40 pupils in the choir team. Oranges Apples 85 ? Boys Girls ? 25 ? 7 units 2 units = 85 5 units 85 1 unit 85 ÷ 5 = 17 5 units 25 1 unit 25 ÷ 5 = 5 (a) Desmond Sean Alan ? 55 ? 5 units 55 1 unit 55 ÷ 5 = 11 7 units – 3 units = 4 units 4 × 11 = 44 Sean gets 44 more candies than Desmond. (b) Total number of candies = 3 units + 7 units + 5 units = 15 units = 15 × 11 = 165 The total number of candies shared by Desmond, Sean and Alan is 165. For Teachers Only
89 Chapter 6 Ratio 5. The ratio of the price of an adult bus ticket to the price of a child train ticket is 7 : 4. Thomas pays Rp 84. 000, 00 for 3 adult bus tickets. What is the price of a child train ticket? 6. The ratio of the length of Square A to the length of Square B is 5 : 3. If the length of Square A is 25 cm, what is the area of Square B? 7. The ratio of the number of red balls to the number of blue balls in a pool is 6 : 1. If there are 98 balls in the pool, how many more red balls than blue balls are there in the pool? Total number of balls = 6 units + 1 unit = 7 units 7 units 98 balls 1 unit 98 ÷ 7 = 14 balls Difference between number of red balls and blue balls = 6 units – 1 unit = 5 units 5 × 14 = 70 There are 70 more red balls than blue balls in the pool. Length of Square A : Length of Square B 5 : 3 × 5 × 5 = 25 : 15 Adult ticket : Child ticket 7 : 4 × 4000 × 4000 = 28 000 : 16 000 Length of Square B = 15 cm Area of square B = 15 cm × 15 cm = 225 cm2 The area of Square B is 225 cm2 . The cost of a child train ticket is Rp 16.000,00. Price of an adult ticket = Rp 84.000,00 ÷ 3 = Rp 28.000,00 For Teachers Only
90 Mathematics Grade 5 8. Mary mixes flour and butter in the ratio 4 : 1. She uses 36 g more flour than butter. (a) How much flour does she use? (b) What is the total mass of the mixture? 9. The masses of James, Jim and Jack are in the ratio 11 : 8 : 7. Jack is 4 kg lighter than Jim. (a) What is James’ mass? (b) What is the total mass of James, Jim and Jack? 10. A rope was cut into three pieces in the ratio 2 : 7 : 8. The length of the longest piece is 48 cm. Find the total length of the three pieces of rope. (a) Flour Butter 36 g ? 4 units – 1 unit = 3 units 3 units 36 g 1 unit 36 g ÷ 3 = 12 g 4 × 12 g = 48 g Mary uses 48 g of flour. (a) James Jim Jack ? 4 kg ? Difference of mass between Jack and Jim = 8 units – 7 units = 1 unit 1 unit 4 kg 11 units 11 × 4 = 44 kg. James’s mass is 44 kg. (b) 4 units + 1 unit = 5 units 5 × 12 g = 60 g The total mass of the mixture is 60 g. (b)11 units + 8 units + 7 units = 26 units 26 × 4 kg = 104 kg The total mass of James, Jim and Jack is 104 kg. 8 units 48 cm 1 unit 48 cm ÷ 8 = 6 cm 2 units + 7 units + 8 units = 17 units 17 × 6 = 102 cm The total length of the three pieces of rope is 102 cm. Rope A Rope B Rope C 48 cm For Teachers Only
91 Chapter 6 Ratio A 72 C 48 B 120 D 24 6. Joe has 12 red pens, 8 blue pens and 20 black pens. Find the ratio of the number of red pens to the total number of pens. A 1 : 2 C 3 : 7 B 1 : 5 D 3 : 10 7. The ratio of the number of boys to the number of girls is 12 : 7. There are 147 girls. How many more boys than girls are there? A 21 C 105 B 84 D 399 8. Farah's mass is 36 kg. Tommy's mass is 54 kg. What is the ratio of Farah's mass to their total mass? A 2 : 3 C 3 : 5 B 2 : 5 D 5 : 2 9. Express 250 cm as a ratio of 10 m. A 1 : 4 C 2 : 5 B 1 : 25 D 4 : 1 10. Express the ratio of 25 min to 1 h 20 min in its simplest form. A 1 : 4 C 4 : 7 B 2 : 3 D 5 : 16 Circle the correct answer. 