Grade 5 Adding and Subtracting Fractions Worksheets | Free Printables - Free Printable

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

1. Find a common denominator for the fractions being added.
2. Rewrite each fraction with the common denominator.
3. Add 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: $\frac{1}{2} + \frac{3}{12}$

- Step 1: Find the common denominator.
- The denominators are 2 and 12. The least common denominator (LCD) is 12.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$
- $\frac{3}{12}$ remains $\frac{3}{12}$.
- Step 3: Add the numerators.
- $\frac{6}{12} + \frac{3}{12} = \frac{6 + 3}{12} = \frac{9}{12}$
- Step 4: Simplify the fraction.
- $\frac{9}{12} = \frac{3}{4}$

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

---

Problem 2: $\frac{1}{8} + \frac{2}{24}$

- Step 1: Find the common denominator.
- The denominators are 8 and 24. The LCD is 24.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$
- $\frac{2}{24}$ remains $\frac{2}{24}$.
- Step 3: Add the numerators.
- $\frac{3}{24} + \frac{2}{24} = \frac{3 + 2}{24} = \frac{5}{24}$
- Step 4: Simplify the fraction.
- $\frac{5}{24}$ is already in simplest form.

Answer: $\boxed{\frac{5}{24}}$

---

Problem 3: $\frac{2}{6} + \frac{3}{12}$

- Step 1: Find the common denominator.
- The denominators are 6 and 12. The LCD is 12.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{2}{6} = \frac{2 \times 2}{6 \times 2} = \frac{4}{12}$
- $\frac{3}{12}$ remains $\frac{3}{12}$.
- Step 3: Add the numerators.
- $\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}$
- Step 4: Simplify the fraction.
- $\frac{7}{12}$ is already in simplest form.

Answer: $\boxed{\frac{7}{12}}$

---

Problem 4: $\frac{1}{4} + \frac{3}{16}$

- Step 1: Find the common denominator.
- The denominators are 4 and 16. The LCD is 16.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}$
- $\frac{3}{16}$ remains $\frac{3}{16}$.
- Step 3: Add the numerators.
- $\frac{4}{16} + \frac{3}{16} = \frac{4 + 3}{16} = \frac{7}{16}$
- Step 4: Simplify the fraction.
- $\frac{7}{16}$ is already in simplest form.

Answer: $\boxed{\frac{7}{16}}$

---

Problem 5: $\frac{1}{3} + \frac{5}{21}$

- Step 1: Find the common denominator.
- The denominators are 3 and 21. The LCD is 21.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}$
- $\frac{5}{21}$ remains $\frac{5}{21}$.
- Step 3: Add the numerators.
- $\frac{7}{21} + \frac{5}{21} = \frac{7 + 5}{21} = \frac{12}{21}$
- Step 4: Simplify the fraction.
- $\frac{12}{21} = \frac{4}{7}$

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

---

Problem 6: $\frac{5}{12} + \frac{6}{24}$

- Step 1: Find the common denominator.
- The denominators are 12 and 24. The LCD is 24.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}$
- $\frac{6}{24}$ remains $\frac{6}{24}$.
- Step 3: Add the numerators.
- $\frac{10}{24} + \frac{6}{24} = \frac{10 + 6}{24} = \frac{16}{24}$
- Step 4: Simplify the fraction.
- $\frac{16}{24} = \frac{2}{3}$

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

---

Problem 7: $\frac{1}{4} + \frac{1}{8}$

- Step 1: Find the common denominator.
- The denominators are 4 and 8. The LCD is 8.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
- $\frac{1}{8}$ remains $\frac{1}{8}$.
- Step 3: Add the numerators.
- $\frac{2}{8} + \frac{1}{8} = \frac{2 + 1}{8} = \frac{3}{8}$
- Step 4: Simplify the fraction.
- $\frac{3}{8}$ is already in simplest form.

Answer: $\boxed{\frac{3}{8}}$

---

Problem 8: $\frac{2}{3} + \frac{6}{9}$

- Step 1: Find the common denominator.
- The denominators are 3 and 9. The LCD is 9.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$
- $\frac{6}{9}$ remains $\frac{6}{9}$.
- Step 3: Add the numerators.
- $\frac{6}{9} + \frac{6}{9} = \frac{6 + 6}{9} = \frac{12}{9}$
- Step 4: Simplify the fraction.
- $\frac{12}{9} = \frac{4}{3}$

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

---

Problem 9: $\frac{1}{5} + \frac{5}{15}$

- Step 1: Find the common denominator.
- The denominators are 5 and 15. The LCD is 15.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$
- $\frac{5}{15}$ remains $\frac{5}{15}$.
- Step 3: Add the numerators.
- $\frac{3}{15} + \frac{5}{15} = \frac{3 + 5}{15} = \frac{8}{15}$
- Step 4: Simplify the fraction.
- $\frac{8}{15}$ is already in simplest form.

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

---

Problem 10: $\frac{1}{3} + \frac{5}{18}$

- Step 1: Find the common denominator.
- The denominators are 3 and 18. The LCD is 18.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{1}{3} = \frac{1 \times 6}{3 \times 6} = \frac{6}{18}$
- $\frac{5}{18}$ remains $\frac{5}{18}$.
- Step 3: Add the numerators.
- $\frac{6}{18} + \frac{5}{18} = \frac{6 + 5}{18} = \frac{11}{18}$
- Step 4: Simplify the fraction.
- $\frac{11}{18}$ is already in simplest form.

Answer: $\boxed{\frac{11}{18}}$

---

Final Answers:

1. $\boxed{\frac{3}{4}}$
2. $\boxed{\frac{5}{24}}$
3. $\boxed{\frac{7}{12}}$
4. $\boxed{\frac{7}{16}}$
5. $\boxed{\frac{4}{7}}$
6. $\boxed{\frac{2}{3}}$
7. $\boxed{\frac{3}{8}}$
8. $\boxed{\frac{4}{3}}$
9. $\boxed{\frac{8}{15}}$
10. $\boxed{\frac{11}{18}}$