Equivalent Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of these equivalent fraction problems step by step. The goal is to find the missing number that makes each pair of fractions equivalent.

We use the principle:
If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$ (cross-multiplication).
Alternatively, we can scale up or down by multiplying/dividing numerator and denominator by the same number.

---

1) $\frac{3}{5} = \frac{?}{20}$

Multiply numerator and denominator of $\frac{3}{5}$ by 4:
$$
\frac{3 \times 4}{5 \times 4} = \frac{12}{20}
$$
✔ Answer: 12

---

2) $\frac{5}{12} = \frac{?}{96}$

Find how many times 12 goes into 96:
$96 ÷ 12 = 8$, so multiply numerator by 8:
$$
\frac{5 \times 8}{12 \times 8} = \frac{40}{96}
$$
✔ Answer: 40

---

3) $\frac{18}{29} = \frac{?}{75}$

Check if 29 divides into 75? No. Let’s cross-multiply:

Let $x$ be the missing numerator:
$$
\frac{18}{29} = \frac{x}{75} \Rightarrow 18 \times 75 = 29x \Rightarrow 1350 = 29x
\Rightarrow x = \frac{1350}{29} \approx 46.55
$$
Not an integer → something wrong?

Wait — perhaps it's not reducible, but let’s check if 18/29 can be scaled to denominator 75.

But 29 and 75 have no common factors. So unless 75 is a multiple of 29, which it isn't, this won’t work.

Wait — maybe the question has a typo? Or perhaps I need to reverse the logic.

Actually, maybe the fraction is meant to be simplified or scaled differently.

But 29 doesn’t divide 75, and 18/29 is already in simplest form.

Let’s try:
$\frac{18}{29} = \frac{x}{75}$

Cross-multiply:
$$
18 \times 75 = 29x \Rightarrow 1350 = 29x \Rightarrow x = \frac{1350}{29} \approx 46.55
$$
Not an integer. So no whole number solution — likely a mistake in problem or expected answer.

Wait — maybe it's supposed to be $\frac{18}{29} = \frac{?}{75}$, but since 29 doesn't divide 75, and 18/29 is irreducible, there is no integer solution.

But the worksheet likely expects one. Let’s double-check.

Wait — could it be a typo? Maybe the denominator should be 58? But it's written as 75.

Alternatively, maybe we’re supposed to simplify or find approximate?

No — probably a typo. But let's skip for now and come back.

Wait — maybe I made a mistake.

Try scaling: 29 × ? = 75 → not possible. So no equivalent fraction with denominator 75 unless numerator is fractional.

So either the problem is flawed, or we must accept decimal.

But since all others are integers, likely error.

Let’s move on and return later.

---

4) $\frac{2}{7} = \frac{?}{49}$

7 × 7 = 49 → multiply numerator by 7:
$$
\frac{2 \times 7}{7 \times 7} = \frac{14}{49}
$$
✔ Answer: 14

---

5) $\frac{12}{17} = \frac{?}{85}$

17 × 5 = 85 → multiply numerator by 5:
$$
\frac{12 \times 5}{17 \times 5} = \frac{60}{85}
$$
✔ Answer: 60

---

6) $\frac{12}{23} = \frac{?}{69}$

23 × 3 = 69 → multiply numerator by 3:
$$
\frac{12 \times 3}{23 \times 3} = \frac{36}{69}
$$
✔ Answer: 36

---

7) $\frac{5}{9} = \frac{?}{45}$

9 × 5 = 45 → multiply numerator by 5:
$$
\frac{5 \times 5}{9 \times 5} = \frac{25}{45}
$$
✔ Answer: 25

---

8) $\frac{13}{15} = \frac{?}{75}$

15 × 5 = 75 → multiply numerator by 5:
$$
\frac{13 \times 5}{15 \times 5} = \frac{65}{75}
$$
✔ Answer: 65

---

9) $\frac{15}{19} = \frac{?}{38}$

19 × 2 = 38 → multiply numerator by 2:
$$
\frac{15 \times 2}{19 \times 2} = \frac{30}{38}
$$
✔ Answer: 30

---

10) $\frac{4}{11} = \frac{?}{44}$

11 × 4 = 44 → multiply numerator by 4:
$$
\frac{4 \times 4}{11 \times 4} = \frac{16}{44}
$$
✔ Answer: 16

---

11) $\frac{9}{19} = \frac{?}{76}$

19 × 4 = 76 → multiply numerator by 4:
$$
\frac{9 \times 4}{19 \times 4} = \frac{36}{76}
$$
✔ Answer: 36

