Fraction arithmetic practice sheet with addition and subtraction equations.

To solve the given problems, we need to perform arithmetic operations on fractions. The operations include addition and subtraction. Let's solve each problem step by step.

Problem 1: $\frac{2}{3} - \frac{1}{5}$

1. Find a common denominator: The denominators are 3 and 5. The least common denominator (LCD) is 15.
2. Convert fractions:
- $\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$
- $\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$
3. Subtract the fractions:
$$
\frac{10}{15} - \frac{3}{15} = \frac{10 - 3}{15} = \frac{7}{15}
$$

Answer: $\frac{7}{15}$

---

Problem 2: $\frac{4}{9} - \frac{1}{9}$

1. Common denominator: Both fractions already have the same denominator (9).
2. Subtract the numerators:
$$
\frac{4}{9} - \frac{1}{9} = \frac{4 - 1}{9} = \frac{3}{9}
$$
3. Simplify:
$$
\frac{3}{9} = \frac{1}{3}
$$

Answer: $\frac{1}{3}$

---

Problem 3: $\frac{3}{7} + \frac{1}{7}$

1. Common denominator: Both fractions already have the same denominator (7).
2. Add the numerators:
$$
\frac{3}{7} + \frac{1}{7} = \frac{3 + 1}{7} = \frac{4}{7}
$$

Answer: $\frac{4}{7}$

---

Problem 4: $\frac{7}{10} - \frac{4}{10}$

1. Common denominator: Both fractions already have the same denominator (10).
2. Subtract the numerators:
$$
\frac{7}{10} - \frac{4}{10} = \frac{7 - 4}{10} = \frac{3}{10}
$$

Answer: $\frac{3}{10}$

---

Problem 5: $\frac{4}{8} - \frac{1}{6}$

1. Find a common denominator: The denominators are 8 and 6. The LCD is 24.
2. Convert fractions:
- $\frac{4}{8} = \frac{4 \times 3}{8 \times 3} = \frac{12}{24}$
- $\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}$
3. Subtract the fractions:
$$
\frac{12}{24} - \frac{4}{24} = \frac{12 - 4}{24} = \frac{8}{24}
$$
4. Simplify:
$$
\frac{8}{24} = \frac{1}{3}
$$

Answer: $\frac{1}{3}$

---

Problem 6: $\frac{2}{4} + \frac{1}{4}$

1. Common denominator: Both fractions already have the same denominator (4).
2. Add the numerators:
$$
\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}
$$

Answer: $\frac{3}{4}$

---

Problem 7: $\frac{1}{3} + \frac{1}{3}$

1. Common denominator: Both fractions already have the same denominator (3).
2. Add the numerators:
$$
\frac{1}{3} + \frac{1}{3} = \frac{1 + 1}{3} = \frac{2}{3}
$$

Answer: $\frac{2}{3}$

---

Problem 8: $\frac{3}{8} - \frac{1}{8}$

1. Common denominator: Both fractions already have the same denominator (8).
2. Subtract the numerators:
$$
\frac{3}{8} - \frac{1}{8} = \frac{3 - 1}{8} = \frac{2}{8}
$$
3. Simplify:
$$
\frac{2}{8} = \frac{1}{4}
$$

Answer: $\frac{1}{4}$

---

Problem 9: $\frac{4}{12} - \frac{12}{12}$

1. Common denominator: Both fractions already have the same denominator (12).
2. Subtract the numerators:
$$
\frac{4}{12} - \frac{12}{12} = \frac{4 - 12}{12} = \frac{-8}{12}
$$
3. Simplify:
$$
\frac{-8}{12} = \frac{-2}{3}
$$

Answer: $-\frac{2}{3}$

---

Problem 10: $\frac{3}{6} + \frac{6}{6}$

1. Common denominator: Both fractions already have the same denominator (6).
2. Add the numerators:
$$
\frac{3}{6} + \frac{6}{6} = \frac{3 + 6}{6} = \frac{9}{6}
$$
3. Simplify:
$$
\frac{9}{6} = \frac{3}{2}
$$

Answer: $\frac{3}{2}$

---

Final Answers:

$$
\boxed{
\begin{aligned}
&\frac{7}{15}, \quad \frac{1}{3}, \quad \frac{4}{7}, \quad \frac{3}{10}, \quad \frac{1}{3}, \quad \frac{3}{4}, \quad \frac{2}{3}, \quad \frac{1}{4}, \quad -\frac{2}{3}, \quad \frac{3}{2}
\end{aligned}
}
$$