Equivalent Fractions worksheet for Grade 3 students to practice finding equivalent fractions.

Let’s solve each problem step by step. We’re finding equivalent fractions — that means fractions that look different but have the same value. To do this, we multiply or divide both the top (numerator) and bottom (denominator) by the same number.

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Problem 1:
Already solved:
1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 ✔

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Problem 2:
Start with 1/3.

- 1/3 = ?/6 → Multiply numerator and denominator by 2 → 2/6
- 1/3 = 3/? → Multiply numerator and denominator by 3 → 9 (because 1×3=3, so 3×3=9)
- 1/3 = ?/12 → Multiply by 4 → 4/12
- 1/3 = 5/? → Multiply numerator and denominator by 5 → 15 (1×5=5, 3×5=15)
- 1/3 = ?/18 → Multiply by 6 → 6/18

So:
1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18

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Problem 3:
Start with 1/7.

We can multiply numerator and denominator by 2, 3, 4, 5, 6:

- ×2 → 2/14
- ×3 → 3/21
- ×4 → 4/28
- ×5 → 5/35
- ×6 → 6/42

So:
1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 6/42

*(Note: Any multiples are acceptable as long as they’re equivalent. These are the first six.)*

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Problem 4:
Start with 2/3.

Given: 2/3 = ?/? = 6/? = ?/12 = ?/15 = 12/?

Let’s fill in:

- First blank: Let’s use ×2 → 4/6
- Next: 6/? → 2×3=6, so 3×3=9 → 6/9
- ?/12 → 3×4=12, so 2×4=8 → 8/12
- ?/15 → 3×5=15, so 2×5=10 → 10/15
- 12/? → 2×6=12, so 3×6=18 → 12/18

So:
2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 12/18

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Problem 5:
Start with 1/4.

Given: 1/4 = 3/? = ?/20 = ?/? = ?/? = ?/?

- 1/4 = 3/? → 1×3=3, so 4×3=12 → 3/12
- ?/20 → 4×5=20, so 1×5=5 → 5/20
- Next: ×6 → 6/24
- ×7 → 7/28
- ×8 → 8/32

So:
1/4 = 3/12 = 5/20 = 6/24 = 7/28 = 8/32

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Problem 6:
Start with 3/8.

Given: 3/8 = ?/? = ?/24 = ?/32 = 15/? = ?/48

- ?/24 → 8×3=24, so 3×3=9 → 9/24
- ?/32 → 8×4=32, so 3×4=12 → 12/32
- 15/? → 3×5=15, so 8×5=40 → 15/40
- ?/48 → 8×6=48, so 3×6=18 → 18/48
- First blank: ×2 → 6/16

So:
3/8 = 6/16 = 9/24 = 12/32 = 15/40 = 18/48

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Problem 7:
Start with 1/5.

Given: 1/5 = ?/10 = ?/15 = ?/? = ?/? = ?/30

- ?/10 → 5×2=10, so 1×2=2 → 2/10
- ?/15 → 5×3=15, so 1×3=3 → 3/15
- Next: ×4 → 4/20
- ×5 → 5/25
- ?/30 → 5×6=30, so 1×6=6 → 6/30

So:
1/5 = 2/10 = 3/15 = 4/20 = 5/25 = 6/30

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Problem 8:
Start with 5/10.

First, simplify: 5/10 = 1/2. But since the worksheet starts with 5/10, we’ll build equivalents from it.

Multiply numerator and denominator by 2, 3, 4, 5, 6:

- ×2 → 10/20
- ×3 → 15/30
- ×4 → 20/40
- ×5 → 25/50
- ×6 → 30/60

Alternatively, you could also go backward to 1/2, but since the pattern is increasing, let’s stick with multiplying up.

So:
5/10 = 10/20 = 15/30 = 20/40 = 25/50 = 30/60

*(Note: You could also write 1/2, 2/4, etc., but since the starting fraction is 5/10, continuing with multiples of 5 is consistent.)*

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Final Answer:

2. 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18
3. 1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 6/42
4. 2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 12/18
5. 1/4 = 3/12 = 5/20 = 6/24 = 7/28 = 8/32
6. 3/8 = 6/16 = 9/24 = 12/32 = 15/40 = 18/48
7. 1/5 = 2/10 = 3/15 = 4/20 = 5/25 = 6/30
8. 5/10 = 10/20 = 15/30 = 20/40 = 25/50 = 30/60