CHAPTER 1 BASIC ARITHMETIC EXERCISE 1, Page 4 1. Evaluate 67 kg – 82 kg + 34 kg without using a calculator 67 kg – 82 kg + 34 kg = 67 kg + 34 kg – 82 kg = 101 kg – 82 kg = 19 kg 2. Evaluate 851 mm – 372 mm without using a calculator 851 - 372 479 Hence, 851 mm – 372 mm = 479 mm 3. Evaluate 124 - 273 + 481 – 398 without using a calculator 124 273 + 481 398 605 671 Hence, 124 - 273 + 481 – 398 = 605 – 671 = - (671 – 605) = - 66 4. Evaluate £927 - £114 + £182 - £183 - £247 without using a calculator 927 114 1109 182 183 544 1109 247 565 544 Hence, £927 - £114 + £182 - £183 - £247 = £1109 - £544 = £565 5. Evaluate 647 – 872 without using a calculator 647 – 872 = - (872 – 647) 872 647 225 Hence, 647 – 872 = - 225 1 © John Bird Published by Taylor and Francis 6. Evaluate 2417 - 487 + 2424 - 1778 – 4712 without using a calculator 2417 - 487 + 2424 - 1778 – 4712 = 2417 + 2424 - 487 - 1778 – 4712 2417 487 6977 2424 1778 - 4841 4841 4712 2136 6977 Hence, 2417 + 2424 - 487 - 1778 – 4712 = 4841 – 6977 = - (6977 – 4841) = - 2136 7. Evaluate £2715 - £18250 + £11471 - £1509 + £113274 without using a calculator £2715 - £18250 + £11471 - £1509 + £113274 = £2715 + £11471 + £113274 - £18250 - £1509 2715 18250 11471 + 1509 + 113274 19759 127460 Hence, £2715 + £11471 + £113274 - £18250 - £1509 = £127460 – £19759 = £107,701 8. Evaluate 47 + (- 74) – (- 23) without using a calculator 47 + (- 74) – (- 23) = 47 – 74 + 23 = 47 + 23 – 74 = 70 – 74 = - 4 9. Evaluate 813 - (- 674) without using a calculator 813 - (- 674) = 813 + 674 813 + 674 1487 Hence, 813 + 674 = 1487 10. Evaluate - 23148 – 47724 without using a calculator 2 © John Bird Published by Taylor and Francis - 23148 – 47724 = - (23148 + 47724) 23148 + 47724 70872 Hence, - 23148 – 47724 = - 70872 11. Evaluate $53774 - $38441 without using a calculator 53774 - 38441 15333 Hence, $53774 - $38441 = $15,333 3 © John Bird Published by Taylor and Francis EXERCISE 2, Page 6 1. Evaluate without using a calculator: (a) 78  6 (b) 124  7 (a) 78 × 6 468 4 Hence, 78  6 = 468 (b) 124 × 7 868 1 2 Hence, 124  7 = 868 2. Evaluate without using a calculator: (a) £261  7 (b) £462  9 (a) 261 × 7 1827 4 Hence, £261  7 = £1827 (b) 462 × 9 4158 5 1 Hence, £462  9 = £4158 3. Evaluate without using a calculator: (a) 783 kg  11 (b) 73 kg  8 (a) 783 × 11 783 7830 8613 1 1 Hence, 783 kg  11 = 8613 kg 4 © John Bird Published by Taylor and Francis (b) 73 × 8 584 2 Hence, 73 kg  8 = 584 kg 4. Evaluate without using a calculator: (a) 27 mm  13 (b) 77 mm  12 (a) 27 × 13 81 270 351 1 Hence, 27 mm  13 = 351 mm (b) 77 × 12 154 770 924 1 Hence, 77 mm  12 = 924 mm 5. Evaluate without using a calculator: (a) 288 m  6 (b) 979 m  11 (a) 48 6 288 Hence, 288 m  6 = 48 mm (b) 89 11 979 Hence, 979 m  11 = 89 mm 1813 896 6. Evaluate without using a calculator: (a) (b) 7 16 5 © John Bird Published by Taylor and Francis 259 (a) 7 1813 1813 Hence, = 1813  7 = 259 7 56 (b) 16 896 896 Hence, = 896  16 = 56 16 88737 7. Evaluate without using a calculator: (a) (b) 46858  14 11 (a) 8067 11 88737 88 73 66 77 77 . . 