Grade 4 Math Worksheets: Equivalent fractions | Worsheets library - Free Printable

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

---

1.

$$
\frac{1}{6} = \frac{?}{24}
$$
To find the missing numerator, we multiply both numerator and denominator of $ \frac{1}{6} $ by 4 (since $ 6 \times 4 = 24 $):
$$
\frac{1 \times 4}{6 \times 4} = \frac{4}{24}
$$
✔ Answer: 4

---

2.

$$
\frac{?}{9} = \frac{42}{63}
$$
Simplify $ \frac{42}{63} $: divide numerator and denominator by 21:
$$
\frac{42 \div 21}{63 \div 21} = \frac{2}{3}
$$
So $ \frac{?}{9} = \frac{2}{3} $. Multiply numerator and denominator of $ \frac{2}{3} $ by 3:
$$
\frac{2 \times 3}{3 \times 3} = \frac{6}{9}
$$
✔ Answer: 6

---

3.

$$
\frac{4}{8} = \frac{?}{24}
$$
Simplify $ \frac{4}{8} = \frac{1}{2} $. Now make $ \frac{1}{2} = \frac{?}{24} $. Multiply numerator and denominator by 12:
$$
\frac{1 \times 12}{2 \times 12} = \frac{12}{24}
$$
✔ Answer: 12

---

4.

$$
\frac{18}{24} = \frac{126}{?}
$$
First simplify $ \frac{18}{24} $: divide by 6 → $ \frac{3}{4} $.
Now $ \frac{3}{4} = \frac{126}{?} $. Find what number times 3 gives 126:
$$
126 \div 3 = 42
$$
So denominator should be $ 4 \times 42 = 168 $
Check: $ \frac{126}{168} $ → divide numerator and denominator by 42 → $ \frac{3}{4} $
✔ Answer: 168

---

5.

$$
\frac{?}{4} = \frac{12}{24}
$$
Simplify $ \frac{12}{24} = \frac{1}{2} $. So $ \frac{?}{4} = \frac{1}{2} $. Multiply numerator and denominator of $ \frac{1}{2} $ by 2:
$$
\frac{1 \times 2}{2 \times 2} = \frac{2}{4}
$$
✔ Answer: 2

---

6.

$$
\frac{9}{12} = \frac{54}{?}
$$
Simplify $ \frac{9}{12} = \frac{3}{4} $. Now $ \frac{3}{4} = \frac{54}{?} $.
Find multiplier: $ 54 \div 3 = 18 $, so denominator = $ 4 \times 18 = 72 $
Check: $ \frac{54}{72} = \frac{3}{4} $
✔ Answer: 72

---

7.

$$
\frac{6}{7} = \frac{?}{96}
$$
We need to scale $ \frac{6}{7} $ so denominator becomes 96.
$ 96 \div 7 \approx 13.71 $ — not a whole number. But let's find a common multiple.

Wait: $ 7 \times 13.71 $ doesn’t work. Let’s instead cross-multiply:

Let $ x $ be missing numerator:
$$
\frac{6}{7} = \frac{x}{96} \Rightarrow 6 \times 96 = 7x \Rightarrow 576 = 7x \Rightarrow x = \frac{576}{7} \approx 82.28
$$
Not an integer. Wait — this suggests a problem.

But wait: maybe it's supposed to be $ \frac{6}{7} = \frac{?}{96} $, but 96 is not a multiple of 7.

Wait — perhaps typo? Or maybe we're meant to find a fraction equivalent to $ \frac{6}{7} $ with denominator 96?

But $ \frac{6}{7} \approx 0.857 $, $ \frac{?}{96} = ? $

Try: $ \frac{6}{7} = \frac{x}{96} \Rightarrow x = \frac{6 \times 96}{7} = \frac{576}{7} \approx 82.28 $ — not integer.

Hmm. Let’s double-check: is this possible?

Wait — maybe I made a mistake. Is there a typo?

Wait — look at the original:
"7. $ \frac{6}{7} = \frac{?}{96} $" — seems odd.

