Let’s solve each problem step by step. We’re looking for equivalent fractions — that means we multiply the numerator and denominator by the same number to get a new fraction that equals the original.
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1.
Start with:
$\frac{2}{7} = \frac{?}{49} = \frac{?}{70}$
To get from 7 to 49, multiply by 7 → so multiply numerator 2 × 7 =
14
To get from 7 to 70, multiply by 10 → so multiply numerator 2 × 10 =
20
✔ Answer: $\frac{2}{7} = \frac{14}{49} = \frac{20}{70}$
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2.
$\frac{3}{5} = \frac{?}{45} = \frac{?}{60}$
5 → 45: multiply by 9 → 3 × 9 =
27
5 → 60: multiply by 12 → 3 × 12 =
36
✔ Answer: $\frac{3}{5} = \frac{27}{45} = \frac{36}{60}$
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3.
$\frac{7}{9} = \frac{?}{27} = \frac{?}{54}$
9 → 27: ×3 → 7×3 =
21
9 → 54: ×6 → 7×6 =
42
✔ Answer: $\frac{7}{9} = \frac{21}{27} = \frac{42}{54}$
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4.
$\frac{9}{10} = \frac{?}{30} = \frac{?}{80}$
10 → 30: ×3 → 9×3 =
27
10 → 80: ×8 → 9×8 =
72
✔ Answer: $\frac{9}{10} = \frac{27}{30} = \frac{72}{80}$
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5.
$\frac{1}{11} = \frac{?}{44} = \frac{?}{66}$
11 → 44: ×4 → 1×4 =
4
11 → 66: ×6 → 1×6 =
6
✔ Answer: $\frac{1}{11} = \frac{4}{44} = \frac{6}{66}$
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6.
$\frac{8}{9} = \frac{?}{36} = \frac{?}{63}$
9 → 36: ×4 → 8×4 =
32
9 → 63: ×7 → 8×7 =
56
✔ Answer: $\frac{8}{9} = \frac{32}{36} = \frac{56}{63}$
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7.
$\frac{7}{8} = \frac{?}{48} = \frac{?}{72}$
8 → 48: ×6 → 7×6 =
42
8 → 72: ×9 → 7×9 =
63
✔ Answer: $\frac{7}{8} = \frac{42}{48} = \frac{63}{72}$
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8.
$\frac{5}{11} = \frac{?}{33} = \frac{?}{88}$
11 → 33: ×3 → 5×3 =
15
11 → 88: ×8 → 5×8 =
40
✔ Answer: $\frac{5}{11} = \frac{15}{33} = \frac{40}{88}$
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9.
$\frac{7}{12} = \frac{?}{24} = \frac{?}{36}$
12 → 24: ×2 → 7×2 =
14
12 → 36: ×3 → 7×3 =
21
✔ Answer: $\frac{7}{12} = \frac{14}{24} = \frac{21}{36}$
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10.
$\frac{11}{12} = \frac{?}{72} = \frac{?}{84}$
12 → 72: ×6 → 11×6 =
66
12 → 84: ×7 → 11×7 =
77
✔ Answer: $\frac{11}{12} = \frac{66}{72} = \frac{77}{84}$
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Final Answer:
1. 14, 20
2. 27, 36
3. 21, 42
4. 27, 72
5. 4, 6
6. 32, 56
7. 42, 63
8. 15, 40
9. 14, 21
10. 66, 77
Parent Tip: Review the logic above to help your child master the concept of free equivalent fraction worksheet.
