Adding, Subtracting, Multiplying And Dividing Fractions Worksheets - Free Printable

To solve the problems involving adding fractions with unlike denominators, we need to follow these steps:

Steps to Add Fractions with Unlike Denominators:

1. Find the Least Common Denominator (LCD): The LCD is the smallest number that both denominators can divide into evenly.
2. Adjust the fractions: Rewrite each fraction with the LCD as the denominator by multiplying both the numerator and the denominator of each fraction by the necessary factor.
3. Add the numerators: Once the denominators are the same, add the numerators and keep 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.

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Problem 1: $\frac{2}{5} + \frac{3}{4}$

1. Find the LCD: The denominators are 5 and 4. The LCD is 20.
2. Adjust the fractions:
- $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$
- $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
3. Add the numerators:
$$
\frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}
$$
4. Simplify: $\frac{23}{20}$ is already in simplest form.

Answer: $\frac{23}{20}$

---

Problem 2: $\frac{1}{8} + \frac{4}{5}$

1. Find the LCD: The denominators are 8 and 5. The LCD is 40.
2. Adjust the fractions:
- $\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}$
- $\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}$
3. Add the numerators:
$$
\frac{5}{40} + \frac{32}{40} = \frac{5 + 32}{40} = \frac{37}{40}
$$
4. Simplify: $\frac{37}{40}$ is already in simplest form.

Answer: $\frac{37}{40}$

---

Problem 3: $\frac{5}{6} + \frac{2}{3}$

1. Find the LCD: The denominators are 6 and 3. The LCD is 6.
2. Adjust the fractions:
- $\frac{5}{6}$ remains $\frac{5}{6}$.
- $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
3. Add the numerators:
$$
\frac{5}{6} + \frac{4}{6} = \frac{5 + 4}{6} = \frac{9}{6}
$$
4. Simplify: $\frac{9}{6} = \frac{3}{2}$.

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

---

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

1. Find the LCD: The denominators are 5 and 4. The LCD is 20.
2. Adjust the fractions:
- $\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$
- $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
3. Add the numerators:
$$
\frac{16}{20} + \frac{5}{20} = \frac{16 + 5}{20} = \frac{21}{20}
$$
4. Simplify: $\frac{21}{20}$ is already in simplest form.

Answer: $\frac{21}{20}$

---

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

1. Find the LCD: The denominators are 8 and 6. The LCD is 24.
2. Adjust the fractions:
- $\frac{6}{8} = \frac{6 \times 3}{8 \times 3} = \frac{18}{24}$
- $\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
3. Add the numerators:
$$
\frac{18}{24} + \frac{20}{24} = \frac{18 + 20}{24} = \frac{38}{24}
$$
4. Simplify: $\frac{38}{24} = \frac{19}{12}$.

Answer: $\frac{19}{12}$

---

Problem 6: $\frac{1}{10} + \frac{3}{5}$

1. Find the LCD: The denominators are 10 and 5. The LCD is 10.
2. Adjust the fractions:
- $\frac{1}{10}$ remains $\frac{1}{10}$.
- $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
3. Add the numerators:
$$
\frac{1}{10} + \frac{6}{10} = \frac{1 + 6}{10} = \frac{7}{10}
$$
4. Simplify: $\frac{7}{10}$ is already in simplest form.

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

---

Problem 7: $\frac{4}{5} + \frac{1}{7}$

1. Find the LCD: The denominators are 5 and 7. The LCD is 35.
2. Adjust the fractions:
- $\frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}$
- $\frac{1}{7} = \frac{1 \times 5}{7 \times 5} = \frac{5}{35}$
3. Add the numerators:
$$
\frac{28}{35} + \frac{5}{35} = \frac{28 + 5}{35} = \frac{33}{35}
$$
4. Simplify: $\frac{33}{35}$ is already in simplest form.

Answer: $\frac{33}{35}$

---

Problem 8: $\frac{3}{9} + \frac{1}{5}$

1. Find the LCD: The denominators are 9 and 5. The LCD is 45.
2. Adjust the fractions:
- $\frac{3}{9} = \frac{3 \times 5}{9 \times 5} = \frac{15}{45}$
- $\frac{1}{5} = \frac{1 \times 9}{5 \times 9} = \frac{9}{45}$
3. Add the numerators:
$$
\frac{15}{45} + \frac{9}{45} = \frac{15 + 9}{45} = \frac{24}{45}
$$
4. Simplify: $\frac{24}{45} = \frac{8}{15}$.