Alternatively, maybe the question is misprinted. But let’s assume it's correct.

But since $ 96 $ is not divisible by 7, and $ 6/7 $ cannot be written as a fraction with denominator 96 unless numerator is fractional, this can't be a whole number.

Wait — perhaps it's $ \frac{6}{7} = \frac{?}{96} $, but maybe we’re supposed to scale up.

Let’s try scaling: $ 7 \times ? = 96 $? No, 96 ÷ 7 ≈ 13.71 — not integer.

So unless the answer is allowed to be non-integer, this isn't valid.

But likely, it's a typo. Let's check if it was meant to be $ \frac{6}{7} = \frac{?}{98} $? 98 ÷ 7 = 14 → $ 6 \times 14 = 84 $

But as given, it's 96.

Wait — perhaps it's $ \frac{6}{7} = \frac{?}{96} $, and we just compute:

$$
x = \frac{6 \times 96}{7} = \frac{576}{7} \approx 82.2857
$$

But since the other answers are integers, this suggests a mistake.

Wait — let me recheck the worksheet image. You said you uploaded an image, but I don’t have access to images. So I’m relying on your text.

But in your list, #7 is:
7. $ \frac{6}{7} = \frac{?}{96} $

This is problematic because 96 is not a multiple of 7.

Wait — could it be $ \frac{6}{7} = \frac{?}{96} $, and the answer is $ \frac{576}{7} $? But that’s not a whole number.

Alternatively, maybe it's $ \frac{6}{7} = \frac{?}{98} $? Then $ 6 \times 14 = 84 $, $ 7 \times 14 = 98 $

But as written, it's 96.

Wait — perhaps it's $ \frac{6}{7} = \frac{?}{96} $, and the missing numerator is $ \frac{576}{7} $, but that’s not an integer.

Alternatively, maybe it's a typo and should be $ \frac{6}{7} = \frac{?}{98} $ or $ \frac{?}{91} $? Not sure.

Wait — let’s skip for now and come back.

---

8.

$$
\frac{5}{10} = \frac{?}{90}
$$
Simplify $ \frac{5}{10} = \frac{1}{2} $. So $ \frac{1}{2} = \frac{?}{90} $. Multiply numerator and denominator by 45:
$$
\frac{1 \times 45}{2 \times 45} = \frac{45}{90}
$$
✔ Answer: 45

---

9.

$$
\frac{1}{2} = \frac{?}{10}
$$
Multiply numerator and denominator by 5:
$$
\frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$
✔ Answer: 5

---

10.

$$
\frac{2}{3} = \frac{12}{?}
$$
We know $ \frac{2}{3} = \frac{12}{?} $. Cross-multiply:
$$
2 \times ? = 3 \times 12 = 36 \Rightarrow ? = 18
$$
Check: $ \frac{12}{18} = \frac{2}{3} $
✔ Answer: 18

---

11.

$$
\frac{?}{5} = \frac{30}{50}
$$
Simplify $ \frac{30}{50} = \frac{3}{5} $. So $ \frac{?}{5} = \frac{3}{5} $ → numerator is 3.
✔ Answer: 3

---

12.

$$
\frac{4}{?} = \frac{40}{100}
$$
Simplify $ \frac{40}{100} = \frac{2}{5} $. So $ \frac{4}{?} = \frac{2}{5} $

Cross-multiply: $ 4 \times 5 = 2 \times ? \Rightarrow 20 = 2? \Rightarrow ? = 10 $

Check: $ \frac{4}{10} = \frac{2}{5} $
✔ Answer: 10

---

13.

$$
\frac{1}{3} = \frac{?}{10}
$$
$ \frac{1}{3} = \frac{?}{10} $. Multiply numerator and denominator by $ \frac{10}{3} $? Not helpful.

Cross-multiply: $ 1 \times 10 = 3 \times ? \Rightarrow 10 = 3? \Rightarrow ? = \frac{10}{3} \approx 3.33 $

Not an integer. But again, this is not possible unless the answer is fractional.

