Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let's solve each problem step by step, carefully handling the addition and subtraction of negative fractions. We'll simplify where needed and find common denominators when necessary.

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Problem 1:

$$
\frac{11}{16} + \left(-\frac{8}{24}\right)
$$

First, simplify $-\frac{8}{24}$:
$$
-\frac{8}{24} = -\frac{1}{3}
$$

Now add:
$$
\frac{11}{16} - \frac{1}{3}
$$

Find a common denominator: LCM of 16 and 3 is 48.

Convert:
- $\frac{11}{16} = \frac{11 \times 3}{48} = \frac{33}{48}$
- $\frac{1}{3} = \frac{16}{48}$

So:
$$
\frac{33}{48} - \frac{16}{48} = \frac{17}{48}
$$

✔ Answer: $\boxed{\frac{17}{48}}$

---

Problem 2:

$$
\left(-\frac{5}{6}\right) - \frac{12}{9}
$$

Simplify $\frac{12}{9} = \frac{4}{3}$

So:
$$
-\frac{5}{6} - \frac{4}{3}
$$

Common denominator: LCM of 6 and 3 is 6.

Convert:
- $-\frac{5}{6}$ stays
- $\frac{4}{3} = \frac{8}{6}$

Now:
$$
-\frac{5}{6} - \frac{8}{6} = -\frac{13}{6}
$$

✔ Answer: $\boxed{-\frac{13}{6}}$ or $-2\frac{1}{6}$

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Problem 3:

$$
- \left(-\frac{3}{12}\right) + \frac{13}{14}
$$

Simplify:
- $-\left(-\frac{3}{12}\right) = +\frac{3}{12} = \frac{1}{4}$

Now:
$$
\frac{1}{4} + \frac{13}{14}
$$

Common denominator: LCM of 4 and 14 is 28.

Convert:
- $\frac{1}{4} = \frac{7}{28}$
- $\frac{13}{14} = \frac{26}{28}$

Add:
$$
\frac{7}{28} + \frac{26}{28} = \frac{33}{28}
$$

✔ Answer: $\boxed{\frac{33}{28}}$ or $1\frac{5}{28}$

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Problem 4:

$$
\left(-\frac{4}{15}\right) + \frac{4}{9}
$$

Common denominator: LCM of 15 and 9 is 45.

Convert:
- $-\frac{4}{15} = -\frac{12}{45}$
- $\frac{4}{9} = \frac{20}{45}$

Add:
$$
-\frac{12}{45} + \frac{20}{45} = \frac{8}{45}
$$

✔ Answer: $\boxed{\frac{8}{45}}$

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Problem 5:

$$
\frac{9}{8} + \left(-\frac{9}{16}\right)
$$

This is:
$$
\frac{9}{8} - \frac{9}{16}
$$

Common denominator: 16.

Convert:
- $\frac{9}{8} = \frac{18}{16}$

So:
$$
\frac{18}{16} - \frac{9}{16} = \frac{9}{16}
$$

✔ Answer: $\boxed{\frac{9}{16}}$

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Problem 6:

$$
\left(-\frac{5}{8}\right) - \frac{3}{10}
$$

Common denominator: LCM of 8 and 10 is 40.

Convert:
- $-\frac{5}{8} = -\frac{25}{40}$
- $\frac{3}{10} = \frac{12}{40}$

Now:
$$
-\frac{25}{40} - \frac{12}{40} = -\frac{37}{40}
$$

✔ Answer: $\boxed{-\frac{37}{40}}$

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Problem 7:

$$
\frac{11}{4} - \left(-\frac{6}{9}\right)
$$

Simplify $-\frac{6}{9} = -\frac{2}{3}$, so subtracting a negative becomes adding:

$$
\frac{11}{4} + \frac{2}{3}
$$

Common denominator: LCM of 4 and 3 is 12.

Convert:
- $\frac{11}{4} = \frac{33}{12}$
- $\frac{2}{3} = \frac{8}{12}$

Add:
$$
\frac{33}{12} + \frac{8}{12} = \frac{41}{12}
$$

✔ Answer: $\boxed{\frac{41}{12}}$ or $3\frac{5}{12}$

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Problem 8:

$$
\frac{3}{8} + \left(-\frac{12}{15}\right)
$$

Simplify $-\frac{12}{15} = -\frac{4}{5}$

So:
$$
\frac{3}{8} - \frac{4}{5}
$$

Common denominator: LCM of 8 and 5 is 40.

Convert:
- $\frac{3}{8} = \frac{15}{40}$
- $\frac{4}{5} = \frac{32}{40}$

Now:
$$
\frac{15}{40} - \frac{32}{40} = -\frac{17}{40}
$$

✔ Answer: $\boxed{-\frac{17}{40}}$

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Problem 9:

$$
\frac{10}{12} + \left(-\frac{5}{8}\right)
$$

Simplify $\frac{10}{12} = \frac{5}{6}$

So:
$$
\frac{5}{6} - \frac{5}{8}
$$

Common denominator: LCM of 6 and 8 is 24.

Convert:
- $\frac{5}{6} = \frac{20}{24}$
- $\frac{5}{8} = \frac{15}{24}$

Now:
$$
\frac{20}{24} - \frac{15}{24} = \frac{5}{24}
$$

✔ Answer: $\boxed{\frac{5}{24}}$

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Problem 10:

$$
- \left(-\frac{6}{7}\right) + \frac{7}{10}
$$

Simplify: $-(-\frac{6}{7}) = +\frac{6}{7}$

So:
$$
\frac{6}{7} + \frac{7}{10}
$$

Common denominator: LCM of 7 and 10 is 70.

Convert:
- $\frac{6}{7} = \frac{60}{70}$
- $\frac{7}{10} = \frac{49}{70}$

Add:
$$
\frac{60}{70} + \frac{49}{70} = \frac{109}{70}
$$

✔ Answer: $\boxed{\frac{109}{70}}$ or $1\frac{39}{70}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{17}{48}$ |
| 2 | $-\frac{13}{6}$ |
| 3 | $\frac{33}{28}$ |
| 4 | $\frac{8}{45}$ |
| 5 | $\frac{9}{16}$ |
| 6 | $-\frac{37}{40}$ |
| 7 | $\frac{41}{12}$ |
| 8 | $-\frac{17}{40}$ |
| 9 | $\frac{5}{24}$ |
| 10 | $\frac{109}{70}$ |

Let me know if you'd like these as mixed numbers or decimals!