Finding Equivalent Fractions Using Multiplication and Division ... - Free Printable

Let’s solve each problem step by step.

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Part 1: Use multiplication to find an equivalent fraction.

We multiply both the numerator and denominator by the same number to get an equivalent fraction.

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Problem 1 (already done):
2/5 = ?/10 → Multiply top and bottom by 2 → 4/10 ✔

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Problem 2:
3/4 = ?/15? Wait — that doesn’t make sense. Let’s look again.

Actually, looking at the diagram:
It shows 3/4 = [ ] / [ ], with arrows showing “× something” on top and bottom.

But in the box, it says “= 15” on the right side — probably meaning the denominator is 15? But 4 × ? = 15? That’s not a whole number.

Wait — maybe I misread. Let me check the image description again.

Ah — actually, in Problem 2, it says:

> 3/4 = [ ] / [ ]
> And there’s a “15” written next to the bottom arrow? Or is it part of the answer?

Looking back at the original instruction: “The first problem has been done for you.” In Problem 1, they multiplied numerator and denominator by 2 to get 4/10.

In Problem 2, if we assume the target denominator is 15, then 4 × ? = 15 → ? = 15/4 = 3.75 — not nice.

Alternatively, maybe the “15” is the numerator? Let’s try that.

If 3/4 = 15/? → Then 3 × 5 = 15, so multiply denominator by 5 → 4 × 5 = 20 → So 15/20.

That makes sense! Probably the “15” is the new numerator.

So:
3/4 = 15/20 → because 3×5=15, 4×5=20.

✔ Answer: 15/20

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Problem 3:
1/2 = ?/18 → Denominator goes from 2 to 18 → 2 × 9 = 18 → So multiply numerator by 9 → 1 × 9 = 9 → 9/18

✔ Answer: 9/18

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Problem 4:
5/9 = ?/27 → Denominator: 9 × 3 = 27 → Numerator: 5 × 3 = 15 → 15/27

✔ Answer: 15/27

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Problem 5:
6/8 = ?/24 → Denominator: 8 × 3 = 24 → Numerator: 6 × 3 = 18 → 18/24

✔ Answer: 18/24

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Problem 6:
7/10 = ?/70 → Denominator: 10 × 7 = 70 → Numerator: 7 × 7 = 49 → 49/70

✔ Answer: 49/70

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Part 2: Use division to find an equivalent fraction.

We divide both numerator and denominator by the same number.

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Problem 7 (already done):
4/12 = 1/3 → Divide top and bottom by 4 → 4÷4=1, 12÷4=3 ✔

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Problem 8:
5/25 = ?/5 → Denominator: 25 ÷ 5 = 5 → So divide numerator by 5 → 5 ÷ 5 = 1 → 1/5

✔ Answer: 1/5

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Problem 9:
12/18 = 4/? → Numerator: 12 ÷ 3 = 4 → So divide denominator by 3 → 18 ÷ 3 = 6 → 4/6

✔ Answer: 4/6

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Now let’s list all answers clearly:

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Final Answer:

Part 1:
2. 15/20
3. 9/18
4. 15/27
5. 18/24
6. 49/70

Part 2:
8. 1/5
9. 4/6