Adding Subtracting Multiplying and Dividing Fractions Worksheets ... - Free Printable

Problem: Solve the given fraction operations.

We will solve each problem step by step, explaining the process for addition, subtraction, multiplication, and division of fractions.

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#### 1. $\frac{17}{3} + \frac{3}{17}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 3 and 17 is $3 \times 17 = 51$.

- Convert $\frac{17}{3}$ to a fraction with denominator 51:
$$
\frac{17}{3} = \frac{17 \times 17}{3 \times 17} = \frac{289}{51}
$$

- Convert $\frac{3}{17}$ to a fraction with denominator 51:
$$
\frac{3}{17} = \frac{3 \times 3}{17 \times 3} = \frac{9}{51}
$$

- Add the fractions:
$$
\frac{289}{51} + \frac{9}{51} = \frac{289 + 9}{51} = \frac{298}{51}
$$

Answer:
$$
\boxed{\frac{298}{51}}
$$

---

#### 2. $\frac{7}{2} + \frac{11}{13}$

The LCD of 2 and 13 is $2 \times 13 = 26$.

- Convert $\frac{7}{2}$ to a fraction with denominator 26:
$$
\frac{7}{2} = \frac{7 \times 13}{2 \times 13} = \frac{91}{26}
$$

- Convert $\frac{11}{13}$ to a fraction with denominator 26:
$$
\frac{11}{13} = \frac{11 \times 2}{13 \times 2} = \frac{22}{26}
$$

- Add the fractions:
$$
\frac{91}{26} + \frac{22}{26} = \frac{91 + 22}{26} = \frac{113}{26}
$$

Answer:
$$
\boxed{\frac{113}{26}}
$$

---

#### 3. $\frac{3}{2} + \frac{20}{3}$

The LCD of 2 and 3 is $2 \times 3 = 6$.

- Convert $\frac{3}{2}$ to a fraction with denominator 6:
$$
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
$$

- Convert $\frac{20}{3}$ to a fraction with denominator 6:
$$
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
$$

- Add the fractions:
$$
\frac{9}{6} + \frac{40}{6} = \frac{9 + 40}{6} = \frac{49}{6}
$$

Answer:
$$
\boxed{\frac{49}{6}}
$$

---

#### 4. $\frac{13}{14} - \frac{12}{22}$

Simplify $\frac{12}{22}$ first:
$$
\frac{12}{22} = \frac{6}{11}
$$

The LCD of 14 and 11 is $14 \times 11 = 154$.

- Convert $\frac{13}{14}$ to a fraction with denominator 154:
$$
\frac{13}{14} = \frac{13 \times 11}{14 \times 11} = \frac{143}{154}
$$

- Convert $\frac{6}{11}$ to a fraction with denominator 154:
$$
\frac{6}{11} = \frac{6 \times 14}{11 \times 14} = \frac{84}{154}
$$

- Subtract the fractions:
$$
\frac{143}{154} - \frac{84}{154} = \frac{143 - 84}{154} = \frac{59}{154}
$$

Answer:
$$
\boxed{\frac{59}{154}}
$$

---

#### 5. $\frac{9}{10} - \frac{3}{15}$

Simplify $\frac{3}{15}$ first:
$$
\frac{3}{15} = \frac{1}{5}
$$

The LCD of 10 and 5 is 10.

- Convert $\frac{1}{5}$ to a fraction with denominator 10:
$$
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
$$

- Subtract the fractions:
$$
\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}
$$

Answer:
$$
\boxed{\frac{7}{10}}
$$

---

#### 6. $\frac{18}{19} - \frac{5}{6}$

The LCD of 19 and 6 is $19 \times 6 = 114$.

