Adding and Subtracting Mixed Numbers | Worksheet - Free Printable

Let's solve each problem step by step using the method shown in the example:

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Example Review:

We are adding and subtracting mixed numbers with unlike denominators.

Steps:
1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with that common denominator.
3. Add or subtract the fractions.
4. Simplify and convert back to a mixed number if needed.

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Problem 1:

$ 3\frac{5}{6} + 1\frac{3}{4} = ? $

Step 1: Find a common denominator.
Denominators: 6 and 4 → LCM is 12.

Step 2: Convert to equivalent fractions.
- $ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} $
- $ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $

Now:
- $ 3\frac{5}{6} = 3\frac{10}{12} $
- $ 1\frac{3}{4} = 1\frac{9}{12} $

Step 3: Add the whole numbers and fractions.
- Whole numbers: $ 3 + 1 = 4 $
- Fractions: $ \frac{10}{12} + \frac{9}{12} = \frac{19}{12} $

Step 4: Simplify and convert.
- $ \frac{19}{12} = 1\frac{7}{12} $
- Total: $ 4 + 1\frac{7}{12} = 5\frac{7}{12} $

✔ Answer: $ 5\frac{7}{12} $

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Problem 2:

$ 6\frac{1}{6} - 3\frac{1}{4} = ? $

Step 1: Common denominator of 6 and 4 → LCM = 12

Step 2: Convert fractions.
- $ \frac{1}{6} = \frac{2}{12} $
- $ \frac{1}{4} = \frac{3}{12} $

So:
- $ 6\frac{1}{6} = 6\frac{2}{12} $
- $ 3\frac{1}{4} = 3\frac{3}{12} $

Step 3: Subtract.
- Whole numbers: $ 6 - 3 = 3 $
- But $ \frac{2}{12} < \frac{3}{12} $, so we need to borrow.

Borrow 1 from 6 → $ 6\frac{2}{12} = 5 + 1 + \frac{2}{12} = 5 + \frac{12}{12} + \frac{2}{12} = 5\frac{14}{12} $

Now subtract:
- $ 5\frac{14}{12} - 3\frac{3}{12} = (5 - 3) + (\frac{14}{12} - \frac{3}{12}) = 2 + \frac{11}{12} $

✔ Answer: $ 2\frac{11}{12} $

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Problem 3:

$ 4\frac{1}{3} + 3\frac{5}{6} = ? $

Common denominator of 3 and 6 → 6

Convert:
- $ \frac{1}{3} = \frac{2}{6} $
- So $ 4\frac{1}{3} = 4\frac{2}{6} $
- $ 3\frac{5}{6} $ stays same

Add:
- Whole numbers: $ 4 + 3 = 7 $
- Fractions: $ \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1\frac{1}{6} $
- Total: $ 7 + 1\frac{1}{6} = 8\frac{1}{6} $

✔ Answer: $ 8\frac{1}{6} $

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Problem 4:

$ 4\frac{1}{4} + 1\frac{1}{3} = ? $

LCM of 4 and 3 → 12

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

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

Add:
- Whole: $ 4 + 1 = 5 $
- Fraction: $ \frac{3}{12} + \frac{4}{12} = \frac{7}{12} $

✔ Answer: $ 5\frac{7}{12} $

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Problem 5:

$ 3\frac{3}{4} + 2\frac{2}{3} = ? $

LCM of 4 and 3 → 12

Convert:
- $ \frac{3}{4} = \frac{9}{12} $
- $ \frac{2}{3} = \frac{8}{12} $

So:
- $ 3\frac{3}{4} = 3\frac{9}{12} $
- $ 2\frac{2}{3} = 2\frac{8}{12} $

Add:
- Whole: $ 3 + 2 = 5 $
- Fraction: $ \frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1\frac{5}{12} $
- Total: $ 5 + 1\frac{5}{12} = 6\frac{5}{12} $

✔ Answer: $ 6\frac{5}{12} $

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Problem 6:

$ 5\frac{1}{2} - 3\frac{1}{3} = ? $

LCM of 2 and 3 → 6

Convert:
- $ \frac{1}{2} = \frac{3}{6} $
- $ \frac{1}{3} = \frac{2}{6} $

So:
- $ 5\frac{1}{2} = 5\frac{3}{6} $
- $ 3\frac{1}{3} = 3\frac{2}{6} $

Subtract:
- Whole: $ 5 - 3 = 2 $
- Fraction: $ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} $

✔ Answer: $ 2\frac{1}{6} $

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Problem 7:

$ 7\frac{1}{8} - 6\frac{1}{4} = ? $

LCM of 8 and 4 → 8

Convert:
- $ \frac{1}{4} = \frac{2}{8} $
- So $ 6\frac{1}{4} = 6\frac{2}{8} $

Now:
- $ 7\frac{1}{8} - 6\frac{2}{8} $

But $ \frac{1}{8} < \frac{2}{8} $, so borrow.

$ 7\frac{1}{8} = 6 + 1 + \frac{1}{8} = 6 + \frac{8}{8} + \frac{1}{8} = 6\frac{9}{8} $

Now subtract:
- $ 6\frac{9}{8} - 6\frac{2}{8} = (6 - 6) + (\frac{9}{8} - \frac{2}{8}) = \frac{7}{8} $

✔ Answer: $ \frac{7}{8} $

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Problem 8:

$ 11\frac{1}{6} - 5\frac{1}{3} = ? $

LCM of 6 and 3 → 6

Convert:
- $ \frac{1}{3} = \frac{2}{6} $
- So $ 5\frac{1}{3} = 5\frac{2}{6} $

Now:
- $ 11\frac{1}{6} - 5\frac{2}{6} $

But $ \frac{1}{6} < \frac{2}{6} $, so borrow.

$ 11\frac{1}{6} = 10 + 1 + \frac{1}{6} = 10 + \frac{6}{6} + \frac{1}{6} = 10\frac{7}{6} $

Now subtract:
- $ 10\frac{7}{6} - 5\frac{2}{6} = (10 - 5) + (\frac{7}{6} - \frac{2}{6}) = 5 + \frac{5}{6} $

✔ Answer: $ 5\frac{5}{6} $

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✔ Final Answers:

1. $ 5\frac{7}{12} $
2. $ 2\frac{11}{12} $
3. $ 8\frac{1}{6} $
4. $ 5\frac{7}{12} $
5. $ 6\frac{5}{12} $
6. $ 2\frac{1}{6} $
7. $ \frac{7}{8} $
8. $ 5\frac{5}{6} $

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