Page 18 - Start Up Mathematics_8 (Non CCE)

− 
 −13  11  5 7
Example 19: Simplify   + +   + .
 20  14  7  10
Solution: LCM of 20, 14, 7, 10 = 2 × 2 × 5 × 7 = 140 2 20, 14, 7, 10
 −13  11  5  7  2 10, 7, 7, 5
− 
  + +   +   5 5, 7, 7, 5
 20  14  7   10 
} {
} {
} {
{ –13 ×7 + 11 × 10 + (–5) × 20 + 7 × 14} 7 1, 7, 7, 1
= 1, 1, 1, 1
140
–91 + 110 – 100 + 98 17
= =
140 140
17
So, the required sum =
140

−3 1  −  7 5 p
Example 20: Express + +   ++4 in the form . 2 4, 2, 3, 1, 6
4 2  3  6 q
2 2, 1, 3, 1, 3
Solution: LCM of 4, 2, 3, 1, 6 = 2 × 2 × 3 = 12
3 1, 1, 3, 1, 3
−3 1  −  7 5 1, 1, 1, 1, 1
+ +   ++4
4 2  3  6
{ (−× } +{16 (−7 ) × } +{412 × }
× } +{
× } +{5 2
4
3
) 3
=
12
6
− ( ) ++ − ( 28 ) + 48 +10 −+ − + + 64 −37 27 9
9
96284810
= = = = =
12 12 12 12 4
EXERCISE 1.5
1. Simplify:
2  − 5  7 −5 5 7 −8 4  3 21 10
− 
(a) +   + (b) + − (c) − +   (d) −+4 −
3  9  6 12 −18 24 9 15  20  16 24
p
2. Simplify and express in the form .
q
4 3  − 2   − 11 −11 1 3 1 −2 5 7  −13 
(a) + +   +   (b) + − +0 − (c) − + −  
3 5  3   5  12 4 −8 2 3 6 24  −36 

3. Evaluate the following:
3  − 2  5  7  6  13 1 2  3   − 5 
− 
0
2
(a) +   − (b)   ++   − (c) − +   ++  
4  3  4  9   7 21 2 3  − 4   6 
− 
13 27 91
4. What should be added to the sum of and to get ?
15 20 60
7 4 9
5. What should be subtracted from the sum of and to get ?
8 15 40

10