Fraction addition and subtraction practice worksheet for students, designed by Math Salamanders.

Problem: Solving the Adding and Subtracting Fractions Worksheet

The worksheet involves adding and subtracting fractions. To solve these problems, we need to:
1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add or subtract the numerators while keeping the denominator the same.
4. Simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Problem 1:

$$
\frac{3}{8} - \frac{1}{6} = \_\_\_\_ - \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 8 and 6. The LCD of 8 and 6 is 24.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{3}{8}$: Multiply numerator and denominator by 3:
$$
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
$$
- For $\frac{1}{6}$: Multiply numerator and denominator by 4:
$$
\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}
$$

#### Step 3: Subtract the fractions
$$
\frac{9}{24} - \frac{4}{24} = \frac{9 - 4}{24} = \frac{5}{24}
$$

#### Final Answer:
$$
\frac{3}{8} - \frac{1}{6} = \frac{9}{24} - \frac{4}{24} = \frac{5}{24}
$$

---

Problem 2:

$$
\frac{2}{3} + \frac{5}{7} = \_\_\_\_ + \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 3 and 7. The LCD of 3 and 7 is 21.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{2}{3}$: Multiply numerator and denominator by 7:
$$
\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}
$$
- For $\frac{5}{7}$: Multiply numerator and denominator by 3:
$$
\frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21}
$$

#### Step 3: Add the fractions
$$
\frac{14}{21} + \frac{15}{21} = \frac{14 + 15}{21} = \frac{29}{21}
$$

#### Final Answer:
$$
\frac{2}{3} + \frac{5}{7} = \frac{14}{21} + \frac{15}{21} = \frac{29}{21}
$$

---

Problem 3:

$$
\frac{7}{9} + \frac{3}{10} = \_\_\_\_ + \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 9 and 10. The LCD of 9 and 10 is 90.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{7}{9}$: Multiply numerator and denominator by 10:
$$
\frac{7}{9} = \frac{7 \times 10}{9 \times 10} = \frac{70}{90}
$$
- For $\frac{3}{10}$: Multiply numerator and denominator by 9:
$$
\frac{3}{10} = \frac{3 \times 9}{10 \times 9} = \frac{27}{90}
$$

#### Step 3: Add the fractions
$$
\frac{70}{90} + \frac{27}{90} = \frac{70 + 27}{90} = \frac{97}{90}
$$

#### Final Answer:
$$
\frac{7}{9} + \frac{3}{10} = \frac{70}{90} + \frac{27}{90} = \frac{97}{90}
$$

---

Problem 4:

$$
\frac{5}{4} - \frac{3}{8} = \_\_\_\_ - \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 4 and 8. The LCD of 4 and 8 is 8.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{5}{4}$: Multiply numerator and denominator by 2:
$$
\frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8}
$$
- For $\frac{3}{8}$: Already has the denominator 8:
$$
\frac{3}{8} = \frac{3}{8}
$$

#### Step 3: Subtract the fractions
$$
\frac{10}{8} - \frac{3}{8} = \frac{10 - 3}{8} = \frac{7}{8}
$$

#### Final Answer:
$$
\frac{5}{4} - \frac{3}{8} = \frac{10}{8} - \frac{3}{8} = \frac{7}{8}
$$

---

Problem 5:

$$
\frac{9}{5} + \frac{2}{7} = \_\_\_\_ + \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 5 and 7. The LCD of 5 and 7 is 35.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{9}{5}$: Multiply numerator and denominator by 7:
$$
\frac{9}{5} = \frac{9 \times 7}{5 \times 7} = \frac{63}{35}
$$
- For $\frac{2}{7}$: Multiply numerator and denominator by 5:
$$
\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}
$$

#### Step 3: Add the fractions
$$
\frac{63}{35} + \frac{10}{35} = \frac{63 + 10}{35} = \frac{73}{35}
$$

#### Final Answer:
$$
\frac{9}{5} + \frac{2}{7} = \frac{63}{35} + \frac{10}{35} = \frac{73}{35}
$$

---

Problem 6:

$$
\frac{4}{3} - \frac{7}{10} = \_\_\_\_ - \_\_\_\_ = \_\_\_\_
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 3 and 10. The LCD of 3 and 10 is 30.

#### Step 2: Rewrite the fractions with the LCD
- For $\frac{4}{3}$: Multiply numerator and denominator by 10:
$$
\frac{4}{3} = \frac{4 \times 10}{3 \times 10} = \frac{40}{30}
$$
- For $\frac{7}{10}$: Multiply numerator and denominator by 3:
$$
\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}
$$

#### Step 3: Subtract the fractions
$$
\frac{40}{30} - \frac{21}{30} = \frac{40 - 21}{30} = \frac{19}{30}
$$

#### Final Answer:
$$
\frac{4}{3} - \frac{7}{10} = \frac{40}{30} - \frac{21}{30} = \frac{19}{30}
$$

---

Final Answers for Problems 1–6:

1. $\frac{3}{8} - \frac{1}{6} = \frac{9}{24} - \frac{4}{24} = \frac{5}{24}$
2. $\frac{2}{3} + \frac{5}{7} = \frac{14}{21} + \frac{15}{21} = \frac{29}{21}$
3. $\frac{7}{9} + \frac{3}{10} = \frac{70}{90} + \frac{27}{90} = \frac{97}{90}$
4. $\frac{5}{4} - \frac{3}{8} = \frac{10}{8} - \frac{3}{8} = \frac{7}{8}$
5. $\frac{9}{5} + \frac{2}{7} = \frac{63}{35} + \frac{10}{35} = \frac{73}{35}$
6. $\frac{4}{3} - \frac{7}{10} = \frac{40}{30} - \frac{21}{30} = \frac{19}{30}$

---

Boxed Final Answers for Problems 1–6:
$$
\boxed{
\begin{aligned}
1. & \quad \frac{5}{24} \\
2. & \quad \frac{29}{21} \\
3. & \quad \frac{97}{90} \\
4. & \quad \frac{7}{8} \\
5. & \quad \frac{73}{35} \\
6. & \quad \frac{19}{30}
\end{aligned}
}
$$