Wait — maybe it's $ \frac{1}{3} = \frac{?}{12} $? Then $ ? = 4 $

But as written: $ \frac{1}{3} = \frac{?}{10} $

No way to write $ \frac{1}{3} $ with denominator 10 using whole numbers.

So either typo or mistake.

Wait — perhaps it's $ \frac{1}{3} = \frac{?}{12} $? But no, it says 10.

Alternatively, maybe $ \frac{1}{3} = \frac{10}{?} $? That would be $ ? = 30 $

But here it's $ \frac{1}{3} = \frac{?}{10} $

So $ ? = \frac{10}{3} $ — not integer.

So likely typo.

But let’s keep going.

---

14.

$$
\frac{3}{7} = \frac{?}{28}
$$
7 × 4 = 28 → multiply numerator by 4: $ 3 × 4 = 12 $
✔ Answer: 12

---

15.

$$
\frac{?}{2} = \frac{6}{12}
$$
Simplify $ \frac{6}{12} = \frac{1}{2} $. So $ \frac{?}{2} = \frac{1}{2} $ → numerator = 1
✔ Answer: 1

---

16.

$$
\frac{?}{9} = \frac{4}{18}
$$
Simplify $ \frac{4}{18} = \frac{2}{9} $. So $ \frac{?}{9} = \frac{2}{9} $ → numerator = 2
✔ Answer: 2

---

17.

$$
\frac{3}{6} = \frac{12}{?}
$$
Simplify $ \frac{3}{6} = \frac{1}{2} $. So $ \frac{1}{2} = \frac{12}{?} $

Then $ ? = 12 \times 2 = 24 $
Check: $ \frac{12}{24} = \frac{1}{2} $
✔ Answer: 24

---

18.

$$
\frac{2}{4} = \frac{?}{16}
$$
Simplify $ \frac{2}{4} = \frac{1}{2} $. So $ \frac{1}{2} = \frac{?}{16} $

Multiply numerator and denominator by 8: $ \frac{1 \times 8}{2 \times 8} = \frac{8}{16} $
✔ Answer: 8

---

Now go back to problematic ones:

---

Revisit #7: $ \frac{6}{7} = \frac{?}{96} $

As before, $ ? = \frac{6 \times 96}{7} = \frac{576}{7} \approx 82.2857 $

Not an integer.

But wait — maybe it's $ \frac{6}{7} = \frac{?}{98} $? Then $ ? = 6 \times 14 = 84 $, $ 7 \times 14 = 98 $

Or maybe $ \frac{6}{7} = \frac{?}{96} $ is a typo and should be $ \frac{6}{7} = \frac{?}{98} $ or $ \frac{?}{84} $

Alternatively, perhaps it's $ \frac{6}{7} = \frac{?}{96} $, and the answer is $ \frac{576}{7} $, but that's not typical for grade 4.

Wait — another idea: maybe the denominator is 98, not 96? Because 98 ÷ 7 = 14, 6 × 14 = 84.

But as written, it's 96.

Similarly, #13: $ \frac{1}{3} = \frac{?}{10} $ → $ ? = \frac{10}{3} $, not integer.

But $ \frac{1}{3} = \frac{?}{12} $ → ? = 4, or $ \frac{1}{3} = \frac{?}{9} $ → ? = 3.

So likely typos.

But assuming the worksheet is correct, perhaps we must accept fractional answers.

But in grade 4, they expect whole numbers.

So let’s re-express:

Wait — maybe #7 is $ \frac{6}{7} = \frac{?}{96} $, but we can scale:

Find LCM of 7 and 96: 7 is prime, 96 = 32×3, so LCM = 672

So $ \frac{6}{7} = \frac{6 \times 96}{7 \times 96} = \frac{576}{672} $, but that’s not helping.

So unless the denominator is a multiple of 7, we can’t have a whole number numerator.

So likely, #7 is mistyped.

Similarly, #13: $ \frac{1}{3} = \frac{?}{10} $ → only possible if ? = 10/3, not integer.

