Page 35 - ICSE Math 7

1  1 2 
= 1+ 2   7 = 7 
1+  
7  2 
1  2 9 
= 1+ 1+  =
9   7 7  
7  1 7 
7
7
= 1 + = 16 = 1   9 = 9 
9 9 9  
 7 
Simplification of complex fractions
Simplifying a complex fraction is similar to division of fractions. For example,
4 9 4 2 4 3 2 4 × 3 2
(a) = ÷ = × = =
2 3 9 3 9 2 3 9 × 2 3

1 3 8 5 8 106 8 25 4 8 × 25 5 20
(b) 5 = = ÷ = × = =
4 6 25 106 25 5 25 5 106 5 × 106 53 53

Simplification of an Expression

While simplifying an expression containing two or more operations, we follow the rule of BODMAS.
Thus, first of all terms inside the brackets are simplified followed by ‘of’, division, multiplication,
addition and subtraction.

Example 15: Simplify the following.
1
7
5
1 4
1
(a) 11 of 5 ÷ 1 (b)  2 × 5  + 8 –1 × (c) 8 of    3  +  5 ÷ 1 – 1     
9 12 14   5 12   9 8 9  5  16 6 2    
1
7
5
Solution: (a) 11 of 5 ÷ 1 = 106 × 65 ÷ 15
9 12 14 9 12 14
13
53 106 × 65 × 14 7
= = 4823 = 59 44
9× 12 6 3 × 15 3 81 81
1 4
9
8
(b)   2 × 5   + 8 –1 × =   2 × 5   + – × 4
 5 12  9 8 9  5 × 12 6  9 8 9
1 8 9 × 4 1 8 1
= + – = + –
6 9 2 8 × 9 6 9 2
= 1 × (18 ÷ 6) + 8 × (18 ÷ 9) – 1 × (18 ÷ 2)
18

= 1 × 3 + 8 × 2 – 1 × 9 = 3 + 16 – 9 = 10 = 5
18 18 18 9
  3  5 1 1      3  5 7 1   
(c) 8 of  +  ÷ 1 –   = 8 of  +  ÷ –  
 5  16 6 2      5  16 6 2    

= 8 of   3  +  5 ÷ 2       7 −  1 = 2  
5   16 3    6 2 3 

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