88737 Hence, = 88737  11 = 8067 11 (b) 3347 14 46858 42 48 42 65 56 98 98 . . Hence, 46858  14 = 3347 8. A screw has a mass of 15 grams. Calculate, in kilograms, the mass of 1200 such screws. (1 kg = 1000 g) Mass of 1200 screws = 1200 × 15 = 18000 g = 18000  1000 = 18 kg 6 © John Bird Published by Taylor and Francis 9. Holes are drilled 36 mm apart in a metal plate. If a row of 26 holes is drilled, determine the distance, in centimetres, between the centres of the first and last holes. The number of spaces if 26 holes are drilled = 25 Hence, distance between the centres of the first and last holes = 36 × 25 = 900 mm Thus, distance in centimetres = 900 ÷ 10 = 90 cm 10. A builder needs to clear a site of bricks and top soil. The total weight to be removed is 696 tonnes. Trucks can carry a maximum load of 24 tonnes. Determine the number of truck loads needed to clear the site. Number of truck loads = 696 ÷ 24 29 24 696 Hence, number of truck loads needed = 29 7 © John Bird Published by Taylor and Francis EXERCISE 3, Page 7 1. Find (a) the HCF and (b) the LCM of the following numbers: 8, 12 (a) 8 = 2 × 2 × 2 12 = 2 × 2 × 3 Hence, HCF = 2 × 2 = 4 i.e. 4 is the highest number that will divide into both 8 and 12 (b) LCM = 2 × 2 × 2 × 3 = 24 i.e. 24 is the lowest number that both 8 and 12 will divide into. 2. Find (a) the HCF and (b) the LCM of the following numbers: 60, 72 (a) 60 = 2 × 2 × 3 × 5 72 = 2 × 2 × 2 × 3 × 3 Hence, HCF = 2 × 2 × 3 = 12 i.e. 12 is the highest number that will divide into both 60 and 72 (b) LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360 i.e. 360 is the lowest number that both 60 and 72 will divide into. 3. Find (a) the HCF and (b) the LCM of the following numbers: 50, 70 (a) 50 = 2 × 5 × 5 70 = 2 × 5 × 7 Hence, HCF = 2 × 5 = 10 i.e. 10 is the highest number that will divide into both 50 and 70 (b) LCM = 2 × 5 × 5 × 7 = 350 i.e. 350 is the lowest number that both 50 and 79 will divide into 4. Find (a) the HCF and (b) the LCM of the following numbers: 270, 900 (a) 270 = 2 × 3 × 3× 3 × 5 900 = 2 × 2 × 3 × 3 × 5 × 5 Hence, HCF = 2 × 3 × 3 × 5 = 90 i.e. 90 is the highest number that will divide into both 270 and 900 8 © John Bird Published by Taylor and Francis (b) LCM = 2 × 2 × 3 × 3 × 3 × 5 × 5 = 2700 i.e. 2700 is the lowest number that both 270 and 900 will divide into 5. Find (a) the HCF and (b) the LCM of the following numbers: 6, 10, 14 (a) 6 = 2 × 3 10 = 2 × 5 14 = 2 × 7 Hence, HCF = 2 i.e. is the highest number that will divide into 6, 10 and 14 (b) LCM = 2 × 3 × 5 × 7 = 210 i.e. 210 is the lowest number that 6, 10 and 14 will divide into 6. Find (a) the HCF and (b) the LCM of the following numbers: 12, 30, 45 (a) 12 = 2 × 2 × 3 30 = 2 × 3 × 5 45 = 3 × 3 × 5 Hence, HCF = 3 i.e. is the highest number that will divide into 12, 30 and 45 (b) LCM = 2 × 2 × 3 × 3 × 5 = 180 i.e. 180 is the lowest number that 12, 30 and 45 will divide into 7. Find (a) the HCF and (b) the LCM of the following numbers: 10, 15, 70, 105 (a) 10 = 2 × 5 15 = 3 × 5 70 = 2 × 5 × 7 105 = 3 × 5 × 7 Hence, HCF = 5 i.e. is the highest number that will divide into 10, 15, 70 and 105 (b) LCM = 2 × 3 × 5 × 7 = 210 i.e. 210 is the lowest number that 10, 15, 70 and 105 will divide into 9 © John Bird Published by Taylor and Francis 8. Find (a) the HCF and (b) the LCM of the following numbers: 90, 105, 300 (a) 90 = 2 × 3 × 3 × 5 105 = 3 × 5 × 7 300 = 2 × 2 × 3 × 5 × 5 Hence, HCF = 3 × 5 = 15 i.e. 15 is the highest number that will divide into 90, 105 and 300 (b) LCM = 2 × 2 × 3 × 3 × 5 × 5 × 7 = 6300 i.e. 6300 is the lowest number that 90, 105 and 300 will divide into 10 © John Bird Published by Taylor and Francis