Adding Fractions Worksheet with 10 Problems for Math Practice

To solve the problems of adding fractions, we need to follow these steps:

1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add the numerators while keeping the denominator the same.
4. Simplify the result if possible.

Let's solve each problem step by step.

---

Problem 1:

$$
\frac{4}{5} + \frac{1}{3}
$$

- Step 1: Find the least common denominator (LCD) of 5 and 3. The LCD is 15.
- Step 2: Rewrite each fraction with the denominator 15:
$$
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}, \quad \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$
- Step 3: Add the fractions:
$$
\frac{12}{15} + \frac{5}{15} = \frac{12 + 5}{15} = \frac{17}{15}
$$
- Step 4: Simplify if possible. $\frac{17}{15}$ is already in simplest form.

Answer:
$$
\boxed{\frac{17}{15}}
$$

---

Problem 2:

$$
\frac{1}{2} + \frac{2}{4}
$$

- Step 1: Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Step 2: Now the problem is:
$$
\frac{1}{2} + \frac{1}{2}
$$
- Step 3: Add the fractions:
$$
\frac{1}{2} + \frac{1}{2} = \frac{1 + 1}{2} = \frac{2}{2} = 1
$$

Answer:
$$
\boxed{1}
$$

---

Problem 3:

$$
\frac{2}{5} + \frac{1}{4}
$$

- Step 1: Find the LCD of 5 and 4. The LCD is 20.
- Step 2: Rewrite each fraction with the denominator 20:
$$
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}, \quad \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
$$
- Step 3: Add the fractions:
$$
\frac{8}{20} + \frac{5}{20} = \frac{8 + 5}{20} = \frac{13}{20}
$$
- Step 4: Simplify if possible. $\frac{13}{20}$ is already in simplest form.

Answer:
$$
\boxed{\frac{13}{20}}
$$

---

Problem 4:

$$
\frac{3}{10} + \frac{1}{5}
$$

- Step 1: Find the LCD of 10 and 5. The LCD is 10.
- Step 2: Rewrite each fraction with the denominator 10:
$$
\frac{3}{10} = \frac{3}{10}, \quad \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
$$
- Step 3: Add the fractions:
$$
\frac{3}{10} + \frac{2}{10} = \frac{3 + 2}{10} = \frac{5}{10}
$$
- Step 4: Simplify if possible. $\frac{5}{10} = \frac{1}{2}$.

Answer:
$$
\boxed{\frac{1}{2}}
$$

---

Problem 5:

$$
\frac{1}{5} + \frac{1}{3}
$$

- Step 1: Find the LCD of 5 and 3. The LCD is 15.
- Step 2: Rewrite each fraction with the denominator 15:
$$
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}, \quad \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$
- Step 3: Add the fractions:
$$
\frac{3}{15} + \frac{5}{15} = \frac{3 + 5}{15} = \frac{8}{15}
$$
- Step 4: Simplify if possible. $\frac{8}{15}$ is already in simplest form.

Answer:
$$
\boxed{\frac{8}{15}}
$$

---

Problem 6:

$$
\frac{1}{2} + \frac{2}{4}
$$

- Step 1: Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Step 2: Now the problem is:
$$
\frac{1}{2} + \frac{1}{2}
$$
- Step 3: Add the fractions:
$$
\frac{1}{2} + \frac{1}{2} = \frac{1 + 1}{2} = \frac{2}{2} = 1
$$

Answer:
$$
\boxed{1}
$$

---

Problem 7:

$$
\frac{2}{10} + \frac{2}{4}
$$

- Step 1: Simplify $\frac{2}{10}$ to $\frac{1}{5}$ and $\frac{2}{4}$ to $\frac{1}{2}$.
- Step 2: Now the problem is:
$$
\frac{1}{5} + \frac{1}{2}
$$
- Step 3: Find the LCD of 5 and 2. The LCD is 10.
- Step 4: Rewrite each fraction with the denominator 10:
$$
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}, \quad \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$
- Step 5: Add the fractions:
$$
\frac{2}{10} + \frac{5}{10} = \frac{2 + 5}{10} = \frac{7}{10}
$$

Answer:
$$
\boxed{\frac{7}{10}}
$$

---

Problem 8:

$$
\frac{8}{10} + \frac{3}{5}
$$

- Step 1: Simplify $\frac{8}{10}$ to $\frac{4}{5}$.
- Step 2: Now the problem is:
$$
\frac{4}{5} + \frac{3}{5}
$$
- Step 3: Add the fractions:
$$
\frac{4}{5} + \frac{3}{5} = \frac{4 + 3}{5} = \frac{7}{5}
$$

Answer:
$$
\boxed{\frac{7}{5}}
$$

---

Problem 9:

$$
\frac{3}{4} + \frac{1}{10}
$$

- Step 1: Find the LCD of 4 and 10. The LCD is 20.
- Step 2: Rewrite each fraction with the denominator 20:
$$
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}, \quad \frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}
$$
- Step 3: Add the fractions:
$$
\frac{15}{20} + \frac{2}{20} = \frac{15 + 2}{20} = \frac{17}{20}
$$
- Step 4: Simplify if possible. $\frac{17}{20}$ is already in simplest form.

Answer:
$$
\boxed{\frac{17}{20}}
$$

---

Problem 10:

$$
\frac{1}{3} + \frac{1}{2}
$$

- Step 1: Find the LCD of 3 and 2. The LCD is 6.
- Step 2: Rewrite each fraction with the denominator 6:
$$
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}, \quad \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
$$
- Step 3: Add the fractions:
$$
\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}
$$
- Step 4: Simplify if possible. $\frac{5}{6}$ is already in simplest form.

Answer:
$$
\boxed{\frac{5}{6}}
$$

---

Final Answers:

1. $\boxed{\frac{17}{15}}$
2. $\boxed{1}$
3. $\boxed{\frac{13}{20}}$
4. $\boxed{\frac{1}{2}}$
5. $\boxed{\frac{8}{15}}$
6. $\boxed{1}$
7. $\boxed{\frac{7}{10}}$
8. $\boxed{\frac{7}{5}}$
9. $\boxed{\frac{17}{20}}$
10. $\boxed{\frac{5}{6}}$