1. 5 : 7 = : 21 A 3 C 12 B 10 D 15 2. PAPAYA What is the ratio of the number of letter P to the number of letter A to the number of letter Y? A 1 : 2 : 3 B 3 : 2 : 1 C 2 : 3 : 1 D 3 : 1 : 2 3. Which of the following is an equivalent ratio of 5 : 3 : 8? A 10 : 6 : 24 B 15 : 6 : 16 C 15 : 6 : 24 D 20 : 12 : 32 4. Aquariums A, B and C contain some goldfish in the ratio 3 : 2 : 1. There are 45 goldfish in Aquarium A. What is the total number of goldfish in the three aquariums? A 135 C 270 B 75 D 90 5. Citra, Helen and Siti shared 240 hair clips among themselves in the ratio 2 : 3 : 5. How many more hair clips did Siti receive than Helen? Mastery Practice For Teachers Only
92 Mathematics Grade 5 11. Diana is 12 years old. Benny is twice her age. What is the ratio of Diana's age to Benny's age in 8 years time? A 1 : 2 C 5 : 8 B 2 : 1 D 8 : 5 12. The length and the breadth of a rectangle are in the ratio 5 : 3. If the length of the rectangle is 15 cm, find the area of the rectangle. A 45 cm2 C 15 cm2 B 135 cm2 D 225 cm2 13. The ratio of the number of mangoes to the number of pineapples in a shop is 7 : 3. If there are 280 fruits altogether, how many more mangoes than pineapples are there? A 84 C 140 B 112 D 168 14. The actual length of the school field is 150 m. It is drawn on a floor plan to a scale of 1 : 500. What is the length of the school field on the floor plan? A 30 m C 3 m B 30 cm D 3 cm 15. Budi's house is 650 m away from the school. It is represented by a length of 13 cm on a map. What is the scale of the map? A 1 : 5 C 1 : 500 B 1 : 50 D 1 : 5000 For Teachers Only
Chapter 7 Speed 93 Chapter 7 Speed Distance and speed A car travelled from State F to State G at the speed of 80 km/h. On the return journey, the car travelled at the speed of 60 km/h and took 3 hours. (a) What was the total distance travelled by the car for the whole journey? (b) What was the total time taken for the whole journey? (c) What was the average speed for the whole journey? Give your answer correct to 2 decimal places. (a) Distance = Speed × Time = 60 × 3 = 180 km The distance between State F and State G was 180 km. Total distance = 2 × 180 km = 360 km Total distance travelled by the car was 360 km. Distance = Speed × Time Average speed = Total distance travelled Total time taken D S T For Teachers Only
Mathematics Grade 5 94 (b) Distance between State F and State G = 180 km Time = Distance Speed = 180 80 = 9 4 = 2 1 4 h Total time taken = 2 1 4 h + 3 h = 5 1 4 h The total time taken for the whole journey was 5 1 4 h. (c) 5 h 15 min = 5 1 4 h = 5.25 h Average speed = Total distance travelled Total time taken = 360 5.25 68.57 km/h The average speed for the whole journey was 68.57 km/h. 9 4 For Teachers Only
Chapter 7 Speed 95 A Fill in each blank with the correct answer. 1. A bowling ball rolls 3 m per second. What is its speed? 2. A toy robot marches at a speed of 2 m/s. How far does it march in 5 seconds? 3. May Ling cycles 1200 m in 8 minutes. What is her cycling speed? 4. A horse gallops 4 km in half an hour. Find its speed. 5. Mr Evans drives at a speed of 108 km/h. How far does he travel in 45 minutes? Exercises 3 m/s 10 m 150 m/min 8 km/h 81 km 1 s = 3 m 1 s = 2 m 5 s = 5 × 2 m = 10 m 8 min = 1200 m 1 min = 1200 m 8 = 150 m 1 2 h = 4 km 1 h = 4 km ÷ 1 2 = 4 km × 2 1 = 8 km 1 h = 60 min 60 min = 108 km 1 min = 108 km 60 = 1.8 km 45 min = 45 × 1.8 km = 81 km 150 1 For Teachers Only