---

12) $\frac{11}{19} = \frac{?}{95}$

19 × 5 = 95 → multiply numerator by 5:
$$
\frac{11 \times 5}{19 \times 5} = \frac{55}{95}
$$
✔ Answer: 55

---

13) $\frac{6}{10} = \frac{?}{60}$

Simplify first: $\frac{6}{10} = \frac{3}{5}$

Now: $\frac{3}{5} = \frac{x}{60}$ → 5 × 12 = 60 → multiply numerator by 12:
$$
\frac{3 \times 12}{5 \times 12} = \frac{36}{60}
$$
Or directly: $\frac{6}{10} = \frac{6 \times 6}{10 \times 6} = \frac{36}{60}$

✔ Answer: 36

---

14) $\frac{2}{13} = \frac{?}{91}$

13 × 7 = 91 → multiply numerator by 7:
$$
\frac{2 \times 7}{13 \times 7} = \frac{14}{91}
$$
✔ Answer: 14

---

15) $\frac{2}{25} = \frac{?}{50}$

25 × 2 = 50 → multiply numerator by 2:
$$
\frac{2 \times 2}{25 \times 2} = \frac{4}{50}
$$
✔ Answer: 4

---

16) $\frac{2}{9} = \frac{?}{63}$

9 × 7 = 63 → multiply numerator by 7:
$$
\frac{2 \times 7}{9 \times 7} = \frac{14}{63}
$$
✔ Answer: 14

---

17) $\frac{4}{11} = \frac{?}{22}$

11 × 2 = 22 → multiply numerator by 2:
$$
\frac{4 \times 2}{11 \times 2} = \frac{8}{22}
$$
✔ Answer: 8

---

18) $\frac{4}{9} = \frac{?}{81}$

9 × 9 = 81 → multiply numerator by 9:
$$
\frac{4 \times 9}{9 \times 9} = \frac{36}{81}
$$
✔ Answer: 36

---

19) $\frac{4}{7} = \frac{?}{56}$

7 × 8 = 56 → multiply numerator by 8:
$$
\frac{4 \times 8}{7 \times 8} = \frac{32}{56}
$$
✔ Answer: 32

---

20) $\frac{5}{13} = \frac{?}{65}$

13 × 5 = 65 → multiply numerator by 5:
$$
\frac{5 \times 5}{13 \times 5} = \frac{25}{65}
$$
✔ Answer: 25

---

21) $\frac{8}{21} = \frac{?}{84}$

21 × 4 = 84 → multiply numerator by 4:
$$
\frac{8 \times 4}{21 \times 4} = \frac{32}{84}
$$
✔ Answer: 32

---

22) $\frac{2}{3} = \frac{?}{30}$

3 × 10 = 30 → multiply numerator by 10:
$$
\frac{2 \times 10}{3 \times 10} = \frac{20}{30}
$$
✔ Answer: 20

---

23) $\frac{7}{11} = \frac{?}{66}$

11 × 6 = 66 → multiply numerator by 6:
$$
\frac{7 \times 6}{11 \times 6} = \frac{42}{66}
$$
✔ Answer: 42

---

24) $\frac{11}{24} = \frac{?}{48}$

24 × 2 = 48 → multiply numerator by 2:
$$
\frac{11 \times 2}{24 \times 2} = \frac{22}{48}
$$
✔ Answer: 22

---

25) $\frac{4}{13} = \frac{?}{39}$

13 × 3 = 39 → multiply numerator by 3:
$$
\frac{4 \times 3}{13 \times 3} = \frac{12}{39}
$$
✔ Answer: 12

---

26) $\frac{17}{7} = \frac{?}{51}$

Wait — $\frac{17}{7}$? That’s greater than 1.

But 7 × ? = 51 → 51 ÷ 7 ≈ 7.285 → not integer.

Wait — is it $\frac{17}{?} = \frac{?}{51}$? No — it says:

26) $\frac{17}{7} = \frac{?}{51}$

So: $\frac{17}{7} = \frac{x}{51}$

Cross-multiply:
$$
17 \times 51 = 7x \Rightarrow 867 = 7x \Rightarrow x = \frac{867}{7} = 123.857...
$$
Not integer.

Wait — is it possible that the fraction is reversed?

Maybe it's a typo? Let’s check if 17/7 simplifies — no.

But 7 × 7.285... = 51 → not helpful.

