Page 70 - classs 6 a_Neat

EQUIVALENT FRACTIONS
(ii) 5 = 5 × 2 = 5 × 3 = 5 × 4 = 5 × 5
7 7 × 2 7 × 3 7 × 4 7 × 5
Look at the figures given below.
5 = 10 = 15 = 20 = 25

1 7 14 21 21 35
2 Hence, the four fractions equivalent to 5 are 10 , 15 , 20 and 25
2 7 14 21 21 35
4 5 8 × 2 8 × 3 8 × 4 8 × 5
3 (iii) 11 = 11 × 2 = 11 × 3 = 11 × 4 = 11 × 5
6 5 16 24 32 40
4 11 = 22 = 33 = 44 = 55

8 8 16 24 32 40
Clearly, the shaded portions of these figures are equal. Hence, the four fractions equivalent to are , , and
1 2 3 4 11 22 33 44 55
= = = =
2 4 6 8 3
EXAMPLE 2: Write afraction equivalent to with numerator 15.
These fractions are called equivalent fractions. 3 15 4
SOLUTION: Let =
1 1 × 2 1 × 3 1 × 4 4
Note that = = =
2 2 × 2 2 × 3 2 × 4 Clearly, 15 = (3 × 5).

So, we multiply the denominator also by 5.
It shows that multiplying the numerator and the denominator of a fraction by the same nonzero number does not 3 3 × 5 15
change the value of the fraction. = =
Similarly, dividing the numerator and the denominator of a fraction by the same nonzero number does not 4 4 × 5 20
change the value of the fraction. 15
All such fractions are known as equivalent fractions. Hence, the required fraction is 20 •
5
EQUIVALENT FRACTIONS Two or more fractions representing the same part of a whole are called EXAMPLE 3: Write ajraction equivalent to with denominator 56.
8
equivalentfractions. 5
SOLUTION: Let =
8 56
RULE:To get afraction equivalent to a givenfraction, we multiply or divide the numerator and the denominator Clearly, 56 = (8 × 7).
of the given fraction by the same nonzero number.
So, we multiply the numerator also by 7.

SOLVED EXAMPLES 5 = 5 × 7 = 35
8 8 × 7 56
EXAMPLE 1. Write four fractions equivalent to each of the following. 35

3 5 8 Hence, the required fraction is •
(a) (b) (c) 56
4 7 11 36

SOLUTION: 3 = 3 × 2 = 3 × 3 = 3 × 4 = 3 × 5 EXAMPLE 4: Write fraction equivalent to 63 with numerator 4.
4 4 × 2 4 × 3 4 × 4 4 × 5 36 4

3 = 6 = 9 = 12 = 15 SOLTUION: Let 63 =
4 8 12 16 20 Clearly, 4 = 36 ÷ 9.

Hence, the four fractions equivalent to are 3 , 6 , 9 , 12 and 15 So, we divide the denominator also by 9.
4 8 12 16 20