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

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

1. Find a Common Denominator: The denominators of the fractions must be the same before adding them. If they are different, 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: $\frac{3}{5} + \frac{1}{4}$

- Step 1: Find the LCD of 5 and 4. The LCD is 20.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}, \quad \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
$$
- Step 3: Add the numerators:
$$
\frac{12}{20} + \frac{5}{20} = \frac{12 + 5}{20} = \frac{17}{20}
$$
- Step 4: The fraction $\frac{17}{20}$ is already in simplest form.
- Answer: $\boxed{\frac{17}{20}}$

---

Problem 2: $\frac{2}{3} + \frac{1}{10}$

- Step 1: Find the LCD of 3 and 10. The LCD is 30.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}, \quad \frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}
$$
- Step 3: Add the numerators:
$$
\frac{20}{30} + \frac{3}{30} = \frac{20 + 3}{30} = \frac{23}{30}
$$
- Step 4: The fraction $\frac{23}{30}$ is already in simplest form.
- Answer: $\boxed{\frac{23}{30}}$

---

Problem 3: $\frac{1}{6} + \frac{4}{11}$

- Step 1: Find the LCD of 6 and 11. The LCD is 66.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{1}{6} = \frac{1 \times 11}{6 \times 11} = \frac{11}{66}, \quad \frac{4}{11} = \frac{4 \times 6}{11 \times 6} = \frac{24}{66}
$$
- Step 3: Add the numerators:
$$
\frac{11}{66} + \frac{24}{66} = \frac{11 + 24}{66} = \frac{35}{66}
$$
- Step 4: The fraction $\frac{35}{66}$ is already in simplest form.
- Answer: $\boxed{\frac{35}{66}}$

---

Problem 4: $\frac{1}{9} + \frac{3}{8}$

- Step 1: Find the LCD of 9 and 8. The LCD is 72.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{1}{9} = \frac{1 \times 8}{9 \times 8} = \frac{8}{72}, \quad \frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72}
$$
- Step 3: Add the numerators:
$$
\frac{8}{72} + \frac{27}{72} = \frac{8 + 27}{72} = \frac{35}{72}
$$
- Step 4: The fraction $\frac{35}{72}$ is already in simplest form.
- Answer: $\boxed{\frac{35}{72}}$

---

Problem 5: $\frac{1}{3} + \frac{5}{15}$

- Step 1: Simplify $\frac{5}{15}$ to $\frac{1}{3}$.
- Step 2: Now add $\frac{1}{3} + \frac{1}{3}$:
$$
\frac{1}{3} + \frac{1}{3} = \frac{1 + 1}{3} = \frac{2}{3}
$$
- Answer: $\boxed{\frac{2}{3}}$

---

Problem 6: $\frac{2}{8} + \frac{4}{11}$

- Step 1: Simplify $\frac{2}{8}$ to $\frac{1}{4}$.
- Step 2: Find the LCD of 4 and 11. The LCD is 44.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{1}{4} = \frac{1 \times 11}{4 \times 11} = \frac{11}{44}, \quad \frac{4}{11} = \frac{4 \times 4}{11 \times 4} = \frac{16}{44}
$$
- Step 4: Add the numerators:
$$
\frac{11}{44} + \frac{16}{44} = \frac{11 + 16}{44} = \frac{27}{44}
$$
- Answer: $\boxed{\frac{27}{44}}$

---

Problem 7: $\frac{5}{10} + \frac{8}{9}$

- Step 1: Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
- Step 2: Find the LCD of 2 and 9. The LCD is 18.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}, \quad \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}
$$
- Step 4: Add the numerators:
$$
\frac{9}{18} + \frac{16}{18} = \frac{9 + 16}{18} = \frac{25}{18}
$$
- Answer: $\boxed{\frac{25}{18}}$

---

Problem 8: $\frac{3}{5} + \frac{6}{20}$

- Step 1: Simplify $\frac{6}{20}$ to $\frac{3}{10}$.
- Step 2: Find the LCD of 5 and 10. The LCD is 10.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}, \quad \frac{3}{10} = \frac{3}{10}
$$
- Step 4: Add the numerators:
$$
\frac{6}{10} + \frac{3}{10} = \frac{6 + 3}{10} = \frac{9}{10}
$$
- Answer: $\boxed{\frac{9}{10}}$

---

Problem 9: $\frac{4}{10} + \frac{7}{12}$

- Step 1: Simplify $\frac{4}{10}$ to $\frac{2}{5}$.
- Step 2: Find the LCD of 5 and 12. The LCD is 60.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60}, \quad \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}
$$
- Step 4: Add the numerators:
$$
\frac{24}{60} + \frac{35}{60} = \frac{24 + 35}{60} = \frac{59}{60}
$$
- Answer: $\boxed{\frac{59}{60}}$

---

Problem 10: $\frac{9}{12} + \frac{5}{24}$

- Step 1: Simplify $\frac{9}{12}$ to $\frac{3}{4}$.
- Step 2: Find the LCD of 4 and 24. The LCD is 24.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}, \quad \frac{5}{24} = \frac{5}{24}
$$
- Step 4: Add the numerators:
$$
\frac{18}{24} + \frac{5}{24} = \frac{18 + 5}{24} = \frac{23}{24}
$$
- Answer: $\boxed{\frac{23}{24}}$

---

Final Answers:

1. $\boxed{\frac{17}{20}}$
2. $\boxed{\frac{23}{30}}$
3. $\boxed{\frac{35}{66}}$
4. $\boxed{\frac{35}{72}}$
5. $\boxed{\frac{2}{3}}$
6. $\boxed{\frac{27}{44}}$
7. $\boxed{\frac{25}{18}}$
8. $\boxed{\frac{9}{10}}$
9. $\boxed{\frac{59}{60}}$
10. $\boxed{\frac{23}{24}}$