Wait — perhaps it's $\frac{17}{?} = \frac{?}{51}$ — but no, the format is clear.

Wait — maybe it's $\frac{17}{7} = \frac{?}{51}$, but again, 17/7 = 2.428..., and 51 divided by 7 is 7.285...

But 17 × 7.285 ≈ 123.85 → not integer.

Wait — maybe it's $\frac{17}{7} = \frac{?}{51}$, but let's see:

If we scale denominator from 7 to 51, multiplier is $51 ÷ 7 = 7.285...$, not rational.

But 17 × 51 = 867, 867 ÷ 7 = 123.857 → not integer.

So no whole number solution.

Wait — is it possible the original fraction was $\frac{17}{?} = \frac{?}{51}$? No.

Wait — perhaps it's $\frac{17}{?} = \frac{?}{51}$ — but no.

Wait — let’s look at the pattern: maybe it's $\frac{17}{?} = \frac{?}{51}$, but the problem says:

"26) $\frac{17}{7} = \frac{?}{51}$"

This seems incorrect. Unless it's a typo.

Wait — maybe it's $\frac{17}{?} = \frac{?}{51}$, but no.

Wait — perhaps it's $\frac{17}{7} = \frac{?}{51}$, and we need to find what multiplies 7 to get 51? But 51 ÷ 7 = 7.285...

Not useful.

Wait — unless it's $\frac{17}{7} = \frac{?}{51}$, and we cross-multiply:

$17 \times 51 = 867$, $7x = 867$, $x = 867 / 7 = 123.857...$

No.

But 51 = 3 × 17 → interesting.

Wait — 17/7 = ? / 51

Let’s write:

$\frac{17}{7} = \frac{x}{51}$

Then $x = \frac{17 \times 51}{7} = \frac{867}{7} = 123.857...$

Still not integer.

So likely a typo.

Wait — perhaps it's $\frac{17}{?} = \frac{?}{51}$, but no.

Wait — maybe it's $\frac{17}{7} = \frac{?}{51}$, but 17 and 7 are both prime.

Alternatively, maybe it's $\frac{17}{7} = \frac{?}{51}$, and the answer is fractional, but unlikely.

Wait — let’s check if 17/7 reduces — no.

Alternatively, maybe it's supposed to be $\frac{17}{?} = \frac{?}{51}$, but no.

Wait — perhaps it's $\frac{17}{?} = \frac{?}{51}$, but the problem says $\frac{17}{7} = \frac{?}{51}$

So unless it's a trick, this is invalid.

But wait — maybe it's $\frac{17}{7} = \frac{?}{51}$, and we want to scale up.

But 7 × 7.285... = 51 → not integer.

Wait — 51 = 3 × 17, so maybe we can write:

$\frac{17}{7} = \frac{17 \times 3}{7 \times 3} = \frac{51}{21}$, but that’s not helping.

Wait — we want denominator 51.

So $\frac{17}{7} = \frac{x}{51}$

So $x = \frac{17 \times 51}{7} = \frac{867}{7} = 123.857...$

Not valid.

So problem 26 appears flawed.

Wait — let’s recheck the image.

Looking back: "26) $\frac{17}{7} = \frac{?}{51}$"

Yes.

But 17/7 is about 2.428, and 51/21 = 2.428... → oh!

Wait — $\frac{17}{7} = \frac{51}{21}$

So if the question was $\frac{17}{7} = \frac{?}{21}$, then answer is 51.

But here it's $\frac{?}{51}$, so we need to solve:

$\frac{17}{7} = \frac{x}{51}$ → $x = \frac{17 \times 51}{7} = \frac{867}{7} = 123.857...$

No.

Unless the fraction is $\frac{17}{?} = \frac{?}{51}$, but it's not.

So likely a typo.

But let’s assume it’s $\frac{17}{?} = \frac{?}{51}$ — no.

Wait — maybe it’s $\frac{17}{7} = \frac{?}{51}$, and we are to write it as equivalent fraction.

But only if we allow non-integer numerators.

But the context suggests whole numbers.

So probably a typo.

Perhaps it’s $\frac{17}{7} = \frac{?}{51}$, and they mean to scale denominator from 7 to 51, but 51 is not divisible by 7.

Wait — 51 ÷ 7 = 7.285… not integer.

So no.

Skip for now.

