Comparing & Ordering Fractions worksheet - Free Printable

Let’s solve each part step by step.

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Part A: Compare the fractions using <, >, or =

We’ll compare each pair by finding a common denominator or converting to decimals (if easier).

1) 1/2 ___ 1/3
→ 1/2 = 0.5, 1/3 ≈ 0.333 → So, 1/2 > 1/3

2) 3/4 ___ 5/6
→ Common denominator is 12.
3/4 = 9/12, 5/6 = 10/12 → So, 3/4 < 5/6

3) 5/11 ___ 3/8
→ Cross multiply: 5×8 = 40, 3×11 = 33 → 40 > 33 → So, 5/11 > 3/8

4) 2/5 ___ 2/3
→ Same numerator? Then smaller denominator means bigger fraction.
3 < 5 → so 2/3 > 2/5 → 2/5 < 2/3

5) 2/7 ___ 3/8
→ Cross multiply: 2×8 = 16, 3×7 = 21 → 16 < 21 → 2/7 < 3/8

6) 5/8 ___ 7/10
→ Common denominator 40:
5/8 = 25/40, 7/10 = 28/40 → 5/8 < 7/10

7) 7/8 ___ 7/9
→ Same numerator → smaller denominator = bigger fraction.
8 < 9 → so 7/8 > 7/9 → 7/8 > 7/9

8) 10/15 ___ 20/30
→ Simplify both:
10/15 = 2/3, 20/30 = 2/3 → 10/15 = 20/30

✔ Part A Answers:
1) >
2) <
3) >
4) <
5) <
6) <
7) >
8) =

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Part B: Order in ascending order (smallest to largest)

a) 1/3, 5/6, 1/2, 7/12

Find common denominator — let’s use 12.

- 1/3 = 4/12
- 5/6 = 10/12
- 1/2 = 6/12
- 7/12 = 7/12

Order: 4/12, 6/12, 7/12, 10/12 →
So: 1/3, 1/2, 7/12, 5/6

b) 13/20, 3/4, 4/10, 5/8

Common denominator? Let’s try 40.

- 13/20 = 26/40
- 3/4 = 30/40
- 4/10 = 16/40
- 5/8 = 25/40

Order: 16/40, 25/40, 26/40, 30/40 →
So: 4/10, 5/8, 13/20, 3/4

✔ Part B Answers:
a) 1/3, 1/2, 7/12, 5/6
b) 4/10, 5/8, 13/20, 3/4

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Part C: Order in descending order (largest to smallest)

c) 3/4, 7/10, 1/2, 4/5

Use common denominator 20.

- 3/4 = 15/20
- 7/10 = 14/20
- 1/2 = 10/20
- 4/5 = 16/20

Descending: 16/20, 15/20, 14/20, 10/20 →
So: 4/5, 3/4, 7/10, 1/2

d) 7/12, 1/6, 2/3, 3/4, 17/24

Common denominator: 24

- 7/12 = 14/24
- 1/6 = 4/24
- 2/3 = 16/24
- 3/4 = 18/24
- 17/24 = 17/24

Descending: 18/24, 17/24, 16/24, 14/24, 4/24 →
So: 3/4, 17/24, 2/3, 7/12, 1/6

✔ Part C Answers:
c) 4/5, 3/4, 7/10, 1/2
d) 3/4, 17/24, 2/3, 7/12, 1/6

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Final Answer:

A)
1) >
2) <
3) >
4) <
5) <
6) <
7) >
8) =

B)
a) 1/3, 1/2, 7/12, 5/6
b) 4/10, 5/8, 13/20, 3/4

C)
c) 4/5, 3/4, 7/10, 1/2
d) 3/4, 17/24, 2/3, 7/12, 1/6