Equivalent Fractions (C) Worksheet | Cazoom Maths Worksheets - Free Printable

Let’s solve this step by step.

We are working with equivalent fractions — that means fractions that look different but have the same value. To find equivalent fractions, we multiply or divide both the numerator (top) and denominator (bottom) by the same number.

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Section A: Write the missing number in these equivalent fractions.

#### First row:
2/9 = ?/27 = 14/? = ?/99

- 2/9 → to get denominator 27: 9 × 3 = 27 → so multiply numerator by 3: 2 × 3 = 6
→ So first blank: 6

- 2/9 = 14/? → 2 × 7 = 14 → so multiply denominator by 7: 9 × 7 = 63
→ Second blank: 63

- 2/9 = ?/99 → 9 × 11 = 99 → so 2 × 11 = 22
→ Third blank: 22

✔ So: 2/9 = 6/27 = 14/63 = 22/99

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#### Second row:
3/4 = ?/24 = 9/? = 21/?

- 3/4 → 4 × 6 = 24 → 3 × 6 = 18
→ First blank: 18

- 3/4 = 9/? → 3 × 3 = 9 → 4 × 3 = 12
→ Second blank: 12

- 3/4 = 21/? → 3 × 7 = 21 → 4 × 7 = 28
→ Third blank: 28

✔ So: 3/4 = 18/24 = 9/12 = 21/28

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#### Third row:
7/10 = ?/80 = 28/? = ?/110

- 7/10 → 10 × 8 = 80 → 7 × 8 = 56
→ First blank: 56

- 7/10 = 28/? → 7 × 4 = 28 → 10 × 4 = 40
→ Second blank: 40

- 7/10 = ?/110 → 10 × 11 = 110 → 7 × 11 = 77
→ Third blank: 77

✔ So: 7/10 = 56/80 = 28/40 = 77/110

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#### Fourth row:
5/12 = ?/96 = 35/? = 60/?

- 5/12 → 12 × 8 = 96 → 5 × 8 = 40
→ First blank: 40

- 5/12 = 35/? → 5 × 7 = 35 → 12 × 7 = 84
→ Second blank: 84

- 5/12 = 60/? → 5 × 12 = 60 → 12 × 12 = 144
→ Third blank: 144

✔ So: 5/12 = 40/96 = 35/84 = 60/144

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Section B: Fill in blanks

#### First row:
10/15 = ?/3 = 30/? = ?/60

First, simplify 10/15 → divide top and bottom by 5 → 2/3

So:

- 2/3 = ?/3 → already is 2/3 → so 2

- 2/3 = 30/? → 2 × 15 = 30 → 3 × 15 = 45

- 2/3 = ?/60 → 3 × 20 = 60 → 2 × 20 = 40

✔ So: 10/15 = 2/3 = 30/45 = 40/60

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#### Second row:
18/24 = ?/72 = 3/? = 9/?

Simplify 18/24 → divide by 6 → 3/4

Now:

- 3/4 = ?/72 → 4 × 18 = 72 → 3 × 18 = 54

- 3/4 = 3/? → already 3 on top → so denominator must be 4

Wait — let’s check original: 18/24 = 3/? → 18 ÷ 6 = 3 → 24 ÷ 6 = 4 → yes, 4

- 3/4 = 9/? → 3 × 3 = 9 → 4 × 3 = 12

✔ So: 18/24 = 54/72 = 3/4 = 9/12

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#### Third row:
12/32 = ?/16 = 48/? = ?/8

Simplify 12/32 → divide by 4 → 3/8

Now:

- 3/8 = ?/16 → 8 × 2 = 16 → 3 × 2 = 6

- 3/8 = 48/? → 3 × 16 = 48 → 8 × 16 = 128

- 3/8 = ?/8 → already is 3/8 → so 3

✔ So: 12/32 = 6/16 = 48/128 = 3/8

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#### Fourth row:
50/125 = ?/25 = 100/? = 2/?

Simplify 50/125 → divide by 25 → 2/5

Now:

- 2/5 = ?/25 → 5 × 5 = 25 → 2 × 5 = 10

- 2/5 = 100/? → 2 × 50 = 100 → 5 × 50 = 250

- 2/5 = 2/? → already 2 on top → so denominator is 5

✔ So: 50/125 = 10/25 = 100/250 = 2/5

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Section C: Create 8 equivalent fractions for each given fraction.

We’ll pick multipliers from 2 to 9 (since 8 needed).

#### For 3/4:

Multiply numerator and denominator by 2 through 9:

- ×2 → 6/8
- ×3 → 9/12
- ×4 → 12/16
- ×5 → 15/20
- ×6 → 18/24
- ×7 → 21/28
- ×8 → 24/32
- ×9 → 27/36

(You can write any 8 of these.)

#### For 2/7:

- ×2 → 4/14
- ×3 → 6/21
- ×4 → 8/28
- ×5 → 10/35
- ×6 → 12/42
- ×7 → 14/49
- ×8 → 16/56
- ×9 → 18/63

#### For 4/9:

- ×2 → 8/18
- ×3 → 12/27
- ×4 → 16/36
- ×5 → 20/45
- ×6 → 24/54
- ×7 → 28/63
- ×8 → 32/72
- ×9 → 36/81

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Extension: Circle the fractions in section B that are in simplest form.

Look at all fractions written in Section B answers:

From Section B:

Row 1: 10/15 → not simplest (simplifies to 2/3), then 2/3 ✔, 30/45 → no (÷15=2/3), 40/60 → no (÷20=2/3)

Row 2: 18/24 → no (÷6=3/4), 54/72 → no (÷18=3/4), 3/4 ✔, 9/12 → no (÷3=3/4)

Row 3: 12/32 → no (÷4=3/8), 6/16 → no (÷2=3/8), 48/128 → no (÷16=3/8), 3/8 ✔

Row 4: 50/125 → no (÷25=2/5), 10/25 → no (÷5=2/5), 100/250 → no (÷50=2/5), 2/5 ✔

So the fractions in simplest form in Section B are:

→ 2/3, 3/4, 3/8, 2/5

These are the ones you would circle.

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Final Answer:

Section A:
2/9 = 6/27 = 14/63 = 22/99
3/4 = 18/24 = 9/12 = 21/28
7/10 = 56/80 = 28/40 = 77/110
5/12 = 40/96 = 35/84 = 60/144

Section B:
10/15 = 2/3 = 30/45 = 40/60
18/24 = 54/72 = 3/4 = 9/12
12/32 = 6/16 = 48/128 = 3/8
50/125 = 10/25 = 100/250 = 2/5

Section C (example answers):
For 3/4: 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36
For 2/7: 4/14, 6/21, 8/28, 10/35, 12/42, 14/49, 16/56, 18/63
For 4/9: 8/18, 12/27, 16/36, 20/45, 24/54, 28/63, 32/72, 36/81

Extension: Circle these in Section B: 2/3, 3/4, 3/8, 2/5