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

We are given a worksheet titled “Adding and Subtracting Two Mixed Fractions (A)” with 10 problems. We need to calculate each result.

Mixed fractions consist of a whole number and a proper fraction. To add or subtract them, we typically:

1. Convert mixed numbers to improper fractions (optional but helpful for some),
2. Find a common denominator for the fractional parts,
3. Add or subtract the whole numbers and fractions separately (or combine everything into improper fractions),
4. Simplify the result and convert back to a mixed number if needed.

Let’s solve each problem step by step.

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Problem 1:

> $ 4\frac{1}{8} - 2\frac{16}{19} $

This is tricky because $ \frac{16}{19} > \frac{1}{8} $, so we’ll need to borrow from the whole number.

Step 1: Convert both to improper fractions.

- $ 4\frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8} $
- $ 2\frac{16}{19} = \frac{2 \times 19 + 16}{19} = \frac{54}{19} $

Step 2: Find LCD of 8 and 19 → 152

Convert:
- $ \frac{33}{8} = \frac{33 \times 19}{152} = \frac{627}{152} $
- $ \frac{54}{19} = \frac{54 \times 8}{152} = \frac{432}{152} $

Step 3: Subtract:
$ \frac{627 - 432}{152} = \frac{195}{152} $

Step 4: Simplify:
$ \frac{195}{152} = 1\frac{43}{152} $ — already in simplest form (GCF of 195 and 152 is 1).

✔ Answer: $ 1\frac{43}{152} $

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Problem 2:

> $ 1\frac{5}{6} + 3\frac{7}{13} $

Add whole numbers and fractions separately.

Whole numbers: $ 1 + 3 = 4 $

Fractions: $ \frac{5}{6} + \frac{7}{13} $

LCD of 6 and 13 = 78

- $ \frac{5}{6} = \frac{65}{78} $
- $ \frac{7}{13} = \frac{42}{78} $
- Sum: $ \frac{65 + 42}{78} = \frac{107}{78} = 1\frac{29}{78} $

Now add to whole part: $ 4 + 1\frac{29}{78} = 5\frac{29}{78} $

✔ Answer: $ 5\frac{29}{78} $

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Problem 3:

> $ 5\frac{1}{3} - 3\frac{1}{4} $

Whole numbers: $ 5 - 3 = 2 $

Fractions: $ \frac{1}{3} - \frac{1}{4} $

LCD = 12

- $ \frac{1}{3} = \frac{4}{12} $
- $ \frac{1}{4} = \frac{3}{12} $
- Difference: $ \frac{1}{12} $

Total: $ 2 + \frac{1}{12} = 2\frac{1}{12} $

✔ Answer: $ 2\frac{1}{12} $

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Problem 4:

> $ 4\frac{1}{3} + 1\frac{1}{13} $

Whole numbers: $ 4 + 1 = 5 $

Fractions: $ \frac{1}{3} + \frac{1}{13} $

LCD = 39

- $ \frac{1}{3} = \frac{13}{39} $
- $ \frac{1}{13} = \frac{3}{39} $
- Sum: $ \frac{16}{39} $

Total: $ 5\frac{16}{39} $

✔ Answer: $ 5\frac{16}{39} $

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Problem 5:

> $ 4\frac{6}{8} + 1\frac{2}{5} $

First, simplify $ \frac{6}{8} = \frac{3}{4} $, so $ 4\frac{6}{8} = 4\frac{3}{4} $

Whole numbers: $ 4 + 1 = 5 $

Fractions: $ \frac{3}{4} + \frac{2}{5} $

LCD = 20

- $ \frac{3}{4} = \frac{15}{20} $
- $ \frac{2}{5} = \frac{8}{20} $
- Sum: $ \frac{23}{20} = 1\frac{3}{20} $

Total: $ 5 + 1\frac{3}{20} = 6\frac{3}{20} $

✔ Answer: $ 6\frac{3}{20} $

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Problem 6:

> $ 4\frac{2}{6} + 1\frac{3}{5} $

Simplify $ \frac{2}{6} = \frac{1}{3} $, so $ 4\frac{2}{6} = 4\frac{1}{3} $

Whole numbers: $ 4 + 1 = 5 $

Fractions: $ \frac{1}{3} + \frac{3}{5} $

LCD = 15

- $ \frac{1}{3} = \frac{5}{15} $
- $ \frac{3}{5} = \frac{9}{15} $
- Sum: $ \frac{14}{15} $

