adding and subtracting fractions
(unlike denominators)
1. $\frac{4}{5} + \frac{1}{2} - \frac{3}{4} =$ \t\t2. $\frac{25}{18} - \frac{2}{9} - \frac{1}{6} =$

3. $\frac{2}{3} - \frac{5}{9} + \frac{11}{12} =$ \t\t4. $\frac{42}{85} + \frac{10}{17} - \frac{2}{5} =$

5. $\frac{3}{7} - \frac{1}{10} - \frac{1}{5} =$ \t\t6. $\frac{5}{6} - \frac{25}{42} + \frac{4}{7} =$

7. $\frac{12}{25} + \frac{8}{15} - \frac{3}{5} =$ \t\t8. $\frac{1}{2} + \frac{2}{3} - \frac{3}{4} =$

9. $\frac{3}{8} + \frac{5}{6} + \frac{7}{12} =$ \t\t10. $\frac{12}{20} + \frac{3}{10} - \frac{2}{5} =$

11. $\frac{20}{50} + \frac{10}{25} - \frac{55}{100} =$ \t\t12. $\frac{40}{99} + \frac{4}{11} + \frac{2}{9} =$

Question

adding and subtracting fractions
(unlike denominators)
1. $\frac{4}{5} + \frac{1}{2} - \frac{3}{4} =$ \t\t2. $\frac{25}{18} - \frac{2}{9} - \frac{1}{6} =$

3. $\frac{2}{3} - \frac{5}{9} + \frac{11}{12} =$ \t\t4. $\frac{42}{85} + \frac{10}{17} - \frac{2}{5} =$

5. $\frac{3}{7} - \frac{1}{10} - \frac{1}{5} =$ \t\t6. $\frac{5}{6} - \frac{25}{42} + \frac{4}{7} =$

7. $\frac{12}{25} + \frac{8}{15} - \frac{3}{5} =$ \t\t8. $\frac{1}{2} + \frac{2}{3} - \frac{3}{4} =$

9. $\frac{3}{8} + \frac{5}{6} + \frac{7}{12} =$ \t\t10. $\frac{12}{20} + \frac{3}{10} - \frac{2}{5} =$

11. $\frac{20}{50} + \frac{10}{25} - \frac{55}{100} =$ \t\t12. $\frac{40}{99} + \frac{4}{11} + \frac{2}{9} =$

Accepted Answer

### Problem 1: $\boldsymbol{\frac{4}{5} + \frac{1}{2} - \frac{3}{4}}$
# Explanation:
## Step 1: Find the least common denominator (LCD) of 5, 2, and 4.
The LCD of 5, 2, and 4 is 20.
## Step 2: Rewrite each fraction with the LCD.
$\frac{4}{5} = \frac{4 	imes 4}{5 	imes 4} = \frac{16}{20}$, $\frac{1}{2} = \frac{1 	imes 10}{2 	imes 10} = \frac{10}{20}$, $\frac{3}{4} = \frac{3 	imes 5}{4 	imes 5} = \frac{15}{20}$
## Step 3: Perform the operations.
$\frac{16}{20} + \frac{10}{20} - \frac{15}{20} = \frac{16 + 10 - 15}{20} = \frac{11}{20}$
# Answer:
$\frac{11}{20}$

### Problem 2: $\boldsymbol{\frac{25}{18} - \frac{2}{9} - \frac{1}{6}}$
# Explanation:
## Step 1: Find the LCD of 18, 9, and 6.
The LCD of 18, 9, and 6 is 18.
## Step 2: Rewrite each fraction with the LCD.
$\frac{2}{9} = \frac{2 	imes 2}{9 	imes 2} = \frac{4}{18}$, $\frac{1}{6} = \frac{1 	imes 3}{6 	imes 3} = \frac{3}{18}$
## Step 3: Perform the operations.
$\frac{25}{18} - \frac{4}{18} - \frac{3}{18} = \frac{25 - 4 - 3}{18} = \frac{18}{18} = 1$
# Answer:
$1$

