Equivalent Fractions (C) | 4th Grade PDF Number and Operations ... - Free Printable

Let’s solve each section step by step.

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

We know that equivalent fractions are made by multiplying or dividing both numerator and denominator by the same number.

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

- 2/9 = ?/27 → 9 × 3 = 27, so 2 × 3 = 6 → 6/27
- 2/9 = 14/? → 2 × 7 = 14, so 9 × 7 = 63 → 14/63
- 2/9 = ?/99 → 9 × 11 = 99, so 2 × 11 = 22 → 22/99

✔ So: 2/9 = 6/27 = 14/63 = 22/99

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Second row (right side):
3/4 = ?/24 = 9/? = 21/?

- 3/4 = ?/24 → 4 × 6 = 24, so 3 × 6 = 18 → 18/24
- 3/4 = 9/? → 3 × 3 = 9, so 4 × 3 = 12 → 9/12
- 3/4 = 21/? → 3 × 7 = 21, so 4 × 7 = 28 → 21/28

✔ So: 3/4 = 18/24 = 9/12 = 21/28

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

- 7/10 = ?/80 → 10 × 8 = 80, so 7 × 8 = 56 → 56/80
- 7/10 = 28/? → 7 × 4 = 28, so 10 × 4 = 40 → 28/40
- 7/10 = ?/110 → 10 × 11 = 110, so 7 × 11 = 77 → 77/110

✔ So: 7/10 = 56/80 = 28/40 = 77/110

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Fourth row (right side):
5/12 = ?/96 = 35/? = 60/?

- 5/12 = ?/96 → 12 × 8 = 96, so 5 × 8 = 40 → 40/96
- 5/12 = 35/? → 5 × 7 = 35, so 12 × 7 = 84 → 35/84
- 5/12 = 60/? → 5 × 12 = 60, so 12 × 12 = 144 → 60/144

✔ So: 5/12 = 40/96 = 35/84 = 60/144

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Section B: Fill in the blanks

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

Simplify 10/15 first → divide top and bottom by 5 → 2/3

So:
- 10/15 = ?/3 → since 10/15 = 2/3, then ? = 2
- 10/15 = 30/? → 10 × 3 = 30, so 15 × 3 = 45 → 30/45
- 10/15 = ?/60 → 15 × 4 = 60, so 10 × 4 = 40 → 40/60

✔ So: 10/15 = 2/3 = 30/45 = 40/60

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Second row (right side):
18/24 = ?/72 = 3/? = 9/?

Simplify 18/24 → divide by 6 → 3/4

So:
- 18/24 = ?/72 → 24 × 3 = 72, so 18 × 3 = 54 → 54/72
- 18/24 = 3/? → 18 ÷ 6 = 3, so 24 ÷ 6 = 4 → 3/4
- 18/24 = 9/? → 18 ÷ 2 = 9, so 24 ÷ 2 = 12 → 9/12

✔ 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

So:
- 12/32 = ?/16 → 32 ÷ 2 = 16, so 12 ÷ 2 = 6 → 6/16
- 12/32 = 48/? → 12 × 4 = 48, so 32 × 4 = 128 → 48/128
- 12/32 = ?/8 → 32 ÷ 4 = 8, so 12 ÷ 4 = 3 → 3/8

✔ So: 12/32 = 6/16 = 48/128 = 3/8

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Fourth row (right side):
50/125 = ?/25 = 100/? = 2/?

Simplify 50/125 → divide by 25 → 2/5

So:
- 50/125 = ?/25 → 125 ÷ 5 = 25, so 50 ÷ 5 = 10 → 10/25
- 50/125 = 100/? → 50 × 2 = 100, so 125 × 2 = 250 → 100/250
- 50/125 = 2/? → 50 ÷ 25 = 2, so 125 ÷ 25 = 5 → 2/5

✔ So: 50/125 = 10/25 = 100/250 = 2/5

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Section C: Create 8 equivalent fractions for each

We’ll multiply numerator and denominator by numbers 2 through 9 to get 8 new fractions.

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For 3/4:

Multiply by 2: 6/8
by 3: 9/12
by 4: 12/16
by 5: 15/20
by 6: 18/24
by 7: 21/28
by 8: 24/32
by 9: 27/36

✔ 8 fractions: 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36

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For 2/7:

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

✔ 8 fractions: 4/14, 6/21, 8/28, 10/35, 12/42, 14/49, 16/56, 18/63

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For 4/9:

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

✔ 8 fractions: 8/18, 12/27, 16/36, 20/45, 24/54, 28/63, 32/72, 36/81

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

Look at all the original fractions given in Section B:

- 10/15 → can simplify (÷5) → not simplest
- 18/24 → can simplify (÷6) → not simplest
- 12/32 → can simplify (÷4) → not simplest
- 50/125 → can simplify (÷25) → not simplest

Wait — but the instruction says “circle the fractions in section B that are in simplest form.” That means look at the *original* fractions listed at the start of each chain.

Actually, let’s check if any of them are already simplified:

- 10/15 → GCF is 5 → not simplest
- 18/24 → GCF is 6 → not simplest
- 12/32 → GCF is 4 → not simplest
- 50/125 → GCF is 25 → not simplest

None of the starting fractions in Section B are in simplest form! But wait — maybe they mean among ALL the fractions written in Section B? Let’s check the filled-in ones too.

In Section B, after filling:

Left column:
- 10/15 → no
- 2/3 → yes! (GCF=1)
- 30/45 → no (÷15)
- 40/60 → no (÷20)

Right column:
- 18/24 → no
- 54/72 → no (÷18)
- 3/4 → yes!
- 9/12 → no (÷3)

Bottom left:
- 12/32 → no
- 6/16 → no (÷2)
- 48/128 → no (÷16)
- 3/8 → yes!

Bottom right:
- 50/125 → no
- 10/25 → no (÷5)
- 100/250 → no (÷50)
- 2/5 → yes!

So the fractions in simplest form in Section B are:
→ 2/3, 3/4, 3/8, 2/5

But note: the question says “Circle the fractions in section B that are in simplest form.” It doesn’t specify only the originals — so we include all that appear in Section B.

However, looking back at the worksheet layout, Section B has four chains, each starting with one fraction. The extension likely refers to those four starting fractions. But none of them are in simplest form.

Wait — perhaps I misread. Let me double-check the problem statement:

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

It doesn’t say “starting” fractions — so it includes all fractions shown in Section B, including the answers we filled in.

So from our work above, the simplest form fractions in Section B are:

- 2/3 (from 10/15 chain)
- 3/4 (from 18/24 chain)
- 3/8 (from 12/32 chain)
- 2/5 (from 50/125 chain)

These are the ones where numerator and denominator have no common factor other than 1.

✔ So circle: 2/3, 3/4, 3/8, 2/5

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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:
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 fractions in Section B: 2/3, 3/4, 3/8, 2/5