Equivalent fractions worksheet with ten problems for students to complete.

Let’s go through each problem one by one. We’re looking for equivalent fractions — that means the value of the fraction stays the same, even though the numbers change.

To find missing numbers in equivalent fractions, we look at how the numerator or denominator changed from the first fraction to the next, and apply the same change to the other part.

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Problem 1:
Start with 1/5
→ Next is 2/? → Multiply numerator by 2 → so multiply denominator by 2 → 5×2 = 10 → but wait, it says 2/15? That doesn’t match. Let me check again.

Wait — actually, looking at the full chain:

1/5 = 2/? = ?/15 = 4/? = ?/25 = 6/? = ?/35

We need to fill in the blanks so all are equal to 1/5.

So:

- 1/5 = 2/x → x = 10 (because 1×2=2, so 5×2=10)
- But the worksheet shows “2 / _” then “_ / 15” — let’s see what fits.

Actually, let’s solve each blank using the base fraction 1/5.

Blank after 2: 2/x = 1/5 → x = 10
Blank before 15: y/15 = 1/5 → y = 3
Blank after 4: 4/z = 1/5 → z = 20
Blank before 25: w/25 = 1/5 → w = 5
Blank after 6: 6/v = 1/5 → v = 30
Blank before 35: u/35 = 1/5 → u = 7

But the worksheet has:

1) 1/5 = 2/_ = _/15 = 4/_ = _/25 = 6/_ = _/35

So blanks are:

After 2: 10
Before 15: 3
After 4: 20
Before 25: 5
After 6: 30
Before 35: 7

✔ So filled: 1/5 = 2/10 = 3/15 = 4/20 = 5/25 = 6/30 = 7/35

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Problem 2:
Start with 3/7

Chain: 3/7 = _/14 = 9/_ = 12/_ = 15/_ = _/42 = 21/_

Find multipliers:

3/7 = x/14 → 7×2=14 → 3×2=6 → so 6/14
3/7 = 9/y → 3×3=9 → 7×3=21 → 9/21
3/7 = 12/z → 3×4=12 → 7×4=28 → 12/28
3/7 = 15/w → 3×5=15 → 7×5=35 → 15/35
3/7 = v/42 → 7×6=42 → 3×6=18 → 18/42
3/7 = 21/u → 3×7=21 → 7×7=49 → 21/49

✔ Filled: 3/7 = 6/14 = 9/21 = 12/28 = 15/35 = 18/42 = 21/49

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Problem 3:
Start with 1/4

Chain: 1/4 = _/8 = _/12 = 4/_ = 5/_ = _/24 = 7/_

1/4 = x/8 → 4×2=8 → 1×2=2 → 2/8
1/4 = y/12 → 4×3=12 → 1×3=3 → 3/12
1/4 = 4/z → 1×4=4 → 4×4=16 → 4/16
1/4 = 5/w → 1×5=5 → 4×5=20 → 5/20
1/4 = v/24 → 4×6=24 → 1×6=6 → 6/24
1/4 = 7/u → 1×7=7 → 4×7=28 → 7/28

✔ Filled: 1/4 = 2/8 = 3/12 = 4/16 = 5/20 = 6/24 = 7/28

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Problem 4:
Start with 1/2

Chain: 1/2 = _/4 = _/6 = _/8 = 5/_ = _/12 = _/14

1/2 = x/4 → 2×2=4 → 1×2=2 → 2/4
1/2 = y/6 → 2×3=6 → 1×3=3 → 3/6
1/2 = z/8 → 2×4=8 → 1×4=4 → 4/8
1/2 = 5/w → 1×5=5 → 2×5=10 → 5/10
1/2 = v/12 → 2×6=12 → 1×6=6 → 6/12
1/2 = u/14 → 2×7=14 → 1×7=7 → 7/14

