Page 137 - Start Up Mathematics_6

6. Express the following as mixed fractions:
35 21 45 55
(a) (b) (c) (d)
8 6 7 9
7. Express the following as improper fractions:
4 1 2 4
(a) 6 (b) 3 (c) 5 (d) 7
5 2 3 5

Equivalent Fractions
Fractions having the same value are called equivalent fractions. On multiplying or dividing the
numerator and denominator of a given fraction by some non-zero number, we obtain equivalent
2 4 6 8
fractions. The fractions , , and represent equivalent fractions as they represent same parts
of a whole. 3 6 9 12

2 4 6 8
3 6 9 12
2 4 6
If we place each of the given squares on one another, then the shaded parts of , , and 8
will coincide, suggesting they represent the same part of the whole. 3 6 9 12
How to check for equivalent fractions?
Two fractions are equivalent, if the product of the numerator of the first and the denominator of
the second is equal to the product of the denominator of the first and the numerator of the second.
This process is called cross multiplication of two fractions. For example, consider the fractions
3 and 12 . On multiplying the numerator of the first fraction with the denominator of the second
5 20
fraction, we get 3 × 20 = 60. Also, on multiplying the denominator of the first fraction with the
numerator of the second fraction, we get 5 × 12 = 60. Since these products are equal, therefore,
3 and 12 are equivalent fractions.
5 20

Simplest Form of a Fraction
A fraction is said to be in its simplest or lowest form if its numerator and denominator have no
common factors except 1.

Example 14: Write the fractions for each of the shaded portions. Are all these equivalent
fractions?

1 2 4 5
Solution: , , and Yes, these are equivalent fractions.
3 6 12 15

129