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: $\frac{1}{6} + \frac{5}{12}$

- Step 1: Find the least common denominator (LCD) of 6 and 12. The LCD is 12.
- Step 2: Rewrite $\frac{1}{6}$ with a denominator of 12:
$$
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
$$
- Step 3: Add the fractions:
$$
\frac{2}{12} + \frac{5}{12} = \frac{2 + 5}{12} = \frac{7}{12}
$$
- Step 4: The fraction $\frac{7}{12}$ is already in simplest form.

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

---

Problem 2: $\frac{1}{8} + \frac{12}{24}$

- Step 1: Find the LCD of 8 and 24. The LCD is 24.
- Step 2: Rewrite $\frac{1}{8}$ with a denominator of 24:
$$
\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
$$
- Step 3: Add the fractions:
$$
\frac{3}{24} + \frac{12}{24} = \frac{3 + 12}{24} = \frac{15}{24}
$$
- Step 4: Simplify $\frac{15}{24}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:
$$
\frac{15 \div 3}{24 \div 3} = \frac{5}{8}
$$

Answer: $\frac{5}{8}$

---

Problem 3: $\frac{2}{3} + \frac{1}{15}$

- Step 1: Find the LCD of 3 and 15. The LCD is 15.
- Step 2: Rewrite $\frac{2}{3}$ with a denominator of 15:
$$
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
$$
- Step 3: Add the fractions:
$$
\frac{10}{15} + \frac{1}{15} = \frac{10 + 1}{15} = \frac{11}{15}
$$
- Step 4: The fraction $\frac{11}{15}$ is already in simplest form.

Answer: $\frac{11}{15}$

---

Problem 4: $\frac{3}{9} + \frac{7}{18}$

- Step 1: Find the LCD of 9 and 18. The LCD is 18.
- Step 2: Rewrite $\frac{3}{9}$ with a denominator of 18:
$$
\frac{3}{9} = \frac{3 \times 2}{9 \times 2} = \frac{6}{18}
$$
- Step 3: Add the fractions:
$$
\frac{6}{18} + \frac{7}{18} = \frac{6 + 7}{18} = \frac{13}{18}
$$
- Step 4: The fraction $\frac{13}{18}$ is already in simplest form.

Answer: $\frac{13}{18}$

---

Problem 5: $\frac{1}{6} + \frac{3}{12}$

- Step 1: Find the LCD of 6 and 12. The LCD is 12.
- Step 2: Rewrite $\frac{1}{6}$ with a denominator of 12:
$$
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
$$
- Step 3: Add the fractions:
$$
\frac{2}{12} + \frac{3}{12} = \frac{2 + 3}{12} = \frac{5}{12}
$$
- Step 4: The fraction $\frac{5}{12}$ is already in simplest form.

Answer: $\frac{5}{12}$

---

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

- Step 1: Find the LCD of 3 and 9. The LCD is 9.
- Step 2: Rewrite $\frac{2}{3}$ with a denominator of 9:
$$
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
$$
- Step 3: Add the fractions:
$$
\frac{6}{9} + \frac{2}{9} = \frac{6 + 2}{9} = \frac{8}{9}
$$
- Step 4: The fraction $\frac{8}{9}$ is already in simplest form.

Answer: $\frac{8}{9}$

---

Problem 7: $\frac{4}{5} + \frac{2}{15}$

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

Answer: $\frac{14}{15}$

---

Problem 8: $\frac{6}{8} + \frac{3}{16}$

- Step 1: Find the LCD of 8 and 16. The LCD is 16.
- Step 2: Rewrite $\frac{6}{8}$ with a denominator of 16:
$$
\frac{6}{8} = \frac{6 \times 2}{8 \times 2} = \frac{12}{16}
$$
- Step 3: Add the fractions:
$$
\frac{12}{16} + \frac{3}{16} = \frac{12 + 3}{16} = \frac{15}{16}
$$
- Step 4: The fraction $\frac{15}{16}$ is already in simplest form.

Answer: $\frac{15}{16}$

---

Problem 9: $\frac{1}{4} + \frac{3}{16}$

- Step 1: Find the LCD of 4 and 16. The LCD is 16.
- Step 2: Rewrite $\frac{1}{4}$ with a denominator of 16:
$$
\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}
$$
- Step 3: Add the fractions:
$$
\frac{4}{16} + \frac{3}{16} = \frac{4 + 3}{16} = \frac{7}{16}
$$
- Step 4: The fraction $\frac{7}{16}$ is already in simplest form.

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

---

Problem 10: $\frac{1}{2} + \frac{2}{6}$

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

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

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Final Answers:

1. $\frac{7}{12}$
2. $\frac{5}{8}$
3. $\frac{11}{15}$
4. $\frac{13}{18}$
5. $\frac{5}{12}$
6. $\frac{8}{9}$
7. $\frac{14}{15}$
8. $\frac{15}{16}$
9. $\frac{7}{16}$
10. $\frac{5}{6}$

$$
\boxed{\frac{7}{12}, \frac{5}{8}, \frac{11}{15}, \frac{13}{18}, \frac{5}{12}, \frac{8}{9}, \frac{14}{15}, \frac{15}{16}, \frac{7}{16}, \frac{5}{6}}
$$