---

27) $\frac{13}{25} = \frac{?}{75}$

25 × 3 = 75 → multiply numerator by 3:
$$
\frac{13 \times 3}{25 \times 3} = \frac{39}{75}
$$
✔ Answer: 39

---

28) $\frac{7}{15} = \frac{?}{30}$

15 × 2 = 30 → multiply numerator by 2:
$$
\frac{7 \times 2}{15 \times 2} = \frac{14}{30}
$$
✔ Answer: 14

---

29) $\frac{5}{19} = \frac{?}{38}$

19 × 2 = 38 → multiply numerator by 2:
$$
\frac{5 \times 2}{19 \times 2} = \frac{10}{38}
$$
✔ Answer: 10

---

30) $\frac{18}{28} = \frac{?}{56}$

Simplify $\frac{18}{28} = \frac{9}{14}$

Now: $\frac{9}{14} = \frac{x}{56}$

14 × 4 = 56 → multiply numerator by 4:
$$
\frac{9 \times 4}{14 \times 4} = \frac{36}{56}
$$
Or directly: $\frac{18}{28} = \frac{18 \times 2}{28 \times 2} = \frac{36}{56}$

✔ Answer: 36

---

Now go back to problematic ones:

---

Revisit 3) $\frac{18}{29} = \frac{?}{75}$

As before, 29 doesn’t divide 75.

Cross-multiply: $18 \times 75 = 1350$, $29x = 1350$ → $x = 1350 / 29 ≈ 46.55$

Not integer → no valid whole number solution.

Likely typo — maybe it's $\frac{18}{29} = \frac{?}{58}$ → 29×2=58 → 18×2=36 → answer 36.

Or maybe $\frac{18}{29} = \frac{?}{75}$ is intended to be simplified, but it's already reduced.

So invalid.

---

26) $\frac{17}{7} = \frac{?}{51}$

As above, $x = \frac{17 \times 51}{7} = \frac{867}{7} = 123.857...$

Not integer.

But note: $\frac{17}{7} = \frac{51}{21}$, so if denominator was 21, answer would be 51.

But here it's 51.

So unless it's $\frac{17}{7} = \frac{?}{51}$, and we're to write 123.857, which is not reasonable.

So likely typo.

Perhaps it's $\frac{17}{?} = \frac{?}{51}$, but no.

Wait — maybe it's $\frac{17}{7} = \frac{?}{51}$, and they expect us to write:

Scale factor: 51 ÷ 7 = 7.285... → not helpful.

Alternatively, maybe it's $\frac{17}{7} = \frac{?}{51}$, and we write:

$\frac{17}{7} = \frac{17 \times 7.285}{7 \times 7.285} = \frac{123.857}{51}$

But not acceptable.

So probably typo.

---

Final Answers:

| # | Answer |
|---|--------|
| 1 | 12 |
| 2 | 40 |
| 3 | ✘ (No integer solution) |
| 4 | 14 |
| 5 | 60 |
| 6 | 36 |
| 7 | 25 |
| 8 | 65 |
| 9 | 30 |
|10 | 16 |
|11 | 36 |
|12 | 55 |
|13 | 36 |
|14 | 14 |
|15 | 4 |
|16 | 14 |
|17 | 8 |
|18 | 36 |
|19 | 32 |
|20 | 25 |
|21 | 32 |
|22 | 20 |
|23 | 42 |
|24 | 22 |
|25 | 12 |
|26 | ✘ (No integer solution) |
|27 | 39 |
|28 | 14 |
|29 | 10 |
|30 | 36 |

---

Likely Corrections:

- #3: Probably meant $\frac{18}{29} = \frac{?}{58}$ → answer: 36
- #26: Probably meant $\frac{17}{7} = \frac{?}{21}$ → answer: 51

But based on given, those two are invalid.

---

✔ Corrected Answers (assuming typos):

But since we must provide answers as per sheet, and assuming they expect whole numbers, here are the valid answers:

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Final Answer List (Only Valid Ones):

1) 12
2) 40
3) No solution (but if forced, ~46.55)
4) 14
5) 60
6) 36
7) 25
8) 65
9) 30
10) 16
11) 36
12) 55
13) 36
14) 14
15) 4
16) 14
17) 8
18) 36
19) 32
20) 25
21) 32
22) 20
23) 42
24) 22
25) 12
26) No solution
27) 39
28) 14
29) 10
30) 36

---

Conclusion:

Most problems are solvable using scaling. Two problems (#3 and #26) appear to have errors because the denominators are not multiples of the original denominators, leading to non-integer numerators.

If you suspect typos, please verify the original fractions.

Otherwise, the rest are correct as solved.