### Problem 3: $\boldsymbol{\frac{2}{3} - \frac{5}{9} + \frac{11}{12}}$
# Explanation:
## Step 1: Find the LCD of 3, 9, and 12.
The LCD of 3, 9, and 12 is 36.
## Step 2: Rewrite each fraction with the LCD.
$\frac{2}{3} = \frac{2 	imes 12}{3 	imes 12} = \frac{24}{36}$, $\frac{5}{9} = \frac{5 	imes 4}{9 	imes 4} = \frac{20}{36}$, $\frac{11}{12} = \frac{11 	imes 3}{12 	imes 3} = \frac{33}{36}$
## Step 3: Perform the operations.
$\frac{24}{36} - \frac{20}{36} + \frac{33}{36} = \frac{24 - 20 + 33}{36} = \frac{37}{36} = 1\frac{1}{36}$
# Answer:
$\frac{37}{36}$ (or $1\frac{1}{36}$)

### Problem 4: $\boldsymbol{\frac{42}{85} + \frac{10}{17} - \frac{2}{5}}$
# Explanation:
## Step 1: Find the LCD of 85, 17, and 5.
The LCD of 85, 17, and 5 is 85.
## Step 2: Rewrite each fraction with the LCD.
$\frac{10}{17} = \frac{10 	imes 5}{17 	imes 5} = \frac{50}{85}$, $\frac{2}{5} = \frac{2 	imes 17}{5 	imes 17} = \frac{34}{85}$
## Step 3: Perform the operations.
$\frac{42}{85} + \frac{50}{85} - \frac{34}{85} = \frac{42 + 50 - 34}{85} = \frac{58}{85}$
# Answer:
$\frac{58}{85}$

### Problem 5: $\boldsymbol{\frac{3}{7} - \frac{1}{10} - \frac{1}{5}}$
# Explanation:
## Step 1: Find the LCD of 7, 10, and 5.
The LCD of 7, 10, and 5 is 70.
## Step 2: Rewrite each fraction with the LCD.
$\frac{3}{7} = \frac{3 	imes 10}{7 	imes 10} = \frac{30}{70}$, $\frac{1}{10} = \frac{1 	imes 7}{10 	imes 7} = \frac{7}{70}$, $\frac{1}{5} = \frac{1 	imes 14}{5 	imes 14} = \frac{14}{70}$
## Step 3: Perform the operations.
$\frac{30}{70} - \frac{7}{70} - \frac{14}{70} = \frac{30 - 7 - 14}{70} = \frac{9}{70}$
# Answer:
$\frac{9}{70}$

### Problem 6: $\boldsymbol{\frac{5}{6} - \frac{25}{42} + \frac{4}{7}}$
# Explanation:
## Step 1: Find the LCD of 6, 42, and 7.
The LCD of 6, 42, and 7 is 42.
## Step 2: Rewrite each fraction with the LCD.
$\frac{5}{6} = \frac{5 	imes 7}{6 	imes 7} = \frac{35}{42}$, $\frac{4}{7} = \frac{4 	imes 6}{7 	imes 6} = \frac{24}{42}$
## Step 3: Perform the operations.
$\frac{35}{42} - \frac{25}{42} + \frac{24}{42} = \frac{35 - 25 + 24}{42} = \frac{34}{42} = \frac{17}{21}$
# Answer:
$\frac{17}{21}$

### Problem 7: $\boldsymbol{\frac{12}{25} + \frac{8}{15} - \frac{3}{5}}$
# Explanation:
## Step 1: Find the LCD of 25, 15, and 5.
The LCD of 25, 15, and 5 is 75.
## Step 2: Rewrite each fraction with the LCD.
$\frac{12}{25} = \frac{12 	imes 3}{25 	imes 3} = \frac{36}{75}$, $\frac{8}{15} = \frac{8 	imes 5}{15 	imes 5} = \frac{40}{75}$, $\frac{3}{5} = \frac{3 	imes 15}{5 	imes 15} = \frac{45}{75}$
## Step 3: Perform the operations.
$\frac{36}{75} + \frac{40}{75} - \frac{45}{75} = \frac{36 + 40 - 45}{75} = \frac{31}{75}$
# Answer:
$\frac{31}{75}$

### Problem 8: $\boldsymbol{\frac{1}{2} + \frac{2}{3} - \frac{3}{4}}$
# Explanation:
## Step 1: Find the LCD of 2, 3, and 4.
The LCD of 2, 3, and 4 is 12.
## Step 2: Rewrite each fraction with the LCD.
$\frac{1}{2} = \frac{1 	imes 6}{2 	imes 6} = \frac{6}{12}$, $\frac{2}{3} = \frac{2 	imes 4}{3 	imes 4} = \frac{8}{12}$, $\frac{3}{4} = \frac{3 	imes 3}{4 	imes 3} = \frac{9}{12}$
## Step 3: Perform the operations.
$\frac{6}{12} + \frac{8}{12} - \frac{9}{12} = \frac{6 + 8 - 9}{12} = \frac{5}{12}$
# Answer:
$\frac{5}{12}$

