Order fractions worksheet for math practice.

Let's solve each problem on the "Ordering Fractions" worksheet step by step. The goal is to order each set of unlike fractions (fractions with different denominators) in increasing order.

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🔧 Strategy:

To compare unlike fractions, we can:
1. Find a common denominator for all fractions.
2. Convert each fraction to an equivalent fraction with that common denominator.
3. Compare the numerators and order them accordingly.

Alternatively, convert each fraction to a decimal for easier comparison.

We’ll use LCM (Least Common Multiple) method to find a common denominator when possible.

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Let’s go through each problem:

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1) 3/4, 2/6, 1/12, 5/18, 4/9

First, simplify where possible:
- 2/6 = 1/3

Now list: 3/4, 1/3, 1/12, 5/18, 4/9

Find LCM of denominators: 4, 3, 12, 18, 9
Prime factors:
- 4 = 2²
- 3 = 3
- 12 = 2² × 3
- 18 = 2 × 3²
- 9 = 3²

LCM = 2² × 3² = 4 × 9 = 36

Convert all to denominator 36:
- 3/4 = (3×9)/(4×9) = 27/36
- 1/3 = 12/36
- 1/12 = 3/36
- 5/18 = (5×2)/(18×2) = 10/36
- 4/9 = (4×4)/(9×4) = 16/36

Now order numerators: 3, 10, 12, 16, 27 → so:
- 1/12, 5/18, 1/3, 4/9, 3/4

✔ Answer:
1/12, 5/18, 1/3, 4/9, 3/4

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2) 4/8, 7/16, 5/12, 1/8, 3/12

Simplify:
- 4/8 = 1/2
- 3/12 = 1/4

So: 1/2, 7/16, 5/12, 1/8, 1/4

Denominators: 2, 16, 12, 8, 4
LCM of 2, 16, 12, 8, 4:

- 16 = 2⁴
- 12 = 2² × 3
- So LCM = 2⁴ × 3 = 16 × 3 = 48

Convert:
- 1/2 = 24/48
- 7/16 = (7×3)/48 = 21/48
- 5/12 = (5×4)/48 = 20/48
- 1/8 = 6/48
- 1/4 = 12/48

Order numerators: 6, 12, 20, 21, 24 →
- 1/8, 1/4, 5/12, 7/16, 1/2

✔ Answer:
1/8, 1/4, 5/12, 7/16, 1/2

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3) 3/8, 1/4, 4/10, 3/6, 5/8

Simplify:
- 4/10 = 2/5
- 3/6 = 1/2

So: 3/8, 1/4, 2/5, 1/2, 5/8

Denominators: 8, 4, 5, 2, 8 → LCM of 8, 4, 5, 2

- 8 = 2³
- 4 = 2²
- 5 = 5
→ LCM = 2³ × 5 = 8 × 5 = 40

Convert:
- 3/8 = 15/40
- 1/4 = 10/40
- 2/5 = 16/40
- 1/2 = 20/40
- 5/8 = 25/40

Order: 10, 15, 16, 20, 25 →
- 1/4, 3/8, 2/5, 1/2, 5/8

✔ Answer:
1/4, 3/8, 2/5, 1/2, 5/8

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4) 2/5, 9/15, 8/10, 7/20, 1/5

Simplify:
- 9/15 = 3/5
- 8/10 = 4/5

So: 2/5, 3/5, 4/5, 7/20, 1/5

Denominators: 5, 5, 5, 20, 5 → LCM = 20

Convert:
- 2/5 = 8/20
- 3/5 = 12/20
- 4/5 = 16/20
- 7/20 = 7/20
- 1/5 = 4/20

Order: 4, 7, 8, 12, 16 →
- 1/5, 7/20, 2/5, 3/5, 4/5

✔ Answer:
1/5, 7/20, 2/5, 3/5, 4/5

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5) 4/9, 9/12, 5/6, 3/18, 1/3

Simplify:
- 9/12 = 3/4
- 3/18 = 1/6

So: 4/9, 3/4, 5/6, 1/6, 1/3

Denominators: 9, 4, 6, 6, 3 → LCM of 9, 4, 6, 3

- 9 = 3²
- 4 = 2²
- 6 = 2 × 3
→ LCM = 2² × 3² = 4 × 9 = 36

Convert:
- 4/9 = 16/36
- 3/4 = 27/36
- 5/6 = 30/36
- 1/6 = 6/36
- 1/3 = 12/36

Order: 6, 12, 16, 27, 30 →
- 1/6, 1/3, 4/9, 3/4, 5/6

✔ Answer:
1/6, 1/3, 4/9, 3/4, 5/6

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6) 5/8, 7/4, 3/4, 1/4, 12/24