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

---

Problem 9: $\frac{2}{7} + \frac{3}{4}$

1. Find the LCD: The denominators are 7 and 4. The LCD is 28.
2. Adjust the fractions:
- $\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28}$
- $\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}$
3. Add the numerators:
$$
\frac{8}{28} + \frac{21}{28} = \frac{8 + 21}{28} = \frac{29}{28}
$$
4. Simplify: $\frac{29}{28}$ is already in simplest form.

Answer: $\frac{29}{28}$

---

Problem 10: $\frac{1}{12} + \frac{3}{8}$

1. Find the LCD: The denominators are 12 and 8. The LCD is 24.
2. Adjust the fractions:
- $\frac{1}{12} = \frac{1 \times 2}{12 \times 2} = \frac{2}{24}$
- $\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$
3. Add the numerators:
$$
\frac{2}{24} + \frac{9}{24} = \frac{2 + 9}{24} = \frac{11}{24}
$$
4. Simplify: $\frac{11}{24}$ is already in simplest form.

Answer: $\frac{11}{24}$

---

Problem 11: $\frac{1}{8} + \frac{5}{5}$

1. Simplify $\frac{5}{5}$: $\frac{5}{5} = 1$.
2. Add: $\frac{1}{8} + 1 = \frac{1}{8} + \frac{8}{8} = \frac{1 + 8}{8} = \frac{9}{8}$.

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

---

Problem 12: $\frac{4}{5} + \frac{8}{10}$

1. Simplify $\frac{8}{10}$: $\frac{8}{10} = \frac{4}{5}$.
2. Add: $\frac{4}{5} + \frac{4}{5} = \frac{4 + 4}{5} = \frac{8}{5}$.

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

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Problem 13: $\frac{9}{10} + \frac{4}{5}$

1. Find the LCD: The denominators are 10 and 5. The LCD is 10.
2. Adjust the fractions:
- $\frac{9}{10}$ remains $\frac{9}{10}$.
- $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$
3. Add the numerators:
$$
\frac{9}{10} + \frac{8}{10} = \frac{9 + 8}{10} = \frac{17}{10}
$$
4. Simplify: $\frac{17}{10}$ is already in simplest form.

Answer: $\frac{17}{10}$

---

Problem 14: $\frac{3}{12} + \frac{2}{4}$

1. Simplify $\frac{3}{12}$: $\frac{3}{12} = \frac{1}{4}$.
2. Simplify $\frac{2}{4}$: $\frac{2}{4} = \frac{1}{2}$.
3. Find the LCD: The denominators are 4 and 2. The LCD is 4.
4. Adjust the fractions:
- $\frac{1}{4}$ remains $\frac{1}{4}$.
- $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
5. Add the numerators:
$$
\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}
$$

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

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Problem 15: $\frac{3}{7} + \frac{2}{8}$

1. Simplify $\frac{2}{8}$: $\frac{2}{8} = \frac{1}{4}$.
2. Find the LCD: The denominators are 7 and 4. The LCD is 28.
3. Adjust the fractions:
- $\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}$
- $\frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}$
4. Add the numerators:
$$
\frac{12}{28} + \frac{7}{28} = \frac{12 + 7}{28} = \frac{19}{28}
$$
5. Simplify: $\frac{19}{28}$ is already in simplest form.

Answer: $\frac{19}{28}$

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Final Answers:

1. $\frac{23}{20}$
2. $\frac{37}{40}$
3. $\frac{3}{2}$
4. $\frac{21}{20}$
5. $\frac{19}{12}$
6. $\frac{7}{10}$
7. $\frac{33}{35}$
8. $\frac{8}{15}$
9. $\frac{29}{28}$
10. $\frac{11}{24}$
11. $\frac{9}{8}$
12. $\frac{8}{5}$
13. $\frac{17}{10}$
14. $\frac{3}{4}$
15. $\frac{19}{28}$

$$
\boxed{\frac{23}{20}, \frac{37}{40}, \frac{3}{2}, \frac{21}{20}, \frac{19}{12}, \frac{7}{10}, \frac{33}{35}, \frac{8}{15}, \frac{29}{28}, \frac{11}{24}, \frac{9}{8}, \frac{8}{5}, \frac{17}{10}, \frac{3}{4}, \frac{19}{28}}
$$