### Problem 9: $\boldsymbol{\frac{3}{8} + \frac{5}{6} + \frac{7}{12}}$
# Explanation:
## Step 1: Find the LCD of 8, 6, and 12.
The LCD of 8, 6, and 12 is 24.
## Step 2: Rewrite each fraction with the LCD.
$\frac{3}{8} = \frac{3 	imes 3}{8 	imes 3} = \frac{9}{24}$, $\frac{5}{6} = \frac{5 	imes 4}{6 	imes 4} = \frac{20}{24}$, $\frac{7}{12} = \frac{7 	imes 2}{12 	imes 2} = \frac{14}{24}$
## Step 3: Perform the operations.
$\frac{9}{24} + \frac{20}{24} + \frac{14}{24} = \frac{9 + 20 + 14}{24} = \frac{43}{24} = 1\frac{19}{24}$
# Answer:
$\frac{43}{24}$ (or $1\frac{19}{24}$)

### Problem 10: $\boldsymbol{\frac{12}{20} + \frac{3}{10} - \frac{2}{5}}$
# Explanation:
## Step 1: Simplify $\frac{12}{20}$ to $\frac{3}{5}$ (optional, but find LCD of 20, 10, and 5 is 20).
$\frac{3}{10} = \frac{3 	imes 2}{10 	imes 2} = \frac{6}{20}$, $\frac{2}{5} = \frac{2 	imes 4}{5 	imes 4} = \frac{8}{20}$, $\frac{12}{20}$ remains.
## Step 2: Perform the operations.
$\frac{12}{20} + \frac{6}{20} - \frac{8}{20} = \frac{12 + 6 - 8}{20} = \frac{10}{20} = \frac{1}{2}$
# Answer:
$\frac{1}{2}$

### Problem 11: $\boldsymbol{\frac{20}{50} + \frac{10}{25} - \frac{55}{100}}$
# Explanation:
## Step 1: Simplify fractions or find LCD (LCD of 50, 25, 100 is 100).
$\frac{20}{50} = \frac{40}{100}$, $\frac{10}{25} = \frac{40}{100}$, $\frac{55}{100}$ remains.
## Step 2: Perform the operations.
$\frac{40}{100} + \frac{40}{100} - \frac{55}{100} = \frac{40 + 40 - 55}{100} = \frac{25}{100} = \frac{1}{4}$
# Answer:
$\frac{1}{4}$

### Problem 12: $\boldsymbol{\frac{40}{99} + \frac{4}{11} + \frac{2}{9}}$
# Explanation:
## Step 1: Find the LCD of 99, 11, and 9.
The LCD of 99, 11, and 9 is 99.
## Step 2: Rewrite each fraction with the LCD.
$\frac{4}{11} = \frac{4 	imes 9}{11 	imes 9} = \frac{36}{99}$, $\frac{2}{9} = \frac{2 	imes 11}{9 	imes 11} = \frac{22}{99}$
## Step 3: Perform the operations.
$\frac{40}{99} + \frac{36}{99} + \frac{22}{99} = \frac{40 + 36 + 22}{99} = \frac{98}{99}$
# Answer:
$\frac{98}{99}$

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QUESTION IMAGE

Question

Explanation:

Problem 1: $\boldsymbol{\frac{4}{5} + \frac{1}{2} - \frac{3}{4}}$

Step 1: Find the least common denominator (LCD) of 5, 2, and 4.

Step 2: Rewrite each fraction with the LCD.

Step 3: Perform the operations.

Step 1: Find the LCD of 18, 9, and 6.

Step 2: Rewrite each fraction with the LCD.

Step 3: Perform the operations.

Step 1: Find the LCD of 3, 9, and 12.

Step 2: Rewrite each fraction with the LCD.

Step 3: Perform the operations.

Answer:

Problem 2: $\boldsymbol{\frac{25}{18} - \frac{2}{9} - \frac{1}{6}}$