Equivalent Fractions & Simplifying Fractions (Worksheets) - Free Printable

Let’s solve each problem step by step. We’re finding equivalent fractions — that means we want to make the two fractions equal by filling in the missing number.

We do this by multiplying or dividing both the numerator (top) and denominator (bottom) by the same number.

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a.
3/4 = ?/8
→ 4 × 2 = 8, so multiply top by 2 too: 3 × 2 = 6
✔ Answer: 6

b.
4/6 = ?/3
→ 6 ÷ 2 = 3, so divide top by 2: 4 ÷ 2 = 2
✔ Answer: 2

c.
1/2 = ?/10
→ 2 × 5 = 10, so multiply top by 5: 1 × 5 = 5
✔ Answer: 5

d.
6/12 = ?/6
→ 12 ÷ 2 = 6, so divide top by 2: 6 ÷ 2 = 3
✔ Answer: 3

e.
1/3 = ?/6
→ 3 × 2 = 6, so multiply top by 2: 1 × 2 = 2
✔ Answer: 2

f.
1/6 = ?/12
→ 6 × 2 = 12, so multiply top by 2: 1 × 2 = 2
✔ Answer: 2

g.
5/10 = ?/6
Wait — let’s simplify first: 5/10 = 1/2
Now, 1/2 = ?/6 → 2 × 3 = 6, so 1 × 3 = 3
✔ Answer: 3

*(Alternatively: cross-multiply? But better to simplify first for clarity.)*

h.
2/3 = ?/9
→ 3 × 3 = 9, so multiply top by 3: 2 × 3 = 6
✔ Answer: 6

i.
2/4 = ?/6
Simplify 2/4 = 1/2
Then 1/2 = ?/6 → 2 × 3 = 6, so 1 × 3 = 3
✔ Answer: 3

j.
1/4 = ?/12
→ 4 × 3 = 12, so multiply top by 3: 1 × 3 = 3
✔ Answer: 3

k.
6/9 = ?/3
Simplify 6/9 = 2/3 → already over 3! So answer is 2
Or: 9 ÷ 3 = 3, so 6 ÷ 3 = 2
✔ Answer: 2

l.
2/5 = ?/10
→ 5 × 2 = 10, so multiply top by 2: 2 × 2 = 4
✔ Answer: 4

m.
6/8 = ?/12
First, simplify 6/8 = 3/4
Now, 3/4 = ?/12 → 4 × 3 = 12, so 3 × 3 = 9
✔ Answer: 9

*(Check: 6/8 = 0.75; 9/12 = 0.75 → correct!)*

n.
5/7 = ?/14
→ 7 × 2 = 14, so multiply top by 2: 5 × 2 = 10
✔ Answer: 10

o.
14/18 = ?/8
Wait — let’s simplify 14/18 first: divide top and bottom by 2 → 7/9
But 7/9 = ?/8? That doesn’t work easily. Maybe typo? Let’s check original.

Actually, looking again: 14/18 = ?/8 — but 18 to 8 isn’t a clean multiple. Perhaps it’s meant to be 14/18 = ?/9? Or maybe 14/18 simplified is 7/9, and if target is 8, then... Hmm.

Wait — perhaps it’s 14/18 = ?/9? Because 18 ÷ 2 = 9, so 14 ÷ 2 = 7 → 7/9. But the problem says /8.

Let me double-check the image description — user wrote “o. 14/18 = _ /8”

That seems odd. Let’s try solving as is:

14/18 = x/8
Cross multiply: 14 × 8 = 18 × x → 112 = 18x → x = 112 ÷ 18 = 56/9 ≈ 6.22 — not a whole number.

But all other answers are whole numbers. Likely a typo in the problem. Probably meant 14/18 = ?/9 → which would be 7.

OR — maybe it’s 14/18 = ?/ something else? Wait — perhaps it’s 14/18 = ?/9? Since 18÷2=9, 14÷2=7.

But user wrote “/8”. Let me re-read the original input:

“o. 14/18 = _ /8”

Hmm. Alternatively, maybe it’s 14/18 = ?/9? Because 9 is half of 18.

Given that all others are clean, I suspect it’s a typo and should be /9.

But since we must solve as given, let’s assume it’s correct and see:

14/18 reduces to 7/9. To get denominator 8, we’d need to scale 7/9 to have denominator 8 — which requires multiplying denominator by 8/9, so numerator becomes 7 × (8/9) = 56/9 — not integer.

This suggests an error. But wait — perhaps it’s 14/18 = ?/9? Then answer is 7.

Looking back at common worksheet patterns, likely it’s meant to be 14/18 = ?/9.

I’ll go with that assumption because otherwise it breaks the pattern.

So: 14/18 = ?/9 → divide both by 2 → 7/9 → answer is 7.

✔ Final decision: 7 (assuming typo, should be /9)

If strictly /8, no whole number solution — but since it’s a school worksheet, almost certainly meant to be /9.

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Final Answers:

a. 6
b. 2
c. 5
d. 3
e. 2
f. 2
g. 3
h. 6
i. 3
j. 3
k. 2
l. 4
m. 9
n. 10
o. 7 *(assuming denominator should be 9, not 8)*

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Final Answer:
a. 6
b. 2
c. 5
d. 3
e. 2
f. 2
g. 3
h. 6
i. 3
j. 3
k. 2
l. 4
m. 9
n. 10
o. 7