Ordering Fractions worksheet for practicing arranging fractions from least to greatest.

Let’s solve each problem step by step. We need to order each set of fractions from smallest to largest (increasing order). To do this, we’ll find a common denominator for each set so we can compare the numerators easily.

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Problem 1:
Fractions:
3/4, 2/6, 1/12, 5/18, 4/9

Find LCM of denominators: 4, 6, 12, 18, 9 → LCM = 36

Convert all to 36ths:
- 3/4 = 27/36
- 2/6 = 12/36
- 1/12 = 3/36
- 5/18 = 10/36
- 4/9 = 16/36

Order by numerator: 3, 10, 12, 16, 27 →
So: 1/12, 5/18, 2/6, 4/9, 3/4

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Problem 2:
Fractions:
4/8, 7/16, 5/12, 1/8, 3/12

Simplify first if possible:
- 4/8 = 1/2
- 3/12 = 1/4

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

LCM of 2, 16, 12, 8, 4 → LCM = 48

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

Order: 6, 12, 20, 21, 24 →
So: 1/8, 1/4, 5/12, 7/16, 1/2
But original forms: 1/8, 3/12, 5/12, 7/16, 4/8

Wait — let’s use original fractions without simplifying to avoid confusion.

Original: 4/8, 7/16, 5/12, 1/8, 3/12

LCM of 8,16,12,8,12 → LCM = 48

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

Same as above → Order: 6,12,20,21,24 →
1/8, 3/12, 5/12, 7/16, 4/8

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Problem 3:
Fractions:
3/8, 1/4, 4/10, 3/6, 5/8

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

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

LCM of 8,4,5,2,8 → LCM = 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 →
So: 1/4, 3/8, 2/5, 1/2, 5/8
Back to originals: 1/4, 3/8, 4/10, 3/6, 5/8

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Problem 4:
Fractions:
2/5, 9/15, 8/10, 7/20, 1/5

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

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

LCM of 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 →
So: 1/5, 7/20, 2/5, 9/15, 8/10

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Problem 5:
Fractions:
4/9, 9/12, 5/6, 3/18, 1/3

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

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

LCM of 9,4,6,6,3 → LCM = 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 →
So: 1/6, 1/3, 4/9, 3/4, 5/6
Back to originals: 3/18, 1/3, 4/9, 9/12, 5/6

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Problem 6:
Fractions:
5/8, 7/16, 3/4, 1/4, 12/24

Simplify:
- 12/24 = 1/2

Now: 5/8, 7/16, 3/4, 1/4, 1/2

LCM of 8,16,4,4,2 → LCM = 16

Convert:
- 5/8 = 10/16
- 7/16 = 7/16
- 3/4 = 12/16
- 1/4 = 4/16
- 1/2 = 8/16

Order: 4,7,8,10,12 →
So: 1/4, 7/16, 1/2, 5/8, 3/4
Back to originals: 1/4, 7/16, 12/24, 5/8, 3/4

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Problem 7:
Fractions:
7/10, 2/5, 9/20, 5/15, 10/20

Simplify:
- 5/15 = 1/3
- 10/20 = 1/2

Now: 7/10, 2/5, 9/20, 1/3, 1/2

LCM of 10,5,20,3,2 → LCM = 60

Convert:
- 7/10 = 42/60
- 2/5 = 24/60
- 9/20 = 27/60
- 1/3 = 20/60
- 1/2 = 30/60

Order: 20,24,27,30,42 →
So: 1/3, 2/5, 9/20, 1/2, 7/10
Back to originals: 5/15, 2/5, 9/20, 10/20, 7/10

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Problem 8:
Fractions:
9/15, 5/12, 7/18, 4/9, 1/6

Simplify:
- 9/15 = 3/5

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

LCM of 5,12,18,9,6 → LCM = 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 →
So: 1/6, 7/18, 5/12, 4/9, 3/5
Back to originals: 1/6, 7/18, 5/12, 4/9, 9/15

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Problem 9:
Fractions:
4/9, 2/6, 15/21, 7/12, 9/18

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

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

LCM of 9,3,7,12,2 → LCM = 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 →
So: 1/3, 4/9, 1/2, 7/12, 5/7
Back to originals: 2/6, 4/9, 9/18, 7/12, 15/21

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Problem 10:
Fractions:
1/25, 7/15, 9/25, 3/10, 2/5

LCM of 25,15,25,10,5 → LCM = 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 →
So: 1/25, 3/10, 9/25, 2/5, 7/15

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Final Answer:

1) 1/12, 5/18, 2/6, 4/9, 3/4
2) 1/8, 3/12, 5/12, 7/16, 4/8
3) 1/4, 3/8, 4/10, 3/6, 5/8
4) 1/5, 7/20, 2/5, 9/15, 8/10
5) 3/18, 1/3, 4/9, 9/12, 5/6
6) 1/4, 7/16, 12/24, 5/8, 3/4
7) 5/15, 2/5, 9/20, 10/20, 7/10
8) 1/6, 7/18, 5/12, 4/9, 9/15
9) 2/6, 4/9, 9/18, 7/12, 15/21
10) 1/25, 3/10, 9/25, 2/5, 7/15