Let’s solve each problem one by one. We’re looking for equivalent fractions — that means the two fractions must represent the same value, even if they look different.
To find an equivalent fraction, we multiply or divide both the numerator and denominator by the same number.
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1) 5/10 = ? / 90
We see that 10 × 9 = 90 → so multiply numerator by 9 too:
5 × 9 =
45
→ Answer:
45
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2) 2/4 = ? / 20
4 × 5 = 20 → so 2 × 5 =
10
→ Answer:
10
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3) 3/7 = ? / 28
7 × 4 = 28 → so 3 × 4 =
12
→ Answer:
12
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4) ? / 15 = 8/3
This is backwards! Let’s think: 8/3 = ? / 15
We need to get from denominator 3 to 15 → 3 × 5 = 15
So multiply numerator 8 × 5 =
40
→ Answer:
40
*(Check: 40/15 simplifies to 8/3? Yes, divide both by 5 → 8/3)*
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5) 9/2 = ? / 40
2 × 20 = 40 → so 9 × 20 =
180
→ Answer:
180
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6) 6/? = 30/45
First, simplify 30/45 → divide top and bottom by 15 → 2/3
So 6/? = 2/3 → cross-multiply: 2 × ? = 6 × 3 → 2×?=18 → ?=9
Or: 6 ÷ 2 = 3, so denominator must be 3 × 3 = 9
→ Answer:
9
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7) ? / 27 = 7/9
9 × 3 = 27 → so 7 × 3 =
21
→ Answer:
21
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8) 39/12 = 13/?
Simplify 39/12 → divide top and bottom by 3 → 13/4
So 13/? = 13/4 → ? =
4
→ Answer:
4
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9) 10/3 = ? / 27
3 × 9 = 27 → so 10 × 9 =
90
→ Answer:
90
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10) 1/6 = ? / 54
6 × 9 = 54 → so 1 × 9 =
9
→ Answer:
9
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11) 4/4 = ? / 12
4/4 = 1 → so ? / 12 = 1 → ? =
12
Or: 4 × 3 = 12 → so 4 × 3 = 12
→ Answer:
12
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12) 1/2 = 5 / ?
1 × 5 = 5 → so 2 × 5 =
10
→ Answer:
10
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13) 4/12 = ? / 6
Simplify 4/12 → divide by 4 → 1/3
So ? / 6 = 1/3 → 6 ÷ 3 = 2 → ? =
2
Or: 12 ÷ 2 = 6 → so 4 ÷ 2 = 2
→ Answer:
2
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14) 1/4 = ? / 48
4 × 12 = 48 → so 1 × 12 =
12
→ Answer:
12
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15) 1/7 = ? / 28
7 × 4 = 28 → so 1 × 4 =
4
→ Answer:
4
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Final Answer:
1) 45
2) 10
3) 12
4) 40
5) 180
6) 9
7) 21
8) 4
9) 90
10) 9
11) 12
12) 10
13) 2
14) 12
15) 4
Parent Tip: Review the logic above to help your child master the concept of math worksheet equivalent fractions.
