Worksheet for practicing addition and subtraction of fractions with step-by-step solutions.

To solve the problems in the image, we need to simplify each expression step by step. Let's go through each problem systematically.

---

Problem 1:

$$
\frac{3}{4} + \frac{5}{6}
$$

#### Step 1: Find the Least Common Denominator (LCD)
The denominators are 4 and 6. The LCD of 4 and 6 is 12.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{3}{4}$: Multiply numerator and denominator by 3:
$$
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$
- For $\frac{5}{6}$: Multiply numerator and denominator by 2:
$$
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
$$

#### Step 3: Add the fractions
$$
\frac{9}{12} + \frac{10}{12} = \frac{9 + 10}{12} = \frac{19}{12}
$$

#### Final Answer:
$$
\boxed{\frac{19}{12}}
$$

---

Problem 2:

$$
\frac{3}{4} - \frac{5}{6}
$$

#### Step 1: Use the same LCD (12) as in Problem 1
- For $\frac{3}{4}$: $\frac{3}{4} = \frac{9}{12}$
- For $\frac{5}{6}$: $\frac{5}{6} = \frac{10}{12}$

#### Step 2: Subtract the fractions
$$
\frac{9}{12} - \frac{10}{12} = \frac{9 - 10}{12} = \frac{-1}{12}
$$

#### Final Answer:
$$
\boxed{\frac{-1}{12}}
$$

---

Problem 3:

$$
\frac{3}{4} \cdot \frac{5}{6}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{3}{4} \cdot \frac{5}{6} = \frac{3 \cdot 5}{4 \cdot 6} = \frac{15}{24}
$$

#### Step 2: Simplify the fraction
The greatest common divisor (GCD) of 15 and 24 is 3:
$$
\frac{15}{24} = \frac{15 \div 3}{24 \div 3} = \frac{5}{8}
$$

#### Final Answer:
$$
\boxed{\frac{5}{8}}
$$

---

Problem 4:

$$
\frac{3}{4} \div \frac{5}{6}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \cdot \frac{6}{5}
$$

#### Step 2: Multiply the fractions
$$
\frac{3}{4} \cdot \frac{6}{5} = \frac{3 \cdot 6}{4 \cdot 5} = \frac{18}{20}
$$

#### Step 3: Simplify the fraction
The GCD of 18 and 20 is 2:
$$
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
$$

#### Final Answer:
$$
\boxed{\frac{9}{10}}
$$

---

Problem 5:

$$
\frac{7}{8} + \frac{1}{4}
$$

#### Step 1: Find the LCD
The denominators are 8 and 4. The LCD of 8 and 4 is 8.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{7}{8}$: It is already in terms of 8.
- For $\frac{1}{4}$: Multiply numerator and denominator by 2:
$$
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
$$

#### Step 3: Add the fractions
$$
\frac{7}{8} + \frac{2}{8} = \frac{7 + 2}{8} = \frac{9}{8}
$$

#### Final Answer:
$$
\boxed{\frac{9}{8}}
$$

---

Problem 6:

$$
\frac{7}{8} - \frac{1}{4}
$$

#### Step 1: Use the same LCD (8) as in Problem 5
- For $\frac{7}{8}$: It is already in terms of 8.
- For $\frac{1}{4}$: $\frac{1}{4} = \frac{2}{8}$

#### Step 2: Subtract the fractions
$$
\frac{7}{8} - \frac{2}{8} = \frac{7 - 2}{8} = \frac{5}{8}
$$

#### Final Answer:
$$
\boxed{\frac{5}{8}}
$$

---

Problem 7:

$$
\frac{7}{8} \cdot \frac{1}{4}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{7}{8} \cdot \frac{1}{4} = \frac{7 \cdot 1}{8 \cdot 4} = \frac{7}{32}
$$

#### Final Answer:
$$
\boxed{\frac{7}{32}}
$$

---

Problem 8:

$$
\frac{7}{8} \div \frac{1}{4}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \cdot \frac{4}{1}
$$

#### Step 2: Multiply the fractions
$$
\frac{7}{8} \cdot \frac{4}{1} = \frac{7 \cdot 4}{8 \cdot 1} = \frac{28}{8}
$$

#### Step 3: Simplify the fraction
The GCD of 28 and 8 is 4:
$$
\frac{28}{8} = \frac{28 \div 4}{8 \div 4} = \frac{7}{2}
$$

