Page 195 - Ganit Kaushal

For example: 1 × 2 = 2 , 1 × 3 = 3 , 1 × 5 = 5
4 × 2 8 4 × 3 12 4 × 5 20
2 3 5 1
∴ , , are equivalent fractions because the value of each fraction is .
8 12 20 4
2 3 4 5 1
And we can write that = = = = .
8 12 16 20 4
Method 2: Divide both the numerator and the denominator of the given fraction by some common factor.
÷
÷
6 6 ÷ 6 1 9 99 1 11 11 11 1
For example: = = , = = , = =
18 18 ÷ 6 3 27 27 ÷ 9 3 33 33 11 3
÷
6 9 11 1
∴ , , are equivalent fractions because the value of each of these fractions is .
18 27 33 3
1
And we can write that 6 = 9 = 11 = .
18 27 33 3
Property of Equivalent Fractions
If two fractions are equivalent, then the product of the numerator of the first fraction and the denominator of
the second fraction is equal to the product of the denominator of the first fraction and the numerator of the
second fraction. These products are called cross products.
5 10
For example: and are equivalent fractions. So, observe that: 5 × 16 = 8 × 10 = 80.
8 16
a c a c
In general, if and are two equivalent fractions, then gives ad = bc.
b d b d
Solved Examples
Ex 1. Write the fraction representing the shaded region.

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j)

Sol. (a) 2 [ 4 parts make a whole, and 2 are shaded. Similarly, we can interpret others.]
4

(b) 8 (c) 4 (d) 1 (e) 3 (f) 3
9 8 4 7 12

(g) 10 (h) 4 (i) 4 (j) 1
10 9 8 2

Fractions 193