Let’s solve each problem one by one. We’re looking for equivalent fractions — that means the two fractions represent the same value, even if they look different.
To find an equivalent fraction, we multiply or divide both the numerator (top) and denominator (bottom) by the same number.
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1.
We have:
□ / 4 = 2 / 8
Look at the right side: 2/8. Can we simplify it? Yes! Divide top and bottom by 2 → 1/4.
So □ / 4 = 1/4 → □ =
1
✔ Check: 1/4 = 2/8? Multiply 1×2=2, 4×2=8 → yes!
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2.
1 / □ = 3 / 9
Simplify 3/9 → divide top and bottom by 3 → 1/3
So 1 / □ = 1/3 → □ =
3
✔ Check: 1/3 = 3/9? Multiply 1×3=3, 3×3=9 → yes!
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3.
2 / 3 = □ / 9
How do we get from 3 to 9 in the denominator? Multiply by 3.
So multiply numerator by 3 too: 2 × 3 = 6
→ □ =
6
✔ Check: 2/3 = 6/9? 2×3=6, 3×3=9 → yes!
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4.
1 / 3 = □ / 15
From 3 to 15 → multiply by 5
So 1 × 5 = 5 → □ =
5
✔ Check: 1/3 = 5/15? 1×5=5, 3×5=15 → yes!
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5.
1 / □ = 10 / 20
Simplify 10/20 → divide by 10 → 1/2
So 1 / □ = 1/2 → □ =
2
✔ Check: 1/2 = 10/20? 1×10=10, 2×10=20 → yes!
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6.
2 / □ = 14 / 21
Simplify 14/21 → divide by 7 → 2/3
So 2 / □ = 2/3 → □ =
3
✔ Check: 2/3 = 14/21? 2×7=14, 3×7=21 → yes!
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7.
1 / □ = 11 / 66
Simplify 11/66 → divide by 11 → 1/6
So 1 / □ = 1/6 → □ =
6
✔ Check: 1/6 = 11/66? 1×11=11, 6×11=66 → yes!
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8.
3 / 4 = □ / 24
From 4 to 24 → multiply by 6
So 3 × 6 = 18 → □ =
18
✔ Check: 3/4 = 18/24? 3×6=18, 4×6=24 → yes!
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9.
1 / 5 = 2 / □
From 1 to 2 in numerator → multiply by 2
So denominator: 5 × 2 = 10 → □ =
10
✔ Check: 1/5 = 2/10? 1×2=2, 5×2=10 → yes!
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10.
1 / □ = 2 / 16
Simplify 2/16 → divide by 2 → 1/8
So 1 / □ = 1/8 → □ =
8
✔ Check: 1/8 = 2/16? 1×2=2, 8×2=16 → yes!
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Final Answer:
1. 1
2. 3
3. 6
4. 5
5. 2
6. 3
7. 6
8. 18
9. 10
10. 8
Parent Tip: Review the logic above to help your child master the concept of equivalent fractions worksheet 5th grade.
