Q1.
Write the following mixed numbers as fractions: a. 31⁄4 b. 72⁄3 c. 94⁄9 d. 31⁄6 e. 23⁄11 f. 39⁄10
Answer
Use Jaya’s idea: change every whole into fractional units, then count all the units.
3 1/4 = (4 × 1/4) + (4 × 1/4) + (4 × 1/4) + (3 × 1/4)
= 4 + 4 + 4 + 3 quarters = 15/4
= 4 + 4 + 4 + 3 quarters = 15/4
The short rule is (whole × denominator) + numerator, kept over the same denominator.
| Mixed number | Working | Fraction |
|---|---|---|
| a. 3 1/4 | (3 × 4) + 1 = 13 | 13/4 |
| b. 7 2/3 | (7 × 3) + 2 = 23 | 23/3 |
| c. 9 4/9 | (9 × 9) + 4 = 85 | 85/9 |
| d. 3 1/6 | (3 × 6) + 1 = 19 | 19/6 |
| e. 2 3/11 | (2 × 11) + 3 = 25 | 25/11 |
| f. 3 9/10 | (3 × 10) + 9 = 39 | 39/10 |
Why multiply by the denominator: one whole roti contains exactly denominator-many fractional units — 4 quarters, 3 thirds, 10 tenths. So 3 wholes contain 3 × 10 = 30 tenths, and 9 more tenths make 39 tenths.