Addition, Subtraction, Multiplication, and Division of Fractions ... - Free Printable

To solve the problems in the image, we will address each section step by step. Let's go through them one by one.

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Section 1: Add the mixed numbers

#### Problem 22: $ 4 \frac{7}{8} + 3 \frac{1}{16} $

1. Convert mixed numbers to improper fractions:
- $ 4 \frac{7}{8} = 4 + \frac{7}{8} = \frac{32}{8} + \frac{7}{8} = \frac{39}{8} $
- $ 3 \frac{1}{16} = 3 + \frac{1}{16} = \frac{48}{16} + \frac{1}{16} = \frac{49}{16} $

2. Find a common denominator:
- The denominators are 8 and 16. The least common denominator (LCD) is 16.
- Convert $ \frac{39}{8} $ to a fraction with denominator 16:
$$
\frac{39}{8} = \frac{39 \times 2}{8 \times 2} = \frac{78}{16}
$$

3. Add the fractions:
$$
\frac{78}{16} + \frac{49}{16} = \frac{78 + 49}{16} = \frac{127}{16}
$$

4. Convert back to a mixed number:
- Divide 127 by 16:
$$
127 \div 16 = 7 \text{ remainder } 15
$$
- So, $ \frac{127}{16} = 7 \frac{15}{16} $

Answer:
$$
\boxed{7 \frac{15}{16}}
$$

---

#### Problem 23: $ 3 \frac{3}{5} + 4 \frac{1}{5} $

1. Convert mixed numbers to improper fractions:
- $ 3 \frac{3}{5} = 3 + \frac{3}{5} = \frac{15}{5} + \frac{3}{5} = \frac{18}{5} $
- $ 4 \frac{1}{5} = 4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5} $

2. Add the fractions:
$$
\frac{18}{5} + \frac{21}{5} = \frac{18 + 21}{5} = \frac{39}{5}
$$

3. Convert back to a mixed number:
- Divide 39 by 5:
$$
39 \div 5 = 7 \text{ remainder } 4
$$
- So, $ \frac{39}{5} = 7 \frac{4}{5} $

Answer:
$$
\boxed{7 \frac{4}{5}}
$$

---

Section 2: Subtract the fractions

#### Problem 24: $ \frac{5}{6} - \frac{1}{3} $

1. Find a common denominator:
- The denominators are 6 and 3. The LCD is 6.
- Convert $ \frac{1}{3} $ to a fraction with denominator 6:
$$
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
$$

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

3. Simplify the fraction:
$$
\frac{3}{6} = \frac{1}{2}
$$

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

---

#### Problem 25: $ \frac{7}{9} - \frac{3}{5} $

1. Find a common denominator:
- The denominators are 9 and 5. The LCD is 45.
- Convert $ \frac{7}{9} $ to a fraction with denominator 45:
$$
\frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{45}
$$
- Convert $ \frac{3}{5} $ to a fraction with denominator 45:
$$
\frac{3}{5} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}
$$

2. Subtract the fractions:
$$
\frac{35}{45} - \frac{27}{45} = \frac{35 - 27}{45} = \frac{8}{45}
$$

Answer:
$$
\boxed{\frac{8}{45}}
$$

---

#### Problem 26: $ \frac{13}{17} - \frac{3}{17} $

1. Subtract the fractions:
$$
\frac{13}{17} - \frac{3}{17} = \frac{13 - 3}{17} = \frac{10}{17}
$$

Answer:
$$
\boxed{\frac{10}{17}}
$$

---

Section 3: Subtract the mixed numbers

#### Problem 27: $ 5 \frac{1}{3} - 4 \frac{2}{3} $

1. Convert mixed numbers to improper fractions:
- $ 5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} $
- $ 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} $

2. Subtract the fractions:
$$
\frac{16}{3} - \frac{14}{3} = \frac{16 - 14}{3} = \frac{2}{3}
$$

Answer:
$$
\boxed{\frac{2}{3}}
$$

---

#### Problem 28: $ 8 \frac{3}{5} - 5 \frac{3}{5} $

1. Subtract the whole numbers and the fractions separately:
- Whole numbers: $ 8 - 5 = 3 $
- Fractions: $ \frac{3}{5} - \frac{3}{5} = 0 $

2. Combine the results:
$$
3 + 0 = 3
$$

Answer:
$$
\boxed{3}
$$

---

Section 4: Multiply the fractions

#### Problem 29: $ \frac{2}{3} \times \frac{1}{8} $

1. Multiply the numerators and the denominators:
$$
\frac{2}{3} \times \frac{1}{8} = \frac{2 \times 1}{3 \times 8} = \frac{2}{24}
$$

2. Simplify the fraction:
$$
\frac{2}{24} = \frac{1}{12}
$$

Answer:
$$
\boxed{\frac{1}{12}}
$$

---

#### Problem 30: $ \frac{1}{5} \times \frac{10}{13} $

1. Multiply the numerators and the denominators:
$$
\frac{1}{5} \times \frac{10}{13} = \frac{1 \times 10}{5 \times 13} = \frac{10}{65}
$$

2. Simplify the fraction:
- The greatest common divisor (GCD) of 10 and 65 is 5.
$$
\frac{10}{65} = \frac{10 \div 5}{65 \div 5} = \frac{2}{13}
$$

Answer:
$$
\boxed{\frac{2}{13}}
$$

---

#### Problem 31: $ \frac{7}{8} \times \frac{16}{21} $

1. Multiply the numerators and the denominators:
$$
\frac{7}{8} \times \frac{16}{21} = \frac{7 \times 16}{8 \times 21} = \frac{112}{168}
$$

2. Simplify the fraction:
- The GCD of 112