#### Final Answer:
$$
\boxed{\frac{7}{2}}
$$

---

Problem 9:

$$
\frac{3}{5} + \frac{2}{3}
$$

#### Step 1: Find the LCD
The denominators are 5 and 3. The LCD of 5 and 3 is 15.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{3}{5}$: Multiply numerator and denominator by 3:
$$
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
$$
- For $\frac{2}{3}$: Multiply numerator and denominator by 5:
$$
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
$$

#### Step 3: Add the fractions
$$
\frac{9}{15} + \frac{10}{15} = \frac{9 + 10}{15} = \frac{19}{15}
$$

#### Final Answer:
$$
\boxed{\frac{19}{15}}
$$

---

Problem 10:

$$
\frac{3}{5} - \frac{2}{3}
$$

#### Step 1: Use the same LCD (15) as in Problem 9
- For $\frac{3}{5}$: $\frac{3}{5} = \frac{9}{15}$
- For $\frac{2}{3}$: $\frac{2}{3} = \frac{10}{15}$

#### Step 2: Subtract the fractions
$$
\frac{9}{15} - \frac{10}{15} = \frac{9 - 10}{15} = \frac{-1}{15}
$$

#### Final Answer:
$$
\boxed{\frac{-1}{15}}
$$

---

Problem 11:

$$
\frac{3}{5} \cdot \frac{2}{3}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{3}{5} \cdot \frac{2}{3} = \frac{3 \cdot 2}{5 \cdot 3} = \frac{6}{15}
$$

#### Step 2: Simplify the fraction
The GCD of 6 and 15 is 3:
$$
\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}
$$

#### Final Answer:
$$
\boxed{\frac{2}{5}}
$$

---

Problem 12:

$$
\frac{3}{5} \div \frac{2}{3}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \cdot \frac{3}{2}
$$

#### Step 2: Multiply the fractions
$$
\frac{3}{5} \cdot \frac{3}{2} = \frac{3 \cdot 3}{5 \cdot 2} = \frac{9}{10}
$$

#### Final Answer:
$$
\boxed{\frac{9}{10}}
$$

---

Problem 13:

$$
\frac{5}{6} + \frac{1}{2}
$$

#### Step 1: Find the LCD
The denominators are 6 and 2. The LCD of 6 and 2 is 6.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{5}{6}$: It is already in terms of 6.
- For $\frac{1}{2}$: Multiply numerator and denominator by 3:
$$
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
$$

#### Step 3: Add the fractions
$$
\frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6}
$$

#### Step 4: Simplify the fraction
The GCD of 8 and 6 is 2:
$$
\frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3}
$$

#### Final Answer:
$$
\boxed{\frac{4}{3}}
$$

---

Problem 14:

$$
\frac{5}{6} - \frac{1}{2}
$$

#### Step 1: Use the same LCD (6) as in Problem 13
- For $\frac{5}{6}$: It is already in terms of 6.
- For $\frac{1}{2}$: $\frac{1}{2} = \frac{3}{6}$

#### Step 2: Subtract the fractions
$$
\frac{5}{6} - \frac{3}{6} = \frac{5 - 3}{6} = \frac{2}{6}
$$

#### Step 3: Simplify the fraction
The GCD of 2 and 6 is 2:
$$
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
$$

#### Final Answer:
$$
\boxed{\frac{1}{3}}
$$

---

Problem 15:

$$
\frac{5}{6} \cdot \frac{1}{2}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{5}{6} \cdot \frac{1}{2} = \frac{5 \cdot 1}{6 \cdot 2} = \frac{5}{12}
$$

#### Final Answer:
$$
\boxed{\frac{5}{12}}
$$

---

Problem 16:

$$
\frac{5}{6} \div \frac{1}{2}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \cdot \frac{2}{1}
$$

#### Step 2: Multiply the fractions
$$
\frac{5}{6} \cdot \frac{2}{1} = \frac{5 \cdot 2}{6 \cdot 1} = \frac{10}{6}
$$

#### Step 3: Simplify the fraction
The GCD of 10 and 6 is 2:
$$
\frac{10}{6} = \frac{10 \div 2}{6 \div 2} = \frac{5}{3}
$$

#### Final Answer:
$$
\boxed{\frac{5}{3}}
$$

---

Problem 17:

$$
\frac{2}{3} + \frac{1}{4}
$$

#### Step 1: Find the LCD
The denominators are 3 and 4. The LCD of 3 and 4 is 12.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{2}{3}$: Multiply numerator and denominator by 4:
$$
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
$$
- For $\frac{1}{4}$: Multiply numerator and denominator by 3:
$$
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
$$

