Adding and Subtracting Two Mixed Fractions with Unlike ... - Free Printable

Let’s solve each problem step by step. We’ll convert mixed numbers to improper fractions, find a common denominator, add or subtract, then simplify and convert back to mixed numbers if needed.

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1. 4 ⁄₈ – 2 ¹⁶⁄₁₉

First, simplify ⁴⁄ → ¹⁄₂
So: 4 ¹⁄₂ – 2 ¹⁶⁄₁₉

Convert to improper fractions:

4 ¹⁄₂ = (4×2 + 1)/2 = 9/2
2 ¹⁶⁄₁₉ = (2×19 + 16)/19 = 54/19

Find LCD of 2 and 19 → 38

9/2 = (9×19)/(2×19) = 171/38
54/19 = (54×2)/(19×2) = 108/38

Subtract: 171/38 – 108/38 = 63/38

Convert to mixed number: 63 ÷ 38 = 1 remainder 25 → 1 ²⁵⁄₈

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2. 1 ⁵⁄₆ + 3 ⁷⁄₁₃

Convert:

1 ⁵₆ = (6+5)/6 = 11/6
3 ⁷⁄₁₃ = (39+7)/13 = 46/13

LCD of 6 and 13 → 78

11/6 = (11×13)/78 = 143/78
46/13 = (46×6)/78 = 276/78

Add: 143 + 276 = 419 → 419/78

Divide: 419 ÷ 78 = 5 remainder 29 → 5 ²⁹⁄₇

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3. 5 ¹⁄₃ – 3 ¹⁄₄

Convert:

5 ¹⁄₃ = 16/3
3 ¹⁄₄ = 13/4

LCD of 3 and 4 → 12

16/3 = 64/12
13/4 = 39/12

Subtract: 64 – 39 = 25 → 25/12

Mixed number: 25 ÷ 12 = 2 r1 → 2 ¹⁄₁₂

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4. 4 ¹⁄₃ + 1 ¹⁄₁₃

Convert:

4 ¹⁄₃ = 13/3
1 ¹⁄₁₃ = 14/13

LCD of 3 and 13 → 39

13/3 = 169/39
14/13 = 42/39

Add: 169 + 42 = 211 → 211/39

Divide: 211 ÷ 39 = 5 r16 → 5 ¹⁶⁄₃₉

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5. 4 ⁶⁄₈ + 1 ²⁄₅

Simplify ⁶⁄ → ³⁄₄

So: 4 ³⁄₄ + 1 ²⁄₅

Convert:

4 ³⁄₄ = 19/4
1 ²⁄₅ = 7/5

LCD of 4 and 5 → 20

19/4 = 95/20
7/5 = 28/20

Add: 95 + 28 = 123 → 123/20

Mixed: 123 ÷ 20 = 6 r3 → 6 ³⁄₂₀

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6. 4 ²⁄₆ + 1 ³⁄₅

Simplify ²⁄₆ → ¹⁄₃

So: 4 ¹⁄₃ + 1 ³⁄₅

Convert:

4 ¹⁄₃ = 13/3
1 ³⁄₅ = 8/5

LCD of 3 and 5 → 15

13/3 = 65/15
8/5 = 24/15

Add: 65 + 24 = 89 → 89/15

Mixed: 89 ÷ 15 = 5 r14 → 5 ¹⁴⁄₁₅

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7. 3 ²⁄₃ + 2 ³⁄₁₆

Convert:

3 ²⁄₃ = 11/3
2 ³⁄₁₆ = 35/16

LCD of 3 and 16 → 48

11/3 = 176/48
35/16 = 105/48

Add: 176 + 105 = 281 → 281/48

Mixed: 281 ÷ 48 = 5 r41 → 5 ⁴¹⁄₄₈

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8. 2 ²⁄₅ – 1 ¹⁄₂

Convert:

2 ²⁄₅ = 12/5
1 ¹⁄₂ = 3/2

LCD of 5 and 2 → 10

12/5 = 24/10
3/2 = 15/10

Subtract: 24 – 15 = 9 → 9/10 → ⁹⁄₁₀

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9. 4 ²⁄₄ – 2 ⁵⁄

Simplify ²₄ → ¹⁄₂

So: 4 ¹⁄₂ – 2 ⁵₉

Convert:

4 ¹⁄₂ = 9/2
2 ⁵⁄ = 23/9

LCD of 2 and 9 → 18

9/2 = 81/18
23/9 = 46/18

Subtract: 81 – 46 = 35 → 35/18

Mixed: 35 ÷ 18 = 1 r17 → 1 ¹⁷⁄₁₈

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10. 4 ²⁄₅ – 1 ⁵₉

Convert:

4 ²⁄₅ = 22/5
1 ⁵⁄ = 14/9

LCD of 5 and 9 → 45

22/5 = 198/45
14/9 = 70/45

Subtract: 198 – 70 = 128 → 128/45

Mixed: 128 ÷ 45 = 2 r38 → 2 ³⁸⁄₅

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Final Answer:
1. 1 ²⁵⁄₈
2. 5 ²⁹⁄₇₈
3. 2 ¹⁄₁₂
4. 5 ¹⁶⁄₃₉
5. 6 ³⁄₂₀
6. 5 ¹⁴⁄₁₅
7. 5 ⁴¹⁄₄₈
8. ⁹⁄₁₀
9. 1 ¹⁷⁄₁₈
10. 2 ³⁸⁄₅