Total: $ 5\frac{14}{15} $

✔ Answer: $ 5\frac{14}{15} $

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Problem 7:

> $ 3\frac{2}{3} + 2\frac{3}{16} $

Whole numbers: $ 3 + 2 = 5 $

Fractions: $ \frac{2}{3} + \frac{3}{16} $

LCD = 48

- $ \frac{2}{3} = \frac{32}{48} $
- $ \frac{3}{16} = \frac{9}{48} $
- Sum: $ \frac{41}{48} $

Total: $ 5\frac{41}{48} $

✔ Answer: $ 5\frac{41}{48} $

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Problem 8:

> $ 2\frac{2}{5} - 1\frac{1}{2} $

Whole numbers: $ 2 - 1 = 1 $

Fractions: $ \frac{2}{5} - \frac{1}{2} $

LCD = 10

- $ \frac{2}{5} = \frac{4}{10} $
- $ \frac{1}{2} = \frac{5}{10} $

Since $ \frac{4}{10} < \frac{5}{10} $, we borrow 1 from the whole number.

So: $ 1 + \frac{4}{10} = \frac{14}{10} $, then subtract $ \frac{5}{10} $

→ $ \frac{14}{10} - \frac{5}{10} = \frac{9}{10} $

But since we borrowed 1, the whole number becomes 0.

✔ Answer: $ \frac{9}{10} $

*(Note: This is a proper fraction, not mixed — acceptable as final answer)*

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Problem 9:

> $ 4\frac{2}{4} - 2\frac{5}{9} $

Simplify $ \frac{2}{4} = \frac{1}{2} $, so $ 4\frac{2}{4} = 4\frac{1}{2} $

Whole numbers: $ 4 - 2 = 2 $

Fractions: $ \frac{1}{2} - \frac{5}{9} $

LCD = 18

- $ \frac{1}{2} = \frac{9}{18} $
- $ \frac{5}{9} = \frac{10}{18} $

Again, $ \frac{9}{18} < \frac{10}{18} $, so borrow 1 from whole number.

New whole number: $ 1 $

Fraction: $ \frac{9}{18} + \frac{18}{18} = \frac{27}{18} $

Now subtract: $ \frac{27}{18} - \frac{10}{18} = \frac{17}{18} $

Total: $ 1\frac{17}{18} $

✔ Answer: $ 1\frac{17}{18} $

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Problem 10:

> $ 4\frac{2}{5} - 1\frac{5}{9} $

Whole numbers: $ 4 - 1 = 3 $

Fractions: $ \frac{2}{5} - \frac{5}{9} $

LCD = 45

- $ \frac{2}{5} = \frac{18}{45} $
- $ \frac{5}{9} = \frac{25}{45} $

Since $ \frac{18}{45} < \frac{25}{45} $, borrow 1 from 3 → becomes 2

Fraction becomes: $ \frac{18}{45} + \frac{45}{45} = \frac{63}{45} $

Subtract: $ \frac{63}{45} - \frac{25}{45} = \frac{38}{45} $

Total: $ 2\frac{38}{45} $

✔ Answer: $ 2\frac{38}{45} $

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## ✔ Final Answers:

1. $ \boxed{1\frac{43}{152}} $
2. $ \boxed{5\frac{29}{78}} $
3. $ \boxed{2\frac{1}{12}} $
4. $ \boxed{5\frac{16}{39}} $
5. $ \boxed{6\frac{3}{20}} $
6. $ \boxed{5\frac{14}{15}} $
7. $ \boxed{5\frac{41}{48}} $
8. $ \boxed{\frac{9}{10}} $
9. $ \boxed{1\frac{17}{18}} $
10. $ \boxed{2\frac{38}{45}} $

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📌 Note: All answers are simplified and presented as mixed numbers unless the result is a proper fraction (like #8). When subtracting and the fraction part is smaller, we borrowed from the whole number — this is standard procedure.

Let me know if you’d like to see any steps visualized differently!