- Convert $\frac{18}{19}$ to a fraction with denominator 114:
$$
\frac{18}{19} = \frac{18 \times 6}{19 \times 6} = \frac{108}{114}
$$

- Convert $\frac{5}{6}$ to a fraction with denominator 114:
$$
\frac{5}{6} = \frac{5 \times 19}{6 \times 19} = \frac{95}{114}
$$

- Subtract the fractions:
$$
\frac{108}{114} - \frac{95}{114} = \frac{108 - 95}{114} = \frac{13}{114}
$$

Answer:
$$
\boxed{\frac{13}{114}}
$$

---

#### 7. $\frac{12}{15} \times \frac{6}{20}$

First, simplify the fractions:
$$
\frac{12}{15} = \frac{4}{5}, \quad \frac{6}{20} = \frac{3}{10}
$$

Now multiply:
$$
\frac{4}{5} \times \frac{3}{10} = \frac{4 \times 3}{5 \times 10} = \frac{12}{50}
$$

Simplify $\frac{12}{50}$:
$$
\frac{12}{50} = \frac{6}{25}
$$

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

---

#### 8. $\frac{23}{18} \times \frac{16}{21}$

Multiply the numerators and denominators:
$$
\frac{23}{18} \times \frac{16}{21} = \frac{23 \times 16}{18 \times 21} = \frac{368}{378}
$$

Simplify $\frac{368}{378}$ by finding the greatest common divisor (GCD) of 368 and 378, which is 2:
$$
\frac{368}{378} = \frac{368 \div 2}{378 \div 2} = \frac{184}{189}
$$

Answer:
$$
\boxed{\frac{184}{189}}
$$

---

#### 9. $\frac{9}{14} \times \frac{22}{24}$

First, simplify $\frac{22}{24}$:
$$
\frac{22}{24} = \frac{11}{12}
$$

Now multiply:
$$
\frac{9}{14} \times \frac{11}{12} = \frac{9 \times 11}{14 \times 12} = \frac{99}{168}
$$

Simplify $\frac{99}{168}$ by finding the GCD of 99 and 168, which is 3:
$$
\frac{99}{168} = \frac{99 \div 3}{168 \div 3} = \frac{33}{56}
$$

Answer:
$$
\boxed{\frac{33}{56}}
$$

---

#### 10. $\frac{26}{52} \div \frac{12}{13}$

First, simplify $\frac{26}{52}$:
$$
\frac{26}{52} = \frac{1}{2}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{1}{2} \div \frac{12}{13} = \frac{1}{2} \times \frac{13}{12} = \frac{1 \times 13}{2 \times 12} = \frac{13}{24}
$$

Answer:
$$
\boxed{\frac{13}{24}}
$$

---

#### 11. $\frac{5}{96} \div \frac{3}{64}$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{5}{96} \div \frac{3}{64} = \frac{5}{96} \times \frac{64}{3} = \frac{5 \times 64}{96 \times 3} = \frac{320}{288}
$$

Simplify $\frac{320}{288}$ by finding the GCD of 320 and 288, which is 32:
$$
\frac{320}{288} = \frac{320 \div 32}{288 \div 32} = \frac{10}{9}
$$

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

---

#### 12. $\frac{27}{21} \div \frac{44}{14}$

First, simplify $\frac{27}{21}$ and $\frac{44}{14}$:
$$
\frac{27}{21} = \frac{9}{7}, \quad \frac{44}{14} = \frac{22}{7}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{9}{7} \div \frac{22}{7} = \frac{9}{7} \times \frac{7}{22} = \frac{9 \times 7}{7 \times 22} = \frac{63}{154}
$$

Simplify $\frac{63}{154}$ by finding the GCD of 63 and 154, which is 7:
$$
\frac{63}{154} = \frac{63 \div 7}{154 \div 7} = \frac{9}{22}
$$

Answer:
$$
\boxed{\frac{9}{22}}
$$

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Final Answers:

1. $\boxed{\frac{298}{51}}$
2. $\boxed{\frac{113}{26}}$
3. $\boxed{\frac{49}{6}}$
4. $\boxed{\frac{59}{154}}$
5. $\boxed{\frac{7}{10}}$
6. $\boxed{\frac{13}{114}}$
7. $\boxed{\frac{6}{25}}$
8. $\boxed{\frac{184}{189}}$
9. $\boxed{\frac{33}{56}}$
10. $\boxed{\frac{13}{24}}$
11. $\boxed{\frac{10}{9}}$
12. $\boxed{\frac{9}{22}}$