Ordering Fractions Worksheets - Math Monks - Free Printable

Let’s solve each part step by step.

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Part A: Order these fractions in increasing order: 1/2, 1/3, 1/4, 3/4

We need to compare them. One easy way is to think about how big each piece is if you split something into equal parts.

- 1/4 means 1 out of 4 equal pieces → smallest
- 1/3 means 1 out of 3 equal pieces → bigger than 1/4
- 1/2 means half → bigger than 1/3
- 3/4 means 3 out of 4 pieces → almost all → biggest

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

Now let’s place them on the number line from 0 to 1.

Number line has marks at:
0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1

Place each fraction:

- 1/4 → already marked
- 1/3 → between 1/4 (which is 2/8) and 3/8? Let’s convert to eighths or twelfths to be sure.

Actually, better to use common denominator or decimal approximations for accuracy.

Convert to decimals:

- 1/4 = 0.25
- 1/3 ≈ 0.333
- 1/2 = 0.5
- 3/4 = 0.75

On the number line with eighths:

- 1/4 = 2/8 → mark at 2/8
- 1/3 ≈ 0.333 → between 2/8 (0.25) and 3/8 (0.375) → closer to 3/8 but not exactly — we can estimate it between 2/8 and 3/8
- 1/2 = 4/8 → mark at 4/8
- 3/4 = 6/8 → mark at 6/8

But since the number line shows eighths, we’ll place them as close as possible.

Order on number line left to right:
1/4 (at 2/8), then 1/3 (between 2/8 and 3/8), then 1/2 (at 4/8), then 3/4 (at 6/8)

✔ Final order for A: 1/4, 1/3, 1/2, 3/4

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Part B: Order these mixed numbers: 2 1/6, 1 1/2, 2 1/3, 1 5/6

First, separate whole numbers and fractions.

List them:

- 1 1/2 → 1 + 0.5 = 1.5
- 1 5/6 → 1 + ~0.833 = ~1.833
- 2 1/6 → 2 + ~0.166 = ~2.166
- 2 1/3 → 2 + ~0.333 = ~2.333

So from smallest to largest:

1 1/2 (1.5) < 1 5/6 (~1.833) < 2 1/6 (~2.166) < 2 1/3 (~2.333)

Check using fractions:

Compare 1 1/2 and 1 5/6 → same whole number, compare 1/2 vs 5/6 → 1/2 = 3/6, so 3/6 < 5/6 → so 1 1/2 < 1 5/6

Then 2 1/6 and 2 1/3 → 1/6 < 1/3 → so 2 1/6 < 2 1/3

And obviously 1.something < 2.something

So order:
1 1/2, 1 5/6, 2 1/6, 2 1/3

Now place on number line from 1 to 3, with marks every 1/6.

Marks: 1, 1 1/6, 1 2/6, 1 3/6, 1 4/6, 1 5/6, 2, 2 1/6, 2 2/6, 2 3/6, 2 4/6, 2 5/6, 3

Place:

- 1 1/2 = 1 3/6 → at 1 3/6
- 1 5/6 → at 1 5/6
- 2 1/6 → at 2 1/6
- 2 1/3 = 2 2/6 → at 2 2/6

Perfect — they land exactly on the marks!

✔ Final order for B: 1 1/2, 1 5/6, 2 1/6, 2 1/3

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Part C: Order these fractions: 1/2, 19/30, 4/5, 4/10

Again, convert to decimals or find common denominator.

Decimals:

- 1/2 = 0.5
- 19/30 ≈ 0.633...
- 4/5 = 0.8
- 4/10 = 0.4

So order: 0.4, 0.5, 0.633..., 0.8 →
4/10, 1/2, 19/30, 4/5

Check with fractions:

4/10 = 2/5 = 0.4
1/2 = 0.5
19/30 ≈ 0.633
4/5 = 0.8

Yes.

To place on number line from 0 to 1 with tenths:

Marks: 0, 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 1

Place:

- 4/10 → at 4/10
- 1/2 = 5/10 → at 5/10
- 19/30 → between 6/10 (0.6) and 7/10 (0.7)? 19/30 = 0.633... → between 6/10 and 7/10, closer to 6/10? Actually 6/10=18/30, so 19/30 is just after 6/10 → between 6/10 and 7/10
- 4/5 = 8/10 → at 8/10

So on number line:
4/10, then 1/2 (5/10), then 19/30 (just after 6/10), then 4/5 (8/10)

✔ Final order for C: 4/10, 1/2, 19/30, 4/5

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Part D: Order these fractions: 3/4, 7/8, 1/2, 1/4

Decimals:

- 1/4 = 0.25
- 1/2 = 0.5
- 3/4 = 0.75
- 7/8 = 0.875

Order: 0.25, 0.5, 0.75, 0.875 →
1/4, 1/2, 3/4, 7/8

Place on number line from 0 to 1 with eighths:

Marks: 0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1

Convert:

- 1/4 = 2/8 → at 2/8
- 1/2 = 4/8 → at 4/8
- 3/4 = 6/8 → at 6/8
- 7/8 → at 7/8

Perfect — all land on marks.

✔ Final order for D: 1/4, 1/2, 3/4, 7/8

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Final Answer:

A) 1/4, 1/3, 1/2, 3/4
B) 1 1/2, 1 5/6, 2 1/6, 2 1/3
C) 4/10, 1/2, 19/30, 4/5
D) 1/4, 1/2, 3/4, 7/8