Add Mixed Numbers with Like Denominators Worksheet (examples ... - Free Printable

You're asked to add mixed numbers. Mixed numbers have a whole number part and a fractional part (like $3\frac{9}{11}$).

The key rule for adding mixed numbers with the same denominator is:

> Add the whole numbers together, then add the fractions together. If the fraction sum is improper (≥ 1), convert it to a mixed number and add the whole number part to the total.

Let’s solve each problem step by step.

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1. $3\frac{9}{11} + 6\frac{2}{11}$

- Whole numbers: $3 + 6 = 9$
- Fractions: $\frac{9}{11} + \frac{2}{11} = \frac{11}{11} = 1$
- Total: $9 + 1 = 10$

✔ Answer: 10

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2. $3\frac{7}{12} + 6\frac{4}{12}$

- Whole numbers: $3 + 6 = 9$
- Fractions: $\frac{7}{12} + \frac{4}{12} = \frac{11}{12}$
- Total: $9 + \frac{11}{12} = 9\frac{11}{12}$

✔ Answer: $9\frac{11}{12}$

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3. $6\frac{6}{7} + 9\frac{5}{7}$

- Whole numbers: $6 + 9 = 15$
- Fractions: $\frac{6}{7} + \frac{5}{7} = \frac{11}{7} = 1\frac{4}{7}$
- Add the extra whole number: $15 + 1 = 16$, plus $\frac{4}{7}$
- Total: $16\frac{4}{7}$

✔ Answer: $16\frac{4}{7}$

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4. $2\frac{2}{10} + 7\frac{1}{10}$

- Whole numbers: $2 + 7 = 9$
- Fractions: $\frac{2}{10} + \frac{1}{10} = \frac{3}{10}$
- Total: $9\frac{3}{10}$

✔ Answer: $9\frac{3}{10}$

*(Note: You could simplify $\frac{3}{10}$, but it's already in simplest form.)*

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5. $5\frac{9}{10} + 6\frac{6}{10}$

- Whole numbers: $5 + 6 = 11$
- Fractions: $\frac{9}{10} + \frac{6}{10} = \frac{15}{10} = 1\frac{5}{10} = 1\frac{1}{2}$ *(simplify $\frac{5}{10}$ to $\frac{1}{2}$)*
- Add the extra whole number: $11 + 1 = 12$, plus $\frac{1}{2}$
- Total: $12\frac{1}{2}$

✔ Answer: $12\frac{1}{2}$

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6. $4\frac{6}{7} + 9\frac{6}{7}$

- Whole numbers: $4 + 9 = 13$
- Fractions: $\frac{6}{7} + \frac{6}{7} = \frac{12}{7} = 1\frac{5}{7}$
- Add the extra whole number: $13 + 1 = 14$, plus $\frac{5}{7}$
- Total: $14\frac{5}{7}$

✔ Answer: $14\frac{5}{7}$

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7. $3\frac{5}{9} + 7\frac{8}{9}$

- Whole numbers: $3 + 7 = 10$
- Fractions: $\frac{5}{9} + \frac{8}{9} = \frac{13}{9} = 1\frac{4}{9}$
- Add the extra whole number: $10 + 1 = 11$, plus $\frac{4}{9}$
- Total: $11\frac{4}{9}$

✔ Answer: $11\frac{4}{9}$

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8. $2\frac{2}{7} + 8\frac{2}{7}$

- Whole numbers: $2 + 8 = 10$
- Fractions: $\frac{2}{7} + \frac{2}{7} = \frac{4}{7}$
- Total: $10\frac{4}{7}$

✔ Answer: $10\frac{4}{7}$

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## ✔ Final Answers:

1. $3\frac{9}{11} + 6\frac{2}{11} = \boxed{10}$
2. $3\frac{7}{12} + 6\frac{4}{12} = \boxed{9\frac{11}{12}}$
3. $6\frac{6}{7} + 9\frac{5}{7} = \boxed{16\frac{4}{7}}$
4. $2\frac{2}{10} + 7\frac{1}{10} = \boxed{9\frac{3}{10}}$
5. $5\frac{9}{10} + 6\frac{6}{10} = \boxed{12\frac{1}{2}}$
6. $4\frac{6}{7} + 9\frac{6}{7} = \boxed{14\frac{5}{7}}$
7. $3\frac{5}{9} + 7\frac{8}{9} = \boxed{11\frac{4}{9}}$
8. $2\frac{2}{7} + 8\frac{2}{7} = \boxed{10\frac{4}{7}}$

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## 💡 Tip:
Always check if the fraction part sums to 1 or more — if so, carry over the whole number! And don’t forget to simplify fractions when possible (like $\frac{5}{10} = \frac{1}{2}$).

Let me know if you want to see how to do these using improper fractions too!