Math worksheet designed to help students practice adding and subtracting fractions, including negative values and conversion to addition problems.

Let's solve each problem step by step, following the instructions: rewrite every subtraction problem as an addition problem, and show all steps.

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1) $\left(-\frac{4}{5}\right) - \frac{7}{8}$

Rewrite subtraction as addition:

$$
-\frac{4}{5} + \left(-\frac{7}{8}\right)
$$

Now find a common denominator. The least common denominator (LCD) of 5 and 8 is 40.

Convert both fractions:

$$
-\frac{4}{5} = -\frac{4 \times 8}{5 \times 8} = -\frac{32}{40}
$$
$$
-\frac{7}{8} = -\frac{7 \times 5}{8 \times 5} = -\frac{35}{40}
$$

Add:

$$
-\frac{32}{40} + \left(-\frac{35}{40}\right) = -\frac{67}{40}
$$

Final answer:
$$
\boxed{-\frac{67}{40}}
$$

---

2) $\frac{1}{3} - \left(-\frac{5}{3}\right)$

Subtracting a negative is the same as adding:

$$
\frac{1}{3} + \frac{5}{3} = \frac{6}{3} = 2
$$

Final answer:
$$
\boxed{2}
$$

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3) $\left(-\frac{1}{3}\right) + \frac{3}{8}$

Different denominators: LCD of 3 and 8 is 24.

Convert:

$$
-\frac{1}{3} = -\frac{8}{24}, \quad \frac{3}{8} = \frac{9}{24}
$$

Add:

$$
-\frac{8}{24} + \frac{9}{24} = \frac{1}{24}
$$

Final answer:
$$
\boxed{\frac{1}{24}}
$$

---

4) $\left(-\frac{10}{7}\right) + \frac{1}{6}$

LCD of 7 and 6 is 42.

Convert:

$$
-\frac{10}{7} = -\frac{60}{42}, \quad \frac{1}{6} = \frac{7}{42}
$$

Add:

$$
-\frac{60}{42} + \frac{7}{42} = -\frac{53}{42}
$$

Final answer:
$$
\boxed{-\frac{53}{42}}
$$

---

5) $\frac{9}{5} + \left(-\frac{4}{3}\right)$

This is the same as:

$$
\frac{9}{5} - \frac{4}{3}
$$

LCD of 5 and 3 is 15.

Convert:

$$
\frac{9}{5} = \frac{27}{15}, \quad \frac{4}{3} = \frac{20}{15}
$$

Subtract:

$$
\frac{27}{15} - \frac{20}{15} = \frac{7}{15}
$$

Final answer:
$$
\boxed{\frac{7}{15}}
$$

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6) $2 - \frac{13}{8}$

Rewrite as addition:

$$
2 + \left(-\frac{13}{8}\right)
$$

Write 2 as a fraction: $ \frac{16}{8} $

$$
\frac{16}{8} - \frac{13}{8} = \frac{3}{8}
$$

Final answer:
$$
\boxed{\frac{3}{8}}
$$

---

7) $\frac{9}{5} - \frac{5}{8}$

Rewrite as:

$$
\frac{9}{5} + \left(-\frac{5}{8}\right)
$$

LCD of 5 and 8 is 40.

Convert:

$$
\frac{9}{5} = \frac{72}{40}, \quad \frac{5}{8} = \frac{25}{40}
$$

Subtract:

$$
\frac{72}{40} - \frac{25}{40} = \frac{47}{40}
$$

Final answer:
$$
\boxed{\frac{47}{40}}
$$

---

8) $\left(-\frac{4}{3}\right) - \left(-\frac{3}{2}\right)$

Subtracting a negative becomes addition:

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

LCD of 3 and 2 is 6.

Convert:

$$
-\frac{4}{3} = -\frac{8}{6}, \quad \frac{3}{2} = \frac{9}{6}
$$

Add:

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

Final answer:
$$
\boxed{\frac{1}{6}}
$$

---

9) $-\frac{6}{9} + \left(-\frac{2}{3}\right)$

First simplify $-\frac{6}{9} = -\frac{2}{3}$

Now:

$$
-\frac{2}{3} + \left(-\frac{2}{3}\right) = -\frac{4}{3}
$$

Final answer:
$$
\boxed{-\frac{4}{3}}
$$

---

10) $-\frac{4}{5} - \left(\frac{3}{7}\right)$

Rewrite as addition:

$$
-\frac{4}{5} + \left(-\frac{3}{7}\right)
$$

LCD of 5 and 7 is 35.

Convert:

$$
-\frac{4}{5} = -\frac{28}{35}, \quad -\frac{3}{7} = -\frac{15}{35}
$$

Add:

$$
-\frac{28}{35} + \left(-\frac{15}{35}\right) = -\frac{43}{35}
$$

Final answer:
$$
\boxed{-\frac{43}{35}}
$$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | $-\frac{67}{40}$ |
| 2) | $2$ |
| 3) | $\frac{1}{24}$ |
| 4) | $-\frac{53}{42}$ |
| 5) | $\frac{7}{15}$ |
| 6) | $\frac{3}{8}$ |
| 7) | $\frac{47}{40}$ |
| 8) | $\frac{1}{6}$ |
| 9) | $-\frac{4}{3}$ |
| 10) | $-\frac{43}{35}$ |

All problems were solved by rewriting subtraction as addition and using common denominators. Let me know if you'd like these answers in mixed number form!