chapter 1 basic arithmetic

446 Pages·2015·6.32 MB·English

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

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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

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- 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

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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

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(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

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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
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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

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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
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(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
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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

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