But maybe it's $ \frac{1}{3} = \frac{?}{12} $? Then ? = 4

Or $ \frac{1}{3} = \frac{?}{9} $? Then ? = 3

But as written, it's 10.

---

Wait — perhaps I misread #7.

You wrote:
"7. $ \frac{6}{7} = \frac{?}{96} $"

But maybe it's $ \frac{6}{7} = \frac{?}{98} $? Then ? = 84

Or $ \frac{6}{7} = \frac{?}{91} $? 91 ÷ 7 = 13 → 6×13=78

But 96 is not divisible by 7.

Similarly, #13: $ \frac{1}{3} = \frac{?}{10} $ — impossible with whole number.

Unless it's $ \frac{1}{3} = \frac{10}{?} $, then ? = 30

But it's written as $ \frac{1}{3} = \frac{?}{10} $

So likely typos.

But let’s assume the worksheet is correct and proceed with exact values.

But for grade 4, these should be whole numbers.

Let’s check online or standard patterns.

Wait — maybe #7 is $ \frac{6}{7} = \frac{?}{96} $, and the answer is $ \frac{576}{7} $, but that’s not expected.

Alternatively, perhaps it's $ \frac{6}{7} = \frac{?}{96} $, and we are to write the missing number as a decimal or fraction.

But unlikely.

Perhaps it's $ \frac{6}{7} = \frac{?}{96} $, and the intended denominator is 98 or 91.

Given the context, let’s assume it’s a typo and move on.

But let’s double-check your input.

You wrote:
> 7. $ \frac{6}{7} = \frac{?}{96} $

And
> 13. $ \frac{1}{3} = \frac{?}{10} $

These two are problematic.

But let’s see if there’s a pattern.

Wait — maybe #7 is $ \frac{6}{7} = \frac{?}{96} $, and the answer is 82.2857..., but that’s not suitable.

Alternatively, maybe it's $ \frac{6}{7} = \frac{?}{96} $, and we use cross-multiplication:

$$
\frac{6}{7} = \frac{x}{96} \Rightarrow x = \frac{6 \times 96}{7} = \frac{576}{7} = 82 \frac{2}{7}
$$

Not a whole number.

So unless the worksheet allows it, this is invalid.

Similarly, #13: $ \frac{1}{3} = \frac{x}{10} \Rightarrow x = \frac{10}{3} \approx 3.33 $

Again, not integer.

So likely, #7 should be $ \frac{6}{7} = \frac{?}{98} $ → ? = 84

And #13 should be $ \frac{1}{3} = \frac{?}{12} $ → ? = 4

But based on your text, I’ll provide answers as per calculation.

---

Final Answers:

1. 4
2. 6
3. 12
4. 168
5. 2
6. 72
7. 576/7 (or ~82.29) — likely typo
8. 45
9. 5
10. 18
11. 3
12. 10
13. 10/3 (or ~3.33) — likely typo
14. 12
15. 1
16. 2
17. 24
18. 8

---

Possible Corrections:

- #7: If denominator is 98, then answer is 84
- #13: If denominator is 12, then answer is 4

But as written, those answers are not whole numbers.

---

Conclusion:

Most problems are solvable with whole numbers except #7 and #13, which may have typos in the denominators.

If you can confirm the correct denominators, I can adjust the answers.

Otherwise, here are the answers based on exact equivalence:

| Problem | Answer |
|--------|--------|
| 1 | 4 |
| 2 | 6 |
| 3 | 12 |
| 4 | 168 |
| 5 | 2 |
| 6 | 72 |
| 7 | 576/7 ≈ 82.29 |
| 8 | 45 |
| 9 | 5 |
| 10 | 18 |
| 11 | 3 |
| 12 | 10 |
| 13 | 10/3 ≈ 3.33 |
| 14 | 12 |
| 15 | 1 |
| 16 | 2 |
| 17 | 24 |
| 18 | 8 |

Let me know if you'd like help correcting the worksheet or checking the image!