Equivalent Fractions Worksheet - Free Printable

Let’s solve each problem step by step. Remember: to find an equivalent fraction, you multiply or divide both the numerator and denominator by the same number.

We’ll go one by one:

1) 2/3 = ?/9 → 3 × 3 = 9, so 2 × 3 = 6 → 6

2) 2/5 = ?/15 → 5 × 3 = 15, so 2 × 3 = 6 → 6

3) 1/7 = ?/14 → 7 × 2 = 14, so 1 × 2 = 2 → 2

4) 3/3 = ?/9 → 3 × 3 = 9, so 3 × 3 = 9 → 9

5) 3/4 = 9/? → 3 × 3 = 9, so 4 × 3 = 12 → 12

6) 1/2 = 6/? → 1 × 6 = 6, so 2 × 6 = 12 → 12

7) 5/6 = ?/18 → 6 × 3 = 18, so 5 × 3 = 15 → 15

8) 1/5 = 3/? → 1 × 3 = 3, so 5 × 3 = 15 → 15

9) 2/9 = ?/18 → 9 × 2 = 18, so 2 × 2 = 4 → 4

10) 3/5 = ?/20 → 5 × 4 = 20, so 3 × 4 = 12 → 12

11) 2/6 = 6/? → Wait — this is tricky. Actually, 2/6 simplifies to 1/3. But here it says 2/6 = 6/? — that would mean we’re multiplying numerator by 3 (2×3=6), so denominator 6×3=18 → 18

But let me double-check: 2/6 = 6/18? Yes, because both reduce to 1/3.

12) 3/7 = 9/? → 3 × 3 = 9, so 7 × 3 = 21 → 21

13) 4/12 = ?/3 → Divide numerator and denominator by 4: 4÷4=1, 12÷4=3 → 1

14) 4/6 = ?/3 → Divide by 2: 4÷2=2, 6÷2=3 → 2

15) 3/6 = 1/? → Divide by 3: 3÷3=1, 6÷3=2 → 2

16) 9/12 = ?/4 → Divide by 3: 9÷3=3, 12÷3=4 → 3

17) 4/10 = ?/5 → Divide by 2: 4÷2=2, 10÷2=5 → 2

18) 5/10 = ?/2 → Divide by 5: 5÷5=1, 10÷5=2 → 1

19) 4/16 = 1/? → Divide by 4: 4÷4=1, 16÷4=4 → 4

20) 8/8 = ?/2 → 8/8 = 1, so 1 = ?/2 → ? = 2 → 2

21) 8/10 = 4/? → Divide by 2: 8÷2=4, 10÷2=5 → 5

22) 2/3 = 8/? → 2 × 4 = 8, so 3 × 4 = 12 → 12

23) 1/3 = 5/? → 1 × 5 = 5, so 3 × 5 = 15 → 15

24) 1/7 = 3/? → 1 × 3 = 3, so 7 × 3 = 21 → 21

25) 2/3 = 4/18? Wait — 2/3 = 4/? → 2 × 2 = 4, so 3 × 2 = 6 → but it says 4/18? That doesn’t match. Let me read again.

Problem 25: 2/3 = 4/18? No — it says “2/3 = 4 / ___” and then “18” is under the blank? Wait, looking back at original:

Actually, in the image, #25 is written as:
“25) 2/3 = 4 / ___” and below it says “18” — no, wait, I think I misread.

Looking carefully: In the user's image description, #25 is:
“25) 2/3 = 4 / ___” and then underneath it says “18” — but that can’t be right because 2/3 ≠ 4/18.

Wait — actually, re-examining the original text provided:

In the user’s message, for #25 it says:
“25) 2/3 = 4 / ___” and then below it says “18” — but that must be a typo in my reading.

Actually, looking at the structure: Each problem has two fractions with one missing part. For #25, it’s likely:
“25) 2/3 = 4 / ?” — and the answer should be 6, since 2×2=4, 3×2=6.

But in the original list, after #25 it says “= 4 / 18” — that doesn’t make sense. Wait, perhaps I misread the formatting.

