Page 83 - ICSE Math 6

3
8. If of a number is 27, then find the number.
5
2 x y
9. If = , then find .
15 y x

10. Find the reciprocal of the following.
4 2 1 1
(a) (b) (c) 3 (d) 5
9 17 2 7
Combination of Fundamental Operations

When two or more operations are used in an expression, then we simplify the expression by first
operating the fractions inside the bracket, then the operation ‘of’ followed by division, multiplication,
addition and subtraction.
Thus, for simplification we follow BODMAS. It stands for:

B O D M A S
↓ ↓ ↓ ↓ ↓ ↓
Bracket Of Division Multiplication Addition Subtraction
4 10 9  2 3 
Example 25: Simplify of ÷ +  +  .
5 11 11  3 4 

4 10 9  2 3  4 10 9  2×4 3×3+ 
Solution: of ÷ +  +  = of ÷ +  
5 11 11  3 4  5 11 11  12 
4 10 9 17 4 10 9 17
= of ÷ + = × ÷ +
5 11 11 12 5 11 11 12

8 9 7 8 11 17
= ÷ + = × +
11 11 12 11 9 12
8 17 8 × 4 + 17 × 3
= + =
9 12 36
32 51+ 83 11
= = = 2
36 36 36
1  5 3  1 5 1 3
Example 26: Prove that 5 × 2 +  2  = 5 ×2 + 5×2 .
4  6 4  4 6 4 4

1  5 3 
Solution: LHS = 5 ×2 + 2 

4  6 4 
+
5×4 1  + 2×6 5 2×4 3  +
= ×  + 
4  6 4 
21  17 11 21  17×2 11×3+ 
= ×  +  = ×  
4  6 4  4  12 

+
21  34 33  21  67  7 21 ×67 469 5
= ×   = ×   = = = 29
4  12  4  12  4× 12 4 16 16

67