#### Step 3: Add the fractions
$$
\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}
$$

#### Final Answer:
$$
\boxed{\frac{11}{12}}
$$

---

Problem 18:

$$
\frac{2}{3} - \frac{1}{4}
$$

#### Step 1: Use the same LCD (12) as in Problem 17
- For $\frac{2}{3}$: $\frac{2}{3} = \frac{8}{12}$
- For $\frac{1}{4}$: $\frac{1}{4} = \frac{3}{12}$

#### Step 2: Subtract the fractions
$$
\frac{8}{12} - \frac{3}{12} = \frac{8 - 3}{12} = \frac{5}{12}
$$

#### Final Answer:
$$
\boxed{\frac{5}{12}}
$$

---

Problem 19:

$$
\frac{2}{3} \cdot \frac{1}{4}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{2}{3} \cdot \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} = \frac{2}{12}
$$

#### Step 2: Simplify the fraction
The GCD of 2 and 12 is 2:
$$
\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}
$$

#### Final Answer:
$$
\boxed{\frac{1}{6}}
$$

---

Problem 20:

$$
\frac{2}{3} \div \frac{1}{4}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{2}{3} \div \frac{1}{4} = \frac{2}{3} \cdot \frac{4}{1}
$$

#### Step 2: Multiply the fractions
$$
\frac{2}{3} \cdot \frac{4}{1} = \frac{2 \cdot 4}{3 \cdot 1} = \frac{8}{3}
$$

#### Final Answer:
$$
\boxed{\frac{8}{3}}
$$

---

Problem 21:

$$
\frac{4}{5} + \frac{3}{10}
$$

#### Step 1: Find the LCD
The denominators are 5 and 10. The LCD of 5 and 10 is 10.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{4}{5}$: Multiply numerator and denominator by 2:
$$
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
$$
- For $\frac{3}{10}$: It is already in terms of 10.

#### Step 3: Add the fractions
$$
\frac{8}{10} + \frac{3}{10} = \frac{8 + 3}{10} = \frac{11}{10}
$$

#### Final Answer:
$$
\boxed{\frac{11}{10}}
$$

---

Problem 22:

$$
\frac{4}{5} - \frac{3}{10}
$$

#### Step 1: Use the same LCD (10) as in Problem 21
- For $\frac{4}{5}$: $\frac{4}{5} = \frac{8}{10}$
- For $\frac{3}{10}$: It is already in terms of 10.

#### Step 2: Subtract the fractions
$$
\frac{8}{10} - \frac{3}{10} = \frac{8 - 3}{10} = \frac{5}{10}
$$

#### Step 3: Simplify the fraction
The GCD of 5 and 10 is 5:
$$
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
$$

#### Final Answer:
$$
\boxed{\frac{1}{2}}
$$

---

Problem 23:

$$
\frac{4}{5} \cdot \frac{3}{10}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{4}{5} \cdot \frac{3}{10} = \frac{4 \cdot 3}{5 \cdot 10} = \frac{12}{50}
$$

#### Step 2: Simplify the fraction
The GCD of 12 and 50 is 2:
$$
\frac{12}{50} = \frac{12 \div 2}{50 \div 2} = \frac{6}{25}
$$

#### Final Answer:
$$
\boxed{\frac{6}{25}}
$$

---

Problem 24:

$$
\frac{4}{5} \div \frac{3}{10}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{4}{5} \div \frac{3}{10} = \frac{4}{5} \cdot \frac{10}{3}
$$

#### Step 2: Multiply the fractions
$$
\frac{4}{5} \cdot \frac{10}{3} = \frac{4 \cdot 10}{5 \cdot 3} = \frac{40}{15}
$$

#### Step 3: Simplify the fraction
The GCD of 40 and 15 is 5:
$$
\frac{40}{15} = \frac{40 \div 5}{15 \div 5} = \frac{8}{3}
$$

#### Final Answer:
$$
\boxed{\frac{8}{3}}
$$

---

Problem 25:

$$
\frac{3}{7} + \frac{2}{5}
$$

#### Step 1: Find the LCD
The denominators are 7 and 5. The LCD of 7 and 5 is 35.

#### Step 2: Rewrite each fraction with the LCD
- For $\frac{3}{7}$: Multiply numerator and denominator by 5:
$$
\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}
$$
- For $\frac{2}{5}$: Multiply numerator and denominator by 7:
$$
\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}
$$