Let me check the original input again:

From user:
“25) 2/3 = 4 / 18” — oh! It’s written as “2/3 = 4 / 18”? But that’s incorrect because 2/3 = 12/18, not 4/18.

Wait — no, looking at the actual problem layout from the image description:

The problems are formatted like:
“1) 2/3 = _/9” meaning fill in the blank.

For #25: “25) 2/3 = 4 / ___” — and the blank is where we put the answer. But in the text, it might be showing the denominator as given? No.

Actually, in the user’s message, for #25 it says:
“25) 2/3 = 4 / 18” — but that can’t be, because 2/3 is not equal to 4/18.

I think there’s a formatting issue. Let me look at the pattern.

In problem #25 as listed: “25) 2/3 = 4 / ___” — and then in the next line it says “18”, but that’s probably the answer for another problem.

Wait, no — in the original text provided by user, it’s:

“25) 2/3 = 4 / 18” — but that must be a mistake in transcription. Because 2/3 = 4/6, not 4/18.

Perhaps it’s “2/3 = ? / 18” — that would make sense. Let me check the numbering.

Looking back at the user’s input:

After #24: “24) 1/7 = 3 / 21”

Then “25) 2/3 = 4 / 18” — but 2/3 = 12/18, not 4/18. So if it’s “2/3 = ? / 18”, then ? = 12.

But it says “= 4 / 18” — which is wrong. Unless it’s “2/3 = 4 / ?” then ? = 6.

I think there’s a typo in how the problem is presented in the text. Let me assume based on standard format.

In most such worksheets, for #25 it’s likely: “2/3 = 4 / ?” so we need to find the denominator.

2/3 = 4/x → cross multiply: 2x = 12 → x=6.

But in the user’s text, it says “= 4 / 18” — which might be the answer key or something. No, I think I need to trust the structure.

Let me list all problems as per common interpretation:

Actually, looking at problem #26: “26) 3/5 = 9 / 15” — that makes sense because 3×3=9, 5×3=15.

Similarly, #25: “2/3 = 4 / ?” — 2×2=4, so 3×2=6 → answer 6.

But in the user’s message, it’s written as “25) 2/3 = 4 / 18” — which is probably a formatting error, and "18" is meant to be the answer for a different problem or it's the denominator given.

Wait, no — in the original image description, for #25 it might be “2/3 = ? / 18” — let me check the sequence.

To avoid confusion, I'll solve based on the most logical interpretation for each.

Let me restart with clear assumptions:

Each problem is of the form A/B = C/D, with one missing.

For #25: If it's "2/3 = 4 / ?", then ? = 6.

If it's "2/3 = ? / 18", then ? = 12.

Given that in #26 it's "3/5 = 9 / 15", which is correct, and #27 is "5/9 = 15 / ?", etc., I think for #25 it's likely "2/3 = 4 / ?" so answer is 6.

But in the user's text, it says "25) 2/3 = 4 / 18" — which is incorrect mathematically. Perhaps "18" is the answer for #25? But 2/3 = 4/6, not 4/18.

Another possibility: maybe it's "2/3 = ? / 18" and the "4" is a typo. But that doesn't fit.

Let's look at the full list from user:

"25) 2/3 = 4 / 18" — this must be a mistake. Perhaps it's "2/3 = 12 / 18" and the "4" is for another problem.

I recall that in some formats, the blank is indicated by underscore, but in text it's shown as numbers.

To resolve this, I'll use the following approach: for each problem, identify what is missing and calculate accordingly, assuming the format is consistent.

Let me list all 32 problems with what is missing:

1) 2/3 = _/9 → num missing → 6

2) 2/5 = _/15 → num missing → 6

3) 1/7 = _/14 → num missing → 2

4) 3/3 = _/9 → num missing → 9

5) 3/4 = 9/_ → den missing → 12

6) 1/2 = 6/_ → den missing → 12

7) 5/6 = _/18 → num missing → 15

8) 1/5 = 3/_ → den missing → 15

9) 2/9 = _/18 → num missing → 4

10) 3/5 = _/20 → num missing → 12

11) 2/6 = 6/_ → den missing → 18 (since 2/6 = 1/3, 6/18 = 1/3)

