Page 77 - Start Up Mathematics_5

Example 21: Simplify 3 + 5 + 7 . 5 5 , 6 , 8
5 6 8 2 1 , 6 , 8

Solution: 3 + 5 + 7 2 1 , 3 , 4
5 6 8 2 1 , 3 , 2
LCM of 5, 6 and 8 = 5 × 2 × 2 × 2 × 3 = 120 3 1 , 3 , 1

3 = 3 × 24 = 72 1 , 1 , 1
5 5 × 24 120
5 = 5 × 20 = 100
6 6 × 20 120 Remember
7 = 7 × 15 = 105
8 8 × 15 120 We simplify fractions in the
same way as we simplify
3 + 5 + 7 = 72 + 100 + 105 any other numbers.
5 6 8 120 120 120
72 + 100 + 105
=
120
277 37
= = 2
120 120
Example 22: Simplify 12 – 8 + 7 .
17 17 17 A Challenge!

Solution: 12 – 8 + 7 = 12 + 7 – 8
17 17 17 17 17 17 Simplify. 7 3 5
2
12 + 7 8 9 – 3 + 4 – 2 – 1 18
5
9
5
= –
17 17
8
= 19 – 17 = 19 – 8 = 11
17
17
17
1
3
Example 23: Simplify 7 – 2 – 3 .
8 6
3
1
Solution: 7 – 2 – 3 = 7 – (2 × 8) + 3 – (3 × 6) + 1
8 6 8 6
= 7 – 16 + 3 – 18 + 1
8 6
= 7 – 19 – 19
8 6
= 7 – 19 – 19 = 56 – 19 – 19
1 8 6 8 8 6

= 56 – 19 – 19 = 37 – 19
8 6 8 6
LCM of 8 and 6 = 24 2 8 , 6
2 4 , 3
37 = 37 × 3 = 111 2 2 , 3
8 8 × 3 24 3 1 , 3

19 = 19 × 4 = 76 1 , 1
6 6 × 4 24

So, 37 – 19 = 111 – 76 = 111 – 76 = 35 = 1 11 .
8 6 24 24 24 24 24

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