✔ Filled: 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14

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Problem 5:
Start with 1/7

Chain: 1/7 = _/14 = _/21 = 4/_ = 5/_ = _/42 = 7/_

1/7 = x/14 → 7×2=14 → 1×2=2 → 2/14
1/7 = y/21 → 7×3=21 → 1×3=3 → 3/21
1/7 = 4/z → 1×4=4 → 7×4=28 → 4/28
1/7 = 5/w → 1×5=5 → 7×5=35 → 5/35
1/7 = v/42 → 7×6=42 → 1×6=6 → 6/42
1/7 = 7/u → 1×7=7 → 7×7=49 → 7/49

✔ Filled: 1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 6/42 = 7/49

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Problem 6:
Start with 1/1

Chain: 1/1 = 2/_ = _/3 = _/4 = _/5 = _/6 = 7/_

1/1 = 2/x → x=2
1/1 = y/3 → y=3
1/1 = z/4 → z=4
1/1 = w/5 → w=5
1/1 = v/6 → v=6
1/1 = 7/u → u=7

✔ Filled: 1/1 = 2/2 = 3/3 = 4/4 = 5/5 = 6/6 = 7/7

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Problem 7:
Start with 1/2

Chain: 1/2 = 2/_ = _/6 = _/8 = 5/_ = 6/_ = 7/_

1/2 = 2/x → x=4
1/2 = y/6 → y=3
1/2 = z/8 → z=4
1/2 = 5/w → w=10
1/2 = 6/v → v=12
1/2 = 7/u → u=14

✔ Filled: 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14

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Problem 8:
Start with 3/8

Chain: 3/8 = _/16 = _/24 = _/32 = _/40 = 18/_ = 21/_

3/8 = x/16 → 8×2=16 → 3×2=6 → 6/16
3/8 = y/24 → 8×3=24 → 3×3=9 → 9/24
3/8 = z/32 → 8×4=32 → 3×4=12 → 12/32
3/8 = w/40 → 8×5=40 → 3×5=15 → 15/40
3/8 = 18/v → 3×6=18 → 8×6=48 → 18/48
3/8 = 21/u → 3×7=21 → 8×7=56 → 21/56

✔ Filled: 3/8 = 6/16 = 9/24 = 12/32 = 15/40 = 18/48 = 21/56

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Problem 9:
Start with 1/3

Chain: 1/3 = _/6 = _/9 = _/12 = 5/_ = 6/_ = _/21

1/3 = x/6 → 3×2=6 → 1×2=2 → 2/6
1/3 = y/9 → 3×3=9 → 1×3=3 → 3/9
1/3 = z/12 → 3×4=12 → 1×4=4 → 4/12
1/3 = 5/w → 1×5=5 → 3×5=15 → 5/15
1/3 = 6/v → 1×6=6 → 3×6=18 → 6/18
1/3 = u/21 → 3×7=21 → 1×7=7 → 7/21

✔ Filled: 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21

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Problem 10:
Start with 7/10

Chain: 7/10 = 14/_ = _/30 = 28/_ = 35/_ = 42/_ = 49/_

7/10 = 14/x → 7×2=14 → 10×2=20 → 14/20
7/10 = y/30 → 10×3=30 → 7×3=21 → 21/30
7/10 = 28/z → 7×4=28 → 10×4=40 → 28/40
7/10 = 35/w → 7×5=35 → 10×5=50 → 35/50
7/10 = 42/v → 7×6=42 → 10×6=60 → 42/60
7/10 = 49/u → 7×7=49 → 10×7=70 → 49/70

✔ Filled: 7/10 = 14/20 = 21/30 = 28/40 = 35/50 = 42/60 = 49/70

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Final Answer:
1) 10, 3, 20, 5, 30, 7
2) 6, 21, 28, 35, 18, 49
3) 2, 3, 16, 20, 6, 28
4) 2, 3, 4, 10, 6, 7
5) 2, 3, 28, 35, 6, 49
6) 2, 3, 4, 5, 6, 7
7) 4, 3, 4, 10, 12, 14
8) 6, 9, 12, 15, 48, 56
9) 2, 3, 4, 15, 18, 7
10) 20, 21, 40, 50, 60, 70