Q1.
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. a. 7⁄2 and 3⁄5 b. 8⁄3 and 5⁄6 c. 3⁄4 and 3⁄5 d. 6⁄7 and 8⁄5 e. 9⁄4 and 5⁄2 f. 1⁄10 and 2⁄9 g. 8⁄3 and 11⁄4 h. 13⁄6 and 1⁄9
Answer
Take a common multiple of the two denominators (the smallest one is easiest) and rewrite both fractions with it.
| Pair | Common denominator | Equivalent fractions |
|---|---|---|
| a. 7/2, 3/5 | 10 | 35/10 and 6/10 |
| b. 8/3, 5/6 | 6 | 16/6 and 5/6 |
| c. 3/4, 3/5 | 20 | 15/20 and 12/20 |
| d. 6/7, 8/5 | 35 | 30/35 and 56/35 |
| e. 9/4, 5/2 | 4 | 9/4 and 10/4 |
| f. 1/10, 2/9 | 90 | 9/90 and 20/90 |
| g. 8/3, 11/4 | 12 | 32/12 and 33/12 |
| h. 13/6, 1/9 | 18 | 39/18 and 2/18 |
Sample working for (d):
6/7 = (6 × 5)/(7 × 5) = 30/35
8/5 = (8 × 7)/(5 × 7) = 56/35
8/5 = (8 × 7)/(5 × 7) = 56/35
Tip: when one denominator is already a multiple of the other — as in (b) 3 and 6, or (e) 2 and 4 — only one fraction needs to be changed.