Equivalent Fractions & Comparing — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. 49 = 12 27 .
Since 9 × 3 = 27, multiply the numerator by 3 too: 4 × 3 = 12, so 49 = 1227.
2. 1520 in simplest form is 34.
The GCF of 15 and 20 is 5. Divide both: 15 ÷ 5 = 3 and 20 ÷ 5 = 4, so 1520 = 34.
3. 67 = 18 21 .
The numerator went from 6 to 18 (×3), so multiply the denominator by 3 too: 7 × 3 = 21.
4. The GCF of 14 and 21 is 7.
The factors of 14 are 1, 2, 7, 14 and the factors of 21 are 1, 3, 7, 21. The largest shared factor is 7.
5. 310 = 9 30 .
Since 10 × 3 = 30, multiply the numerator by 3 as well: 3 × 3 = 9, so 310 = 930.
6. 1624 in simplest form is 23.
The GCF of 16 and 24 is 8. Divide both: 16 ÷ 8 = 2 and 24 ÷ 8 = 3, so 1624 = 23.
7. 58 = 25 40 .
The numerator went from 5 to 25 (×5), so multiply the denominator by 5 too: 8 × 5 = 40.
8. To simplify 2128, divide both by 7.
The GCF of 21 and 28 is 7. Dividing both by 7 gives 21 ÷ 7 = 3 and 28 ÷ 7 = 4, so 2128 = 34.
9. 89 = 32 36 .
Since 9 × 4 = 36, multiply the numerator by 4 as well: 8 × 4 = 32, so 89 = 3236.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
912
→ 34
59
1416
→ 78
25
615
→ 25
34
1018
→ 59
78
Correct matches: 912 → 34; 1416 → 78; 615 → 25; 1018 → 59.