Page 34 - ICSE Math 7

(b) 14 ÷ 7 = 14 × 25   Reciprocal of 7 is 25 
15 25 15 7   25 7  
2 14 × 25 5 10 1
= = = 3
3 15 × 7 3 3
1
2
(c) 2 ÷ 1 = 16 ÷ 15 = 16 × 14   Reciprocal of 15 is 14 
7 14 7 14 7 15   14 15  
2
16× 14 32 2
= = = 2
7 ×15 15 15
Operation ‘of’
Quantities connected by ‘of’ denote a single quantity whereas quantities connected by multiplication
denote different quantities. Therefore, the operation ‘of’ is performed before multiplication.
Example 13: Evaluate.
3 4 5
(a) of 150 (b) of 3
5 9 30 16

3
Solution: (a) 3 of 150 = × 150 = 3× 150 = 90
5 5 5
5
4
17
(b) 4 of 3 = × 53 = 4 ×53 = 53 = 1
9 16 9 16 9× 16 4 36 36
Fraction as an Operator
A fraction can be used to operate on a quantity. In other words, when a fraction of an amount is required,
the fraction acts as a mathematical operator on the amount. The original amount is multiplied by the
numerator and divided by the denominator of the fraction. For example,
10
3 3 3 × 50 2 8 13
(a) of 50 = × 50 = = 30 (b) 2 of 39 = × 39 = 104
5 5 5 3 3
Continued Fraction
1
A continued fraction is a complex fraction of the form .
3– 1 3
1+
7
A continued fraction can be written as an expression within brackets as 1÷   3– 1÷     1+ 3       .
   7  
As in simplification of expression, we start from the innermost bracket, similarly in continued fraction,
we start from the lowest step and then move upwards.
1
Example 14: Simplify 1+ 1 .
1+
3+ 1
2
1 1  1 7 
Solution: 1+ 1 = 1+   3 + = 
1+ 1 1+ 1  2 2 
7
3+
2 2

20