Math worksheet for practicing adding and subtracting fractions with unlike denominators, featuring matching exercises.

Problem Overview:

The task involves matching equivalent calculations for adding and subtracting fractions with unlike denominators. We need to simplify each fraction expression on both sides and match them accordingly.

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Section A: Adding Fractions

#### Step 1: Simplify each addition problem.
We will convert all fractions to have a common denominator and then add them.

##### Left Column:
1. $\frac{5}{8} + \frac{1}{4}$
- Convert $\frac{1}{4}$ to eighths: $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$

2. $\frac{1}{8} + \frac{3}{4}$
- Convert $\frac{3}{4}$ to eighths: $\frac{3}{4} = \frac{6}{8}$
- Add: $\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$

3. $\frac{3}{8} + \frac{1}{4}$
- Convert $\frac{1}{4}$ to eighths: $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

4. $\frac{1}{8} + \frac{1}{2}$
- Convert $\frac{1}{2}$ to eighths: $\frac{1}{2} = \frac{4}{8}$
- Add: $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$

5. $\frac{2}{8} + \frac{3}{4}$
- Convert $\frac{3}{4}$ to eighths: $\frac{3}{4} = \frac{6}{8}$
- Add: $\frac{2}{8} + \frac{6}{8} = \frac{8}{8} = 1$

##### Right Column:
1. $\frac{1}{8} + \frac{6}{8}$
- Add: $\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$

2. $\frac{2}{8} + \frac{6}{8}$
- Add: $\frac{2}{8} + \frac{6}{8} = \frac{8}{8} = 1$

3. $\frac{5}{8} + \frac{2}{8}$
- Add: $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$

4. $\frac{1}{8} + \frac{4}{8}$
- Add: $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$

5. $\frac{3}{8} + \frac{2}{8}$
- Add: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

#### Step 2: Match the simplified results.
- $\frac{5}{8} + \frac{1}{4} = \frac{7}{8}$ matches with $\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$
- $\frac{1}{8} + \frac{3}{4} = \frac{7}{8}$ matches with $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$
- $\frac{3}{8} + \frac{1}{4} = \frac{5}{8}$ matches with $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$
- $\frac{1}{8} + \frac{1}{2} = \frac{5}{8}$ matches with $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$
- $\frac{2}{8} + \frac{3}{4} = 1$ matches with $\frac{2}{8} + \frac{6}{8} = 1$

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Section B: Subtracting Fractions

#### Step 1: Simplify each subtraction problem.
We will convert all fractions to have a common denominator and then subtract them.

##### Left Column:
1. $\frac{7}{9} - \frac{1}{3}$
- Convert $\frac{1}{3}$ to ninths: $\frac{1}{3} = \frac{3}{9}$
- Subtract: $\frac{7}{9} - \frac{3}{9} = \frac{4}{9}$

2. $\frac{7}{9} - \frac{2}{3}$
- Convert $\frac{2}{3}$ to ninths: $\frac{2}{3} = \frac{6}{9}$
- Subtract: $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$

3. $\frac{8}{9} - \frac{1}{3}$
- Convert $\frac{1}{3}$ to ninths: $\frac{1}{3} = \frac{3}{9}$
- Subtract: $\frac{8}{9} - \frac{3}{9} = \frac{5}{9}$

4. $\frac{8}{9} - \frac{2}{3}$
- Convert $\frac{2}{3}$ to ninths: $\frac{2}{3} = \frac{6}{9}$
- Subtract: $\frac{8}{9} - \frac{6}{9} = \frac{2}{9}$

##### Right Column:
1. $\frac{7}{9} - \frac{3}{9}$
- Subtract: $\frac{7}{9} - \frac{3}{9} = \frac{4}{9}$

2. $\frac{8}{9} - \frac{6}{9}$
- Subtract: $\frac{8}{9} - \frac{6}{9} = \frac{2}{9}$

3. $\frac{7}{9} - \frac{6}{9}$
- Subtract: $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$

4. $\frac{8}{9} - \frac{3}{9}$
- Subtract: $\frac{8}{9} - \frac{3}{9} = \frac{5}{9}$

#### Step 2: Match the simplified results.
- $\frac{7}{9} - \frac{1}{3} = \frac{4}{9}$ matches with $\frac{7}{9} - \frac{3}{9} = \frac{4}{9}$
- $\frac{7}{9} - \frac{2}{3} = \frac{1}{9}$ matches with $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$
- $\frac{8}{9} - \frac{1}{3} = \frac{5}{9}$ matches with $\frac{8}{9} - \frac{3}{9} = \frac{5}{9}$
- $\frac{8}{9} - \frac{2}{3} = \frac{2}{9}$ matches with $\frac{8}{9} - \frac{6}{9} = \frac{2}{9}$

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Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & \frac{5}{8} + \frac{1}{4} \to \frac{1}{8} + \frac{6}{8}, \quad \frac{1}{8} + \frac{3}{4} \to \frac{5}{8} + \frac{2}{8}, \\
& \frac{3}{8} + \frac{1}{4} \to \frac{1}{8} + \frac{4}{8}, \quad \frac{1}{8} + \frac{1}{2} \to \frac{3}{8} + \frac{2}{8}, \\
& \frac{2}{8} + \frac{3}{4} \to \frac{2}{8} + \frac{6}{8}. \\
\text{Section B:} & \frac{7}{9} - \frac{1}{3} \to \frac{7}{9} - \frac{3}{9}, \quad \frac{7}{9} - \frac{2}{3} \to \frac{7}{9} - \frac{6}{9}, \\
& \frac{8}{9} - \frac{1}{3} \to \frac{8}{9} - \frac{3}{9}, \quad \frac{8}{9} - \frac{2}{3} \to \frac{8}{9} - \frac{6}{9}.
\end{array}
}
\]