Grade 6 Adding Fractions Worksheets | Free Printables | Math ... - Free Printable

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

1. Find a Common Denominator: The denominators of the fractions must be the same before we can add them. If they are different, we find the least common denominator (LCD).
2. Adjust the Fractions: Rewrite each fraction with the common denominator.
3. Add the Numerators: Add the numerators while keeping the denominator the same.
4. Simplify the Result: Reduce the resulting fraction to its simplest form if possible.

Let's solve each problem step by step.

---

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

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

---

Problem 2: $\frac{4}{5} + \frac{1}{6}$

- Step 1: Find the LCD of 5 and 6. The LCD is 30.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}, \quad \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
$$
- Step 3: Add the numerators:
$$
\frac{24}{30} + \frac{5}{30} = \frac{24 + 5}{30} = \frac{29}{30}
$$
- Step 4: The fraction $\frac{29}{30}$ is already in simplest form.
- Answer: $\frac{29}{30}$

---

Problem 3: $\frac{3}{5} + \frac{2}{7}$

- Step 1: Find the LCD of 5 and 7. The LCD is 35.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}, \quad \frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}
$$
- Step 3: Add the numerators:
$$
\frac{21}{35} + \frac{10}{35} = \frac{21 + 10}{35} = \frac{31}{35}
$$
- Step 4: The fraction $\frac{31}{35}$ is already in simplest form.
- Answer: $\frac{31}{35}$

---

Problem 4: $\frac{4}{5} + \frac{1}{8}$

- Step 1: Find the LCD of 5 and 8. The LCD is 40.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}, \quad \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}
$$
- Step 3: Add the numerators:
$$
\frac{32}{40} + \frac{5}{40} = \frac{32 + 5}{40} = \frac{37}{40}
$$
- Step 4: The fraction $\frac{37}{40}$ is already in simplest form.
- Answer: $\frac{37}{40}$

---

Problem 5: $\frac{5}{8} + \frac{2}{11}$

- Step 1: Find the LCD of 8 and 11. The LCD is 88.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{8} = \frac{5 \times 11}{8 \times 11} = \frac{55}{88}, \quad \frac{2}{11} = \frac{2 \times 8}{11 \times 8} = \frac{16}{88}
$$
- Step 3: Add the numerators:
$$
\frac{55}{88} + \frac{16}{88} = \frac{55 + 16}{88} = \frac{71}{88}
$$
- Step 4: The fraction $\frac{71}{88}$ is already in simplest form.
- Answer: $\frac{71}{88}$

---

Problem 6: $\frac{5}{8} + \frac{2}{9}$

- Step 1: Find the LCD of 8 and 9. The LCD is 72.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}, \quad \frac{2}{9} = \frac{2 \times 8}{9 \times 8} = \frac{16}{72}
$$
- Step 3: Add the numerators:
$$
\frac{45}{72} + \frac{16}{72} = \frac{45 + 16}{72} = \frac{61}{72}
$$
- Step 4: The fraction $\frac{61}{72}$ is already in simplest form.
- Answer: $\frac{61}{72}$

---

Problem 7: $\frac{4}{7} + \frac{5}{14}$

- Step 1: Find the LCD of 7 and 14. The LCD is 14.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{4}{7} = \frac{4 \times 2}{7 \times 2} = \frac{8}{14}, \quad \frac{5}{14} = \frac{5}{14}
$$
- Step 3: Add the numerators:
$$
\frac{8}{14} + \frac{5}{14} = \frac{8 + 5}{14} = \frac{13}{14}
$$
- Step 4: The fraction $\frac{13}{14}$ is already in simplest form.
- Answer: $\frac{13}{14}$

---

Problem 8: $\frac{3}{5} + \frac{4}{12}$

- Step 1: Simplify $\frac{4}{12}$ to $\frac{1}{3}$.
- Step 2: Find the LCD of 5 and 3. The LCD is 15.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}, \quad \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$
- Step 4: Add the numerators:
$$
\frac{9}{15} + \frac{5}{15} = \frac{9 + 5}{15} = \frac{14}{15}
$$
- Step 5: The fraction $\frac{14}{15}$ is already in simplest form.
- Answer: $\frac{14}{15}$

---

Problem 9: $\frac{7}{9} + \frac{1}{18}$

- Step 1: Find the LCD of 9 and 18. The LCD is 18.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}, \quad \frac{1}{18} = \frac{1}{18}
$$
- Step 3: Add the numerators:
$$
\frac{14}{18} + \frac{1}{18} = \frac{14 + 1}{18} = \frac{15}{18}
$$
- Step 4: Simplify $\frac{15}{18}$ to $\frac{5}{6}$.
- Answer: $\frac{5}{6}$

---

Problem 10: $\frac{2}{10} + \frac{8}{30}$

- Step 1: Simplify $\frac{2}{10}$ to $\frac{1}{5}$ and $\frac{8}{30}$ to $\frac{4}{15}$.
- Step 2: Find the LCD of 5 and 15. The LCD is 15.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}, \quad \frac{4}{15} = \frac{4}{15}
$$
- Step 4: Add the numerators:
$$
\frac{3}{15} + \frac{4}{15} = \frac{3 + 4}{15} = \frac{7}{15}
$$
- Step 5: The fraction $\frac{7}{15}$ is already in simplest form.
- Answer: $\frac{7}{15}$

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Final Answers

$$
\boxed{
\begin{array}{ll}
1. & \frac{5}{6} \\
2. & \frac{29}{30} \\
3. & \frac{31}{35} \\
4. & \frac{37}{40} \\
5. & \frac{71}{88} \\
6. & \frac{61}{72} \\
7. & \frac{13}{14} \\
8. & \frac{14}{15} \\
9. & \frac{5}{6} \\
10. & \frac{7}{15} \\
\end{array}
}
$$