#### Step 3: Add the fractions
$$
\frac{15}{35} + \frac{14}{35} = \frac{15 + 14}{35} = \frac{29}{35}
$$

#### Final Answer:
$$
\boxed{\frac{29}{35}}
$$

---

Problem 26:

$$
\frac{3}{7} - \frac{2}{5}
$$

#### Step 1: Use the same LCD (35) as in Problem 25
- For $\frac{3}{7}$: $\frac{3}{7} = \frac{15}{35}$
- For $\frac{2}{5}$: $\frac{2}{5} = \frac{14}{35}$

#### Step 2: Subtract the fractions
$$
\frac{15}{35} - \frac{14}{35} = \frac{15 - 14}{35} = \frac{1}{35}
$$

#### Final Answer:
$$
\boxed{\frac{1}{35}}
$$

---

Problem 27:

$$
\frac{3}{7} \cdot \frac{2}{5}
$$

#### Step 1: Multiply the numerators and denominators
$$
\frac{3}{7} \cdot \frac{2}{5} = \frac{3 \cdot 2}{7 \cdot 5} = \frac{6}{35}
$$

#### Final Answer:
$$
\boxed{\frac{6}{35}}
$$

---

Problem 28:

$$
\frac{3}{7} \div \frac{2}{5}
$$

#### Step 1: Rewrite division as multiplication by the reciprocal
$$
\frac{3}{7} \div \frac{2}{5} = \frac{3}{7} \cdot \frac{5}{2}
$$

#### Step 2: Multiply the fractions
$$
\frac{3}{7} \cdot \frac{5}{2} = \frac{3 \cdot 5}{7 \cdot 2} = \frac{15}{14}
$$

#### Final Answer:
$$
\boxed{\frac{15}{14}}
$$

---

Final Summary of Answers:

1. $\boxed{\frac{19}{12}}$
2. $\boxed{\frac{-1}{12}}$
3. $\boxed{\frac{5}{8}}$
4. $\boxed{\frac{9}{10}}$
5. $\boxed{\frac{9}{8}}$
6. $\boxed{\frac{5}{8}}$
7. $\boxed{\frac{7}{32}}$
8. $\boxed{\frac{7}{2}}$
9. $\boxed{\frac{19}{15}}$
10. $\boxed{\frac{-1}{15}}$
11. $\boxed{\frac{2}{5}}$
12. $\boxed{\frac{9}{10}}$
13. $\boxed{\frac{4}{3}}$
14. $\boxed{\frac{1}{3}}$
15. $\boxed{\frac{5}{12}}$
16. $\boxed{\frac{5}{3}}$
17. $\boxed{\frac{11}{12}}$
18. $\boxed{\frac{5}{12}}$
19. $\boxed{\frac{1}{6}}$
20. $\boxed{\frac{8}{3}}$
21. $\boxed{\frac{11}{10}}$
22. $\boxed{\frac{1}{2}}$
23. $\boxed{\frac{6}{25}}$
24. $\boxed{\frac{8}{3}}$
25. $\boxed{\frac{29}{35}}$
26. $\boxed{\frac{1}{35}}$
27. $\boxed{\frac{6}{35}}$
28. $\boxed{\frac{15}{14}}$

Final Answer Boxed:
$$
\boxed{
\begin{array}{ll}
1. \frac{19}{12} & 2. \frac{-1}{12} \\
3. \frac{5}{8} & 4. \frac{9}{10} \\
5. \frac{9}{8} & 6. \frac{5}{8} \\
7. \frac{7}{32} & 8. \frac{7}{2} \\
9. \frac{19}{15} & 10. \frac{-1}{15} \\
11. \frac{2}{5} & 12. \frac{9}{10} \\
13. \frac{4}{3} & 14. \frac{1}{3} \\
15. \frac{5}{12} & 16. \frac{5}{3} \\
17. \frac{11}{12} & 18. \frac{5}{12} \\
19. \frac{1}{6} & 20. \frac{8}{3} \\
21. \frac{11}{10} & 22. \frac{1}{2} \\
23. \frac{6}{25} & 24. \frac{8}{3} \\
25. \frac{29}{35} & 26. \frac{1}{35} \\
27. \frac{6}{35} & 28. \frac{15}{14} \\
\end{array}
}
$$