Ordering fractions worksheet with mixed numbers for math practice.

Let’s solve each problem step by step. We need to order the mixed numbers from smallest to largest (increasing order).

To compare mixed numbers, we can:
1. Look at the whole number part first — smaller whole number = smaller number.
2. If whole numbers are the same, compare the fractions by finding a common denominator or converting to decimals.

We’ll go one by one.

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Problem 1:
2 ³⁄₁₀ , 3 ²⁄₅ , 1 ¹⁄₂₀ , 2 ²⁄₁₅

Whole numbers: 2, 3, 1, 2 → So 1 ¹⁄₂₀ is smallest.

Now compare the two with whole number 2: 2 ³⁄₁₀ and 2 ²⁄₁₅
Compare ³⁄₁₀ and ²⁄₁₅
LCM of 10 and 15 is 30.
³⁄₁₀ = 9⁄30, ²⁄₁₅ = 4⁄30 → so 2 ²⁄₁₅ < 2 ³⁄₁₀

Then 3 ²⁄₅ is largest.

Order:
1 ¹⁄₂₀ , 2 ²⁄₁₅ , 2 ³⁄₁₀ , 3 ²⁄₅

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Problem 2:
1 ¹⁄₁₂ , 3 ⁵⁄₆ , 1 ⁷⁄₁₈ , 5 ²⁄₃

Whole numbers: 1, 3, 1, 5 → So 5 ²⁄₃ is largest, then 3 ⁵⁄₆.

Now compare the two with whole number 1: 1 ¹⁄₁₂ and 1 ⁷⁄₁₈
Compare ¹⁄₁₂ and ⁷⁄₁₈
LCM of 12 and 18 is 36.
¹⁄₁₂ = 3⁄36, ⁷⁄₁₈ = 14⁄36 → so 1 ¹⁄₁₂ < 1 ⁷⁄₁₈

Order:
1 ¹⁄₁₂ , 1 ⁷⁄₁₈ , 3 ⁵⁄₆ , 5 ²⁄₃

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Problem 3:
1 ⁵⁄₈ , 2 ³⁄₄ , 3 ¹⁄₂ , 2 ³⁄₁₀

Whole numbers: 1, 2, 3, 2 → So 1 ⁵₈ is smallest, then 3 ¹⁄₂ is largest.

Now compare the two with whole number 2: 2 ³⁄₄ and 2 ³⁄₁₀
Compare ³⁄₄ and ³⁄₁₀ → since numerators are same, larger denominator = smaller fraction → ³⁄₁₀ < ³⁄₄

So order:
1 ⁵⁄ , 2 ³₁₀ , 2 ³⁄₄ , 3 ¹⁄₂

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Problem 4:
5 ¹⁄₄ , 1 ³⁄₈ , 3 ¹⁄₂ , 2 ⁵₆

Whole numbers: 5, 1, 3, 2 → So order by whole numbers:
1 ³⁄₈ , 2 ⁵⁄ , 3 ¹₂ , 5 ¹⁄₄

No ties in whole numbers, so done.

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Problem 5:
1 ¹⁄₁₂ , 3 ⁵⁄ , 2 ¹₁₂ , 1 ⁷⁄₁₈

Whole numbers: 1, 3, 2, 1 → So 3 ⁵₆ is largest.

Now group the 1s: 1 ¹⁄₁₂ and 1 ⁷₁₈
As before: ¹⁄₁₂ = 3⁄36, ⁷⁄₁₈ = 14⁄36 → so 1 ¹⁄₁₂ < 1 ⁷⁄₁₈

Then 2 ¹⁄₁₂ comes next.

Order:
1 ¹⁄₁₂ , 1 ⁷⁄₁₈ , 2 ¹⁄₁₂ , 3 ⁵⁄₆

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Problem 6:
2 ³⁄₁₀ , 1 ³⁄₅ , 2 ¹¹⁄₂₀ , 3 ²⁄₁₅

Whole numbers: 2, 1, 2, 3 → So 1 ³⁄₅ is smallest, 3 ²⁄₁₅ is largest.