Simplify:
- 12/24 = 1/2

So: 5/8, 7/4, 3/4, 1/4, 1/2

Denominators: 8, 4, 4, 4, 2 → LCM = 8

Convert:
- 5/8 = 5/8
- 7/4 = 14/8
- 3/4 = 6/8
- 1/4 = 2/8
- 1/2 = 4/8

Order: 2, 4, 5, 6, 14 →
- 1/4, 1/2, 5/8, 3/4, 7/4

✔ Answer:
1/4, 1/2, 5/8, 3/4, 7/4

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7) 7/10, 2/5, 9/20, 5/16, 1/20

Denominators: 10, 5, 20, 16, 20 → LCM of 10, 5, 20, 16

- 10 = 2×5
- 5 = 5
- 20 = 2²×5
- 16 = 2⁴
→ LCM = 2⁴ × 5 = 16 × 5 = 80

Convert:
- 7/10 = 56/80
- 2/5 = 32/80
- 9/20 = 36/80
- 5/16 = 25/80
- 1/20 = 4/80

Order: 4, 25, 32, 36, 56 →
- 1/20, 5/16, 2/5, 9/20, 7/10

✔ Answer:
1/20, 5/16, 2/5, 9/20, 7/10

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8) 9/15, 5/12, 7/18, 4/9, 1/6

Simplify:
- 9/15 = 3/5

So: 3/5, 5/12, 7/18, 4/9, 1/6

Denominators: 5, 12, 18, 9, 6 → LCM of 5, 12, 18, 9, 6

- 5 = 5
- 12 = 2²×3
- 18 = 2×3²
- 9 = 3²
- 6 = 2×3
→ LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180

Convert:
- 3/5 = 108/180
- 5/12 = 75/180
- 7/18 = 70/180
- 4/9 = 80/180
- 1/6 = 30/180

Order: 30, 70, 75, 80, 108 →
- 1/6, 7/18, 5/12, 4/9, 3/5

✔ Answer:
1/6, 7/18, 5/12, 4/9, 3/5

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9) 4/9, 2/6, 15/21, 7/12, 9/18

Simplify:
- 2/6 = 1/3
- 15/21 = 5/7
- 9/18 = 1/2

So: 4/9, 1/3, 5/7, 7/12, 1/2

Denominators: 9, 3, 7, 12, 2 → LCM of 9, 3, 7, 12, 2

- 9 = 3²
- 3 = 3
- 7 = 7
- 12 = 2²×3
- 2 = 2
→ LCM = 2² × 3² × 7 = 4 × 9 × 7 = 252

Convert:
- 4/9 = 112/252
- 1/3 = 84/252
- 5/7 = 180/252
- 7/12 = 147/252
- 1/2 = 126/252

Order: 84, 112, 126, 147, 180 →
- 1/3, 4/9, 1/2, 7/12, 5/7

✔ Answer:
1/3, 4/9, 1/2, 7/12, 5/7

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10) 1/25, 7/15, 9/25, 3/10, 2/5

Denominators: 25, 15, 25, 10, 5 → LCM of 25, 15, 10, 5

- 25 = 5²
- 15 = 3×5
- 10 = 2×5
- 5 = 5
→ LCM = 2 × 3 × 5² = 2 × 3 × 25 = 150

Convert:
- 1/25 = 6/150
- 7/15 = 70/150
- 9/25 = 54/150
- 3/10 = 45/150
- 2/5 = 60/150

Order: 6, 45, 54, 60, 70 →
- 1/25, 3/10, 9/25, 2/5, 7/15

✔ Answer:
1/25, 3/10, 9/25, 2/5, 7/15

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✔ Final Answers:

1) 1/12, 5/18, 1/3, 4/9, 3/4
2) 1/8, 1/4, 5/12, 7/16, 1/2
3) 1/4, 3/8, 2/5, 1/2, 5/8
4) 1/5, 7/20, 2/5, 3/5, 4/5
5) 1/6, 1/3, 4/9, 3/4, 5/6
6) 1/4, 1/2, 5/8, 3/4, 7/4
7) 1/20, 5/16, 2/5, 9/20, 7/10
8) 1/6, 7/18, 5/12, 4/9, 3/5
9) 1/3, 4/9, 1/2, 7/12, 5/7
10) 1/25, 3/10, 9/25, 2/5, 7/15

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