Ordering Fractions exercise - Free Printable

Sure! Let’s solve each problem step by step, explaining how to compare and order fractions.

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Problem 1: Arrange the fractions in order. Begin with the smallest!

Fractions:
3/4, 1/8, 1/2

✔ Step 1: Find a common denominator
The denominators are 4, 8, and 2. The least common denominator (LCD) is 8.

✔ Step 2: Convert all fractions to have denominator 8

- 3/4 = (3 × 2)/(4 × 2) = 6/8
- 1/8 = 1/8 (already has denominator 8)
- 1/2 = (1 × 4)/(2 × 4) = 4/8

✔ Step 3: Compare numerators

Now we have:
1/8, 4/8, 6/8

So from smallest to largest:
→ 1/8, 1/2, 3/4

✔ Answer for Problem 1:
1/8 → 1/2 → 3/4

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Problem 2: Arrange the fractions in order. Begin with the greatest!

Fractions:
3/4, 2/5, 1/2, 3/10

✔ Step 1: Find a common denominator
Denominators: 4, 5, 2, 10 → LCD is 20

✔ Step 2: Convert all to denominator 20

- 3/4 = (3 × 5)/(4 × 5) = 15/20
- 2/5 = (2 × 4)/(5 × 4) = 8/20
- 1/2 = (1 × 10)/(2 × 10) = 10/20
- 3/10 = (3 × 2)/(10 × 2) = 6/20

✔ Step 3: Compare numerators (from greatest to smallest)

Numerators: 15, 10, 8, 6 → so order is:
15/20 > 10/20 > 8/20 > 6/20

Which means:
→ 3/4 > 1/2 > 2/5 > 3/10

✔ Answer for Problem 2:
3/4 → 1/2 → 2/5 → 3/10

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Problem 3: Arrange the fractions in order. Begin with the greatest!

Fractions:
4/5, 1/2, 4/6, 7/10

✔ Step 1: Find a common denominator
Denominators: 5, 2, 6, 10 → LCD is 30

✔ Step 2: Convert all to denominator 30

- 4/5 = (4 × 6)/(5 × 6) = 24/30
- 1/2 = (1 × 15)/(2 × 15) = 15/30
- 4/6 = (4 × 5)/(6 × 5) = 20/30
- 7/10 = (7 × 3)/(10 × 3) = 21/30

✔ Step 3: Compare numerators (greatest to smallest)

Numerators: 24, 21, 20, 15 → so order is:
24/30 > 21/30 > 20/30 > 15/30

Which means:
→ 4/5 > 7/10 > 4/6 > 1/2

*(Note: 4/6 can be simplified to 2/3, but since we’re comparing, converting to common denominator is fine.)*

✔ Answer for Problem 3:
4/5 → 7/10 → 4/6 → 1/2

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## ✔ Final Answers:

1. Smallest to Greatest:

1/8 → 1/2 → 3/4

2. Greatest to Smallest:

3/4 → 1/2 → 2/5 → 3/10

3. Greatest to Smallest:

4/5 → 7/10 → 4/6 → 1/2

You can now fill in the boxes on your worksheet accordingly! 🎉