Adding and Subtracting Unlike Denominators worksheet - Free Printable

To solve the problems involving addition and subtraction of fractions with unlike denominators, we need to follow these steps:

1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add or subtract the numerators, keeping the common denominator.
4. Simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Problem 1: \( \frac{2}{3} + \frac{1}{2} \)

- Step 1: Find the common denominator.
The denominators are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]

- Step 3: Add the numerators.
\[
\frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6}
\]

- Step 4: Simplify if possible.
\(\frac{7}{6}\) is already in simplest form.

Answer: \( \frac{7}{6} \)

---

Problem 2: \( \frac{2}{5} + \frac{1}{10} \)

- Step 1: Find the common denominator.
The denominators are 5 and 10. The LCM of 5 and 10 is 10.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]
\[
\frac{1}{10} = \frac{1}{10}
\]

- Step 3: Add the numerators.
\[
\frac{4}{10} + \frac{1}{10} = \frac{4 + 1}{10} = \frac{5}{10}
\]

- Step 4: Simplify if possible.
\(\frac{5}{10} = \frac{1}{2}\).

Answer: \( \frac{1}{2} \)

---

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

- Step 1: Find the common denominator.
The denominators are 5 and 4. The LCM of 5 and 4 is 20.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
\]
\[
\frac{2}{4} = \frac{2 \times 5}{4 \times 5} = \frac{10}{20}
\]

- Step 3: Add the numerators.
\[
\frac{4}{20} + \frac{10}{20} = \frac{4 + 10}{20} = \frac{14}{20}
\]

- Step 4: Simplify if possible.
\(\frac{14}{20} = \frac{7}{10}\).

Answer: \( \frac{7}{10} \)

---

Problem 4: \( \frac{3}{5} + \frac{3}{8} \)

- Step 1: Find the common denominator.
The denominators are 5 and 8. The LCM of 5 and 8 is 40.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}
\]
\[
\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}
\]

- Step 3: Add the numerators.
\[
\frac{24}{40} + \frac{15}{40} = \frac{24 + 15}{40} = \frac{39}{40}
\]

- Step 4: Simplify if possible.
\(\frac{39}{40}\) is already in simplest form.

Answer: \( \frac{39}{40} \)

---

Problem 5: \( \frac{2}{7} + \frac{1}{4} \)

- Step 1: Find the common denominator.
The denominators are 7 and 4. The LCM of 7 and 4 is 28.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28}
\]
\[
\frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}
\]

- Step 3: Add the numerators.
\[
\frac{8}{28} + \frac{7}{28} = \frac{8 + 7}{28} = \frac{15}{28}
\]

- Step 4: Simplify if possible.
\(\frac{15}{28}\) is already in simplest form.

Answer: \( \frac{15}{28} \)

---

Problem 6: \( \frac{3}{5} - \frac{3}{10} \)

- Step 1: Find the common denominator.
The denominators are 5 and 10. The LCM of 5 and 10 is 10.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
\]
\[
\frac{3}{10} = \frac{3}{10}
\]

- Step 3: Subtract the numerators.
\[
\frac{6}{10} - \frac{3}{10} = \frac{6 - 3}{10} = \frac{3}{10}
\]

- Step 4: Simplify if possible.
\(\frac{3}{10}\) is already in simplest form.

Answer: \( \frac{3}{10} \)

---

Problem 7: \( \frac{4}{6} - \frac{1}{12} \)

- Step 1: Find the common denominator.
The denominators are 6 and 12. The LCM of 6 and 12 is 12.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{4}{6} = \frac{4 \times 2}{6 \times 2} = \frac{8}{12}
\]
\[
\frac{1}{12} = \frac{1}{12}
\]

- Step 3: Subtract the numerators.
\[
\frac{8}{12} - \frac{1}{12} = \frac{8 - 1}{12} = \frac{7}{12}
\]

- Step 4: Simplify if possible.
\(\frac{7}{12}\) is already in simplest form.

Answer: \( \frac{7}{12} \)

---

Problem 8: \( \frac{4}{6} - \frac{1}{2} \)

- Step 1: Find the common denominator.
The denominators are 6 and 2. The LCM of 6 and 2 is 6.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{4}{6} = \frac{4}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]

- Step 3: Subtract the numerators.
\[
\frac{4}{6} - \frac{3}{6} = \frac{4 - 3}{6} = \frac{1}{6}
\]

- Step 4: Simplify if possible.
\(\frac{1}{6}\) is already in simplest form.

Answer: \( \frac{1}{6} \)

---

Problem 9: \( \frac{3}{4} - \frac{1}{3} \)

- Step 1: Find the common denominator.
The denominators are 4 and 3. The LCM of 4 and 3 is 12.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
\[
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\]

- Step 3: Subtract the numerators.
\[
\frac{9}{12} - \frac{4}{12} = \frac{9 - 4}{12} = \frac{5}{12}
\]

- Step 4: Simplify if possible.
\(\frac{5}{12}\) is already in simplest form.

Answer: \( \frac{5}{12} \)

---

Problem 10: \( \frac{7}{8} - \frac{3}{4} \)

- Step 1: Find the common denominator.
The denominators are 8 and 4. The LCM of 8 and 4 is 8.

- Step 2: Rewrite each fraction with the common denominator.
\[
\frac{7}{8} = \frac{7}{8}
\]
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]

- Step 3: Subtract the numerators.
\[
\frac{7}{8} - \frac{6}{8} = \frac{7 - 6}{8} = \frac{1}{8}
\]

- Step 4: Simplify if possible.
\(\frac{1}{8}\) is already in simplest form.

Answer: \( \frac{1}{8} \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{7}{6} \\
2. & \frac{1}{2} \\
3. & \frac{7}{10} \\
4. & \frac{39}{40} \\
5. & \frac{15}{28} \\
6. & \frac{3}{10} \\
7. & \frac{7}{12} \\
8. & \frac{1}{6} \\
9. & \frac{5}{12} \\
10. & \frac{1}{8} \\
\end{array}
}
\]