Fraction addition and subtraction worksheet with same denominators for practice.

Problem Explanation and Solution

The worksheet focuses on adding and subtracting fractions with the same denominator. Let's solve each section step by step.

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#### Section A: Solve (Fractions with the Same Denominator)

General Rule: When adding or subtracting fractions with the same denominator, you simply add or subtract the numerators while keeping the denominator the same.

##### Problems and Solutions

1. $\frac{1}{4} + \frac{1}{4}$
- Add the numerators: $1 + 1 = 2$
- Keep the denominator: $4$
- Result: $\frac{2}{4}$

2. $\frac{2}{4} + \frac{1}{4}$
- Add the numerators: $2 + 1 = 3$
- Keep the denominator: $4$
- Result: $\frac{3}{4}$

3. $\frac{1}{4} + \frac{2}{4}$
- Add the numerators: $1 + 2 = 3$
- Keep the denominator: $4$
- Result: $\frac{3}{4}$

4. $\frac{2}{4} + \frac{2}{4}$
- Add the numerators: $2 + 2 = 4$
- Keep the denominator: $4$
- Result: $\frac{4}{4} = 1$

5. $\frac{3}{4} - \frac{1}{4}$
- Subtract the numerators: $3 - 1 = 2$
- Keep the denominator: $4$
- Result: $\frac{2}{4}$

6. $\frac{4}{4} - \frac{2}{4}$
- Subtract the numerators: $4 - 2 = 2$
- Keep the denominator: $4$
- Result: $\frac{2}{4}$

7. $\frac{3}{4} - \frac{2}{4}$
- Subtract the numerators: $3 - 2 = 1$
- Keep the denominator: $4$
- Result: $\frac{1}{4}$

8. $\frac{3}{4} - \frac{3}{4}$
- Subtract the numerators: $3 - 3 = 0$
- Keep the denominator: $4$
- Result: $\frac{0}{4} = 0$

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#### Section B: Solve (Fractions with Different Denominators)

General Rule: When adding or subtracting fractions with different denominators, you need to find a common denominator first. Then, adjust the numerators accordingly before performing the addition or subtraction.

##### Problems and Solutions

1. $\frac{1}{5} + \frac{2}{5}$
- The denominators are the same ($5$).
- Add the numerators: $1 + 2 = 3$
- Keep the denominator: $5$
- Result: $\frac{3}{5}$

2. $\frac{6}{8} - \frac{2}{8}$
- The denominators are the same ($8$).
- Subtract the numerators: $6 - 2 = 4$
- Keep the denominator: $8$
- Simplify: $\frac{4}{8} = \frac{1}{2}$
- Result: $\frac{1}{2}$

3. $\frac{3}{11} + \frac{7}{11}$
- The denominators are the same ($11$).
- Add the numerators: $3 + 7 = 10$
- Keep the denominator: $11$
- Result: $\frac{10}{11}$

4. $\frac{5}{6} - \frac{1}{6}$
- The denominators are the same ($6$).
- Subtract the numerators: $5 - 1 = 4$
- Keep the denominator: $6$
- Simplify: $\frac{4}{6} = \frac{2}{3}$
- Result: $\frac{2}{3}$

5. $\frac{7}{9} + \frac{2}{9}$
- The denominators are the same ($9$).
- Add the numerators: $7 + 2 = 9$
- Keep the denominator: $9$
- Simplify: $\frac{9}{9} = 1$
- Result: $1$

6. $\frac{9}{10} - \frac{4}{10}$
- The denominators are the same ($10$).
- Subtract the numerators: $9 - 4 = 5$
- Keep the denominator: $10$
- Simplify: $\frac{5}{10} = \frac{1}{2}$
- Result: $\frac{1}{2}$

7. $\frac{8}{9} - \frac{7}{9}$
- The denominators are the same ($9$).
- Subtract the numerators: $8 - 7 = 1$
- Keep the denominator: $9$
- Result: $\frac{1}{9}$

8. $\frac{6}{10} + \frac{3}{10}$
- The denominators are the same ($10$).
- Add the numerators: $6 + 3 = 9$
- Keep the denominator: $10$
- Result: $\frac{9}{10}$

9. $\frac{4}{11} - \frac{2}{11}$
- The denominators are the same ($11$).
- Subtract the numerators: $4 - 2 = 2$
- Keep the denominator: $11$
- Result: $\frac{2}{11}$

10. $\frac{1}{12} + \frac{7}{12} + \frac{3}{12}$
- The denominators are the same ($12$).
- Add the numerators: $1 + 7 + 3 = 11$
- Keep the denominator: $12$
- Result: $\frac{11}{12}$

11. $\frac{8}{11} - \frac{3}{11} + \frac{5}{11}$
- The denominators are the same ($11$).
- Perform operations in order:
- Subtract: $8 - 3 = 5$
- Add: $5 + 5 = 10$
- Keep the denominator: $11$
- Result: $\frac{10}{11}$

12. $\frac{10}{12} - \frac{4}{12} - \frac{5}{12}$
- The denominators are the same ($12$).
- Perform operations in order:
- Subtract: $10 - 4 = 6$
- Subtract: $6 - 5 = 1$
- Keep the denominator: $12$
- Result: $\frac{1}{12}$

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Final Answers

#### Section A
1. $\frac{2}{4}$
2. $\frac{3}{4}$
3. $\frac{3}{4}$
4. $1$
5. $\frac{2}{4}$
6. $\frac{2}{4}$
7. $\frac{1}{4}$
8. $0$

#### Section B
1. $\frac{3}{5}$
2. $\frac{1}{2}$
3. $\frac{10}{11}$
4. $\frac{2}{3}$
5. $1$
6. $\frac{1}{2}$
7. $\frac{1}{9}$
8. $\frac{9}{10}$
9. $\frac{2}{11}$
10. $\frac{11}{12}$
11. $\frac{10}{11}$
12. $\frac{1}{12}$

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Boxed Final Answer

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & 1. \frac{2}{4}, 2. \frac{3}{4}, 3. \frac{3}{4}, 4. 1, 5. \frac{2}{4}, 6. \frac{2}{4}, 7. \frac{1}{4}, 8. 0 \\
\text{Section B:} & 1. \frac{3}{5}, 2. \frac{1}{2}, 3. \frac{10}{11}, 4. \frac{2}{3}, 5. 1, 6. \frac{1}{2}, 7. \frac{1}{9}, 8. \frac{9}{10}, 9. \frac{2}{11}, 10. \frac{11}{12}, 11. \frac{10}{11}, 12. \frac{1}{12}
\end{array}
}
\]