Now compare the two 2s: 2 ³⁄₁₀ and 2 ¹¹₂₀
Convert to twentieths: ³⁄₁₀ = 6⁄20, ¹¹⁄₂₀ = 11⁄20 → so 2 ³⁄₁₀ < 2 ¹¹₂₀

Order:
1 ³⁄₅ , 2 ³⁄₁₀ , 2 ¹¹⁄₂₀ , 3 ²⁄₁₅

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Problem 7:
3 ¹⁄₁₀ , 2 ³⁄₂₀ , 5 ⁴⁄₅ , 1 ⁹⁄₂₅

Whole numbers: 3, 2, 5, 1 → Order by whole numbers:
1 ⁹₂₅ , 2³⁄₂₀ , 3 ¹⁄₁₀ , 5 ⁴₅

Done.

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Problem 8:
2 ⁄₁₅ , 3 ²⁄₉ , 2 ⁵₁₂ , 1 ¹⁄₁₈

Whole numbers: 2, 3, 2, 1 → So 1 ¹⁄₁₈ is smallest, 3 ²⁄₉ is largest.

Now compare the two 2s: 2 ⁷₁₅ and 2⁵⁄₁₂
Find LCM of 15 and 12 → 60
⁷⁄₁₅ = 28⁄60, ⁵⁄₁₂ = 25⁄60 → so 2 ⁵₁₂ < 2 ⁷⁄₁₅

Order:
1 ¹⁄₁₈ , 2 ⁵⁄₁₂ , 2 ⁷₁₅ , 3²⁄₉

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Problem 9:
2 ⁷⁄₈ , 1 ¹⁄₁₂ , 3 ⁵⁄₆ , 3 ³⁄₄

Whole numbers: 2, 1, 3, 3 → So 1 ¹⁄₁₂ is smallest.

Then 2 ⁷⁄₈.

Now compare the two 3s: 3 ⁵⁄ and 3 ³₄
LCM of 6 and 4 is 12.
⁵⁄₆ = 10⁄12, ³⁄₄ = 9⁄12 → so 3 ³⁄₄ < 3 ⁵₆

Order:
1 ¹⁄₁₂ , 2 ⁷⁄₈ , 3 ³⁄₄ , 3 ⁵₆

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Problem 10:
2 ¹⁄₁₂ , 1 ⁵⁄₈ , 3 ¹⁄₄ , 1 ⁷⁄₁₆

Whole numbers: 2, 1, 3, 1 → So 3 ¹⁄₄ is largest.

Group the 1s: 1 ⁵₈ and 1 ⁷⁄₁₆
Convert to sixteenths: ⁵⁄₈ = 10⁄16, ⁷⁄₁₆ = 7⁄16 → so 1 ⁷⁄₁₆ < 1 ⁵⁄

Then 2 ¹⁄₁₂ comes next.

Order:
1 ⁷⁄₁₆ , 1 ⁵⁄₈ , 2 ¹⁄₁₂ , 3 ¹⁄₄

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Final Answer:

1) 1 ¹⁄₂₀ , 2 ²⁄₁₅ , 2 ³⁄₁₀ , 3 ²⁄₅
2) 1 ¹⁄₁₂ , 1 ⁷⁄₁₈ , 3 ⁵⁄₆ , 5 ²⁄₃
3) 1 ⁵⁄₈ , 2 ³⁄₁₀ , 2 ³⁄₄ , 3 ¹⁄₂
4) 1 ³⁄₈ , 2 ⁵⁄₆ , 3 ¹⁄₂ , 5 ¹⁄₄
5) 1 ¹⁄₁₂ , 1 ⁷⁄₁₈ , 2 ¹⁄₁₂ , 3 ⁵⁄₆
6) 1 ³⁄₅ , 2 ³⁄₁₀ , 2 ¹¹⁄₂₀ , 3 ²⁄₁₅
7) 1 ⁹⁄₂₅ , 2 ³⁄₂₀ , 3 ¹⁄₁₀ , 5 ⁴⁄₅
8) 1 ¹⁄₁₈ , 2 ⁵⁄₁₂ , 2 ⁷₁₅ , 3 ²⁄₉
9) 1 ¹⁄₁₂ , 2 ⁷⁄₈ , 3 ³⁄₄ , 3 ⁵₆
10) 1 ⁷⁄₁₆ , 1 ⁵⁄ , 2 ¹₁₂ , 3 ¹⁄₄