This worksheet provides structured practice for adding and subtracting fractions with different denominators, showing students how to find common denominators step by step.

To solve the problems on the "Adding Subtracting Fractions Sheet 3," we need to follow these steps:

1. Find a Common Denominator: When adding or subtracting fractions, the denominators must be the same. If they are not, find the least common denominator (LCD).

2. Adjust the Fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator by the necessary factor.

3. Add or Subtract the Numerators: Once the denominators are the same, add or subtract the numerators as indicated.

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:

\[
\frac{1}{3} + \frac{2}{5} = \frac{1 \times 5}{3 \times 5} + \frac{2 \times 3}{5 \times 3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}
\]

Problem 2:

\[
\frac{1}{2} - \frac{1}{3} = \frac{1 \times 3}{2 \times 3} - \frac{1 \times 2}{3 \times 2} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}
\]

Problem 3:

\[
\frac{1}{4} + \frac{1}{3} = \frac{1 \times 3}{4 \times 3} + \frac{1 \times 4}{3 \times 4} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}
\]

Problem 4:

\[
\frac{1}{4} - \frac{1}{5} = \frac{1 \times 5}{4 \times 5} - \frac{1 \times 4}{5 \times 4} = \frac{5}{20} - \frac{4}{20} = \frac{1}{20}
\]

Problem 5:

\[
\frac{2}{3} - \frac{1}{4} = \frac{2 \times 4}{3 \times 4} - \frac{1 \times 3}{4 \times 3} = \frac{8}{12} - \frac{3}{12} = \frac{5}{12}
\]

Problem 6:

\[
\frac{2}{3} + \frac{2}{9} = \frac{2 \times 3}{3 \times 3} + \frac{2}{9} = \frac{6}{9} + \frac{2}{9} = \frac{8}{9}
\]

Problem 7:

\[
\frac{1}{3} + \frac{2}{5} = \frac{1 \times 5}{3 \times 5} + \frac{2 \times 3}{5 \times 3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}
\]

Problem 8:

\[
\frac{7}{8} - \frac{1}{2} = \frac{7}{8} - \frac{1 \times 4}{2 \times 4} = \frac{7}{8} - \frac{4}{8} = \frac{3}{8}
\]

Problem 9:

\[
\frac{4}{5} - \frac{1}{2} = \frac{4 \times 2}{5 \times 2} - \frac{1 \times 5}{2 \times 5} = \frac{8}{10} - \frac{5}{10} = \frac{3}{10}
\]

Problem 10:

\[
\frac{1}{8} + \frac{2}{3} = \frac{1 \times 3}{8 \times 3} + \frac{2 \times 8}{3 \times 8} = \frac{3}{24} + \frac{16}{24} = \frac{19}{24}
\]

Problem 11:

\[
\frac{9}{10} - \frac{4}{5} = \frac{9}{10} - \frac{4 \times 2}{5 \times 2} = \frac{9}{10} - \frac{8}{10} = \frac{1}{10}
\]

Problem 12:

\[
\frac{2}{7} + \frac{1}{4} = \frac{2 \times 4}{7 \times 4} + \frac{1 \times 7}{4 \times 7} = \frac{8}{28} + \frac{7}{28} = \frac{15}{28}
\]

Problem 13:

\[
\frac{2}{3} - \frac{3}{5} = \frac{2 \times 5}{3 \times 5} - \frac{3 \times 3}{5 \times 3} = \frac{10}{15} - \frac{9}{15} = \frac{1}{15}
\]

Problem 14:

\[
\frac{1}{5} + \frac{2}{7} = \frac{1 \times 7}{5 \times 7} + \frac{2 \times 5}{7 \times 5} = \frac{7}{35} + \frac{10}{35} = \frac{17}{35}
\]

Problem 15:

\[
\frac{1}{6} + \frac{5}{12} = \frac{1 \times 2}{6 \times 2} + \frac{5}{12} = \frac{2}{12} + \frac{5}{12} = \frac{7}{12}
\]

Problem 16:

\[
\frac{4}{5} - \frac{1}{9} = \frac{4 \times 9}{5 \times 9} - \frac{1 \times 5}{9 \times 5} = \frac{36}{45} - \frac{5}{45} = \frac{31}{45}
\]

Problem 17:

\[
\frac{3}{4} + \frac{1}{5} = \frac{3 \times 5}{4 \times 5} + \frac{1 \times 4}{5 \times 4} = \frac{15}{20} + \frac{4}{20} = \frac{19}{20}
\]

Problem 18:

\[
\frac{5}{8} - \frac{2}{5} = \frac{5 \times 5}{8 \times 5} - \frac{2 \times 8}{5 \times 8} = \frac{25}{40} - \frac{16}{40} = \frac{9}{40}
\]

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \frac{11}{15} \\
2) & \frac{1}{6} \\
3) & \frac{7}{12} \\
4) & \frac{1}{20} \\
5) & \frac{5}{12} \\
6) & \frac{8}{9} \\
7) & \frac{11}{15} \\
8) & \frac{3}{8} \\
9) & \frac{3}{10} \\
10) & \frac{19}{24} \\
11) & \frac{1}{10} \\
12) & \frac{15}{28} \\
13) & \frac{1}{15} \\
14) & \frac{17}{35} \\
15) & \frac{7}{12} \\
16) & \frac{31}{45} \\
17) & \frac{19}{20} \\
18) & \frac{9}{40} \\
\end{array}
}
\]