12) 3/7 = 9/_ → den missing → 21

13) 4/12 = _/3 → num missing → 1 (simplify)

14) 4/6 = _/3 → num missing → 2 (simplify)

15) 3/6 = 1/_ → den missing → 2 (simplify)

16) 9/12 = _/4 → num missing → 3 (simplify)

17) 4/10 = _/5 → num missing → 2 (simplify)

18) 5/10 = _/2 → num missing → 1 (simplify)

19) 4/16 = 1/_ → den missing → 4 (simplify)

20) 8/8 = _/2 → num missing → 2 (since 8/8=1, 1=2/2)

21) 8/10 = 4/_ → den missing → 5 (simplify)

22) 2/3 = 8/_ → den missing → 12 (2*4=8, 3*4=12)

23) 1/3 = 5/_ → den missing → 15 (1*5=5, 3*5=15)

24) 1/7 = 3/_ → den missing → 21 (1*3=3, 7*3=21)

25) 2/3 = 4/_ → den missing → 6 (2*2=4, 3*2=6)

26) 3/5 = 9/_ → den missing → 15 (3*3=9, 5*3=15)

27) 5/9 = 15/_ → den missing → 27 (5*3=15, 9*3=27)

28) 4/5 = 16/_ → den missing → 20 (4*4=16, 5*4=20)

29) 3/10 = 12/_ → den missing → 40 (3*4=12, 10*4=40)

30) _/9 = 8/36 → num missing → 2 (because 8/36 simplify by 4: 2/9, so num=2)

31) 5/7 = _/35 → num missing → 25 (5*5=25, 7*5=35)

32) 6/11 = 18/_ → den missing → 33 (6*3=18, 11*3=33)

Now, for #25, if it's "2/3 = 4 / ?", then answer is 6.

In the user's text, it says "25) 2/3 = 4 / 18" — but that must be a typo, and "18" is probably the answer for #27 or something else. I'll proceed with calculation.

Similarly, for #30: "_/9 = 8/36" — 8/36 reduces to 2/9, so numerator is 2.

Let me verify all:

1) 6

2) 6

3) 2

4) 9

5) 12

6) 12

7) 15

8) 15

9) 4

10) 12

11) 18

12) 21

13) 1

14) 2

15) 2

16) 3

17) 2

18) 1

19) 4

20) 2

21) 5

22) 12

23) 15

24) 21

25) 6 [assuming 2/3 = 4/?]

26) 15

27) 27 [5/9 = 15/? → 5*3=15, 9*3=27]

28) 20 [4/5 = 16/? → 4*4=16, 5*4=20]

29) 40 [3/10 = 12/? → 3*4=12, 10*4=40]

30) 2 [?/9 = 8/36 → 8/36 = 2/9, so ?=2]

31) 25 [5/7 = ?/35 → 5*5=25, 7*5=35]

32) 33 [6/11 = 18/? → 6*3=18, 11*3=33]

Now, to confirm, let's spot-check a few:

#11: 2/6 = 6/18? 2/6 = 1/3, 6/18 = 1/3 → yes.

#13: 4/12 = 1/3 → yes.

#20: 8/8 = 1, and 2/2 = 1 → yes.

#30: 2/9 = 8/36? 2/9 = 8/36? Cross multiply: 2*36=72, 9*8=72 → yes.

All seem correct.

So the answers are:

1) 6
2) 6
3) 2
4) 9
5) 12
6) 12
7) 15
8) 15
9) 4
10) 12
11) 18
12) 21
13) 1
14) 2
15) 2
16) 3
17) 2
18) 1
19) 4
20) 2
21) 5
22) 12
23) 15
24) 21
25) 6
26) 15
27) 27
28) 20
29) 40
30) 2
31) 25
32) 33

Final Answer:
1) 6
2) 6
3) 2
4) 9
5) 12
6) 12
7) 15
8) 15
9) 4
10) 12
11) 18
12) 21
13) 1
14) 2
15) 2
16) 3
17) 2
18) 1
19) 4
20) 2
21) 5
22) 12
23) 15
24) 21
25) 6
26) 15
27) 27
28) 20
29) 40
30) 2
31) 25
32) 33