Page 72 - Maths Skill - 6

70 Maths

A closer look will make it clear that shaded portions in each figure ((i), (ii), (iii), (iv) and (v)) represents the same
part of the circle, i.e.,
1 2 4 8 16
2 = = = 16 = 32
8
4
1 2 4 8 16
Thus , , , and are equivalent fractions as they represent the same part of a whole.
2 4 8 16 32
BUILDING EQUIVALENT FRACTIONS

For writing equivalent fractions for a given fraction, we multiply or divide the numerator and the denominator of
the given fraction by the same number.
1
Example: Write two equivalent fractions for .
3
1 1
Solution: Given fraction =
3 3

1 1 × 2 2 2
First equivalent fraction of = =
3 3 × 2 6 6
1 1 × 3 3 3
Second equivalent fraction of = =
3 3 × 3 9 9

VERIFYING WHETHER THE TWO GIVEN FRACTIONS ARE EQUIVALENT OR NOT
For verifying whether the two given fractions are equivalent, we multiply numerator of the first fraction with
denominator of the second and also multiply denominator of the first fraction with numerator of second fraction.
If product in both cases is the same, then the fractions are equivalent.

REDUCING A FRACTION INTO ITS LOWEST TERMS

For reducing a fraction into its simplest form (lowest terms), divide the numerator and denominator of the given
fraction by their H.C.F.

Let’s Attempt

1 12 16
Example 1: Verify whether and 24 are equivalent Example 2: Reduce 56 into its lowest terms.
2
or not. 16
1 12 Solution: Given fraction =
Solution: Given fractions are and . 56
2 24
We have, 1 × 24 = 24 and 2 × 12 = 24 H.C.F. of 16 and 56 = 8
Thus, 1 × 24 = 2 × 12 Dividing both numerator and
denominator by 8,
Hence, given fractions are equivalent. 16 ÷ 8 2
Challenge we get 56 ÷ 8 = 7

1 12 Half of half and Thus, 16 is expressed in its
56
2 24 one-third of three 2
quarters are equal. lowest terms as ·
Do you agree? 7