Equivalent fractions for the given fractions are as follows:
(i) ³/₄: 6/8, 9/12, 12/16, 15/20
(ii) ⁴/₅: 8/10, 12/15, 16/20, 20/25
(iii) ⁶/₇: 12/14, 18/21, 24/28, 30/35
(iv) ⁴/₆: 2/3, 8/12, 10/15, 16/24
Equivalent fractions are fractions that represent the same part of a whole, even though the numerical values of the fractions may differ. To find equivalent fractions, you can multiply or divide both the numerator and denominator by the same nonzero number. Here are four equivalent fractions for each given fraction:
(i) 3/4:
Equivalent fractions:
6/8
9/12
12/16
15/20
(ii) 4/5:
Equivalent fractions:
8/10
12/15
16/20
20/25
(iii) 6/7:
Equivalent fractions:
12/14
18/21
24/28
30/35
(iv) 4/6:
Equivalent fractions:
2/3
8/12
10/15
16/24
In each case, the equivalent fractions maintain the same proportion of the whole, even though the numbers in the fractions have changed. For example, 6/8 is equivalent to 3/4 because both represent three-fourths of a whole, just expressed with different numerator and denominator values.