Equivalent Fractions Worksheet - Free Printable

Let’s solve each problem step by step.

We’re working with equivalent fractions — that means two fractions that look different but have the same value. To find an equivalent fraction, you multiply or divide both the numerator (top) and denominator (bottom) by the same number.

Also, remember:
→ If the top number (numerator) is bigger than the bottom number (denominator), it’s an improper fraction. We’ll spot those as we go.

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Problems 1 to 24: Fill in the blank to make equivalent fractions

We’ll do them one by one.

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1) $\frac{3}{3} = \frac{?}{9}$
To get from 3 to 9 in the denominator, multiply by 3.
So multiply numerator by 3 too: $3 × 3 = 9$
→ Answer: 9

2) $\frac{2}{8} = \frac{?}{32}$
8 → 32: multiply by 4
2 × 4 = 8
→ Answer: 8

3) $\frac{4}{7} = \frac{?}{28}$
7 → 28: multiply by 4
4 × 4 = 16
→ Answer: 16

4) $\frac{4}{9} = \frac{?}{45}$
9 → 45: multiply by 5
4 × 5 = 20
→ Answer: 20

5) $\frac{3}{4} = \frac{?}{36}$
4 → 36: multiply by 9
3 × 9 = 27
→ Answer: 27

6) $\frac{1}{8} = \frac{?}{48}$
8 → 48: multiply by 6
1 × 6 = 6
→ Answer: 6

7) $\frac{2}{9} = \frac{12}{?}$
Numerator: 2 → 12: multiply by 6
So denominator: 9 × 6 = 54
→ Answer: 54

8) $\frac{3}{10} = \frac{21}{?}$
3 → 21: multiply by 7
10 × 7 = 70
→ Answer: 70

9) $\frac{4}{3} = \frac{?}{18}$ ← This is improper! (4 > 3)
3 → 18: multiply by 6
4 × 6 = 24
→ Answer: 24

10) $\frac{2}{6} = \frac{?}{60}$
6 → 60: multiply by 10
2 × 10 = 20
→ Answer: 20

11) $\frac{6}{5} = \frac{18}{?}$ ← Improper! (6 > 5)
6 → 18: multiply by 3
5 × 3 = 15
→ Answer: 15

12) $\frac{4}{7} = \frac{24}{?}$
4 → 24: multiply by 6
7 × 6 = 42
→ Answer: 42

13) $\frac{5}{12} = \frac{?}{60}$
12 → 60: multiply by 5
5 × 5 = 25
→ Answer: 25

14) $\frac{7}{11} = \frac{28}{?}$
7 → 28: multiply by 4
11 × 4 = 44
→ Answer: 44

15) $\frac{5}{4} = \frac{35}{?}$ ← Improper! (5 > 4)
5 → 35: multiply by 7
4 × 7 = 28
→ Answer: 28

16) $\frac{11}{12} = \frac{?}{72}$
12 → 72: multiply by 6
11 × 6 = 66
→ Answer: 66

17) $\frac{4}{9} = \frac{?}{81}$
9 → 81: multiply by 9
4 × 9 = 36
→ Answer: 36

18) $\frac{9}{10} = \frac{54}{?}$
9 → 54: multiply by 6
10 × 6 = 60
→ Answer: 60

19) $\frac{4}{13} = \frac{?}{52}$
13 → 52: multiply by 4
4 × 4 = 16
→ Answer: 16

20) $\frac{8}{3} = \frac{24}{?}$ ← Improper! (8 > 3)
8 → 24: multiply by 3
3 × 3 = 9
→ Answer: 9

21) $\frac{3}{10} = \frac{?}{60}$
10 → 60: multiply by 6
3 × 6 = 18
→ Answer: 18

22) $\frac{5}{2} = \frac{?}{12}$ ← Improper! (5 > 2)
2 → 12: multiply by 6
5 × 6 = 30
→ Answer: 30

23) $\frac{9}{12} = \frac{3}{?}$
We can simplify: 9 ÷ 3 = 3, so 12 ÷ 3 = 4
→ Answer: 4

24) $\frac{5}{?} = \frac{30}{54}$
Look at numerators: 5 → 30: multiply by 6
So denominator must be 54 ÷ 6 = 9
Check: $\frac{5}{9} = \frac{30}{54}$? Yes, because 5×6=30, 9×6=54
→ Answer: 9

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Problems 25 to 32: Compare fractions using >, <, or =

We’ll convert them to have the same denominator or simplify to compare.

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25) $\frac{3}{7}$ ___ $\frac{10}{14}$
Simplify $\frac{10}{14}$: divide top and bottom by 2 → $\frac{5}{7}$
Now compare $\frac{3}{7}$ and $\frac{5}{7}$ → 3 < 5
→ So $\frac{3}{7} < \frac{10}{14}$
Answer: <

26) $\frac{2}{3}$ ___ $\frac{8}{15}$
Find common denominator: 3 and 15 → LCM is 15
$\frac{2}{3} = \frac{10}{15}$
Compare $\frac{10}{15}$ and $\frac{8}{15}$ → 10 > 8
→ So $\frac{2}{3} > \frac{8}{15}$
Answer: >

27) $\frac{1}{2}$ ___ $\frac{12}{20}$
Simplify $\frac{12}{20}$: divide by 4 → $\frac{3}{5}$
Now compare $\frac{1}{2}$ and $\frac{3}{5}$
Common denominator: 10
$\frac{1}{2} = \frac{5}{10}$, $\frac{3}{5} = \frac{6}{10}$ → 5 < 6
→ So $\frac{1}{2} < \frac{12}{20}$
Answer: <

28) $\frac{4}{5}$ ___ $\frac{16}{20}$
Simplify $\frac{16}{20}$: divide by 4 → $\frac{4}{5}$
They are equal!
→ So $\frac{4}{5} = \frac{16}{20}$
Answer: =

29) $\frac{3}{7}$ ___ $\frac{5}{14}$
Common denominator: 14
$\frac{3}{7} = \frac{6}{14}$
Compare $\frac{6}{14}$ and $\frac{5}{14}$ → 6 > 5
→ So $\frac{3}{7} > \frac{5}{14}$
Answer: >

30) $\frac{4}{9}$ ___ $\frac{8}{18}$
Simplify $\frac{8}{18}$: divide by 2 → $\frac{4}{9}$
Equal!
→ So $\frac{4}{9} = \frac{8}{18}$
Answer: =

31) $\frac{1}{6}$ ___ $\frac{3}{24}$
Simplify $\frac{3}{24}$: divide by 3 → $\frac{1}{8}$
Now compare $\frac{1}{6}$ and $\frac{1}{8}$
Same numerator — smaller denominator means larger fraction → $\frac{1}{6} > \frac{1}{8}$
→ So $\frac{1}{6} > \frac{3}{24}$
Answer: >

32) $\frac{2}{3}$ ___ $\frac{7}{9}$
Common denominator: 9
$\frac{2}{3} = \frac{6}{9}$
Compare $\frac{6}{9}$ and $\frac{7}{9}$ → 6 < 7
→ So $\frac{2}{3} < \frac{7}{9}$
Answer: <

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Final Answer:

1) 9
2) 8
3) 16
4) 20
5) 27
6) 6
7) 54
8) 70
9) 24
10) 20
11) 15
12) 42
13) 25
14) 44
15) 28
16) 66
17) 36
18) 60
19) 16
20) 9
21) 18
22) 30
23) 4
24) 9
25) <
26) >
27) <
28) =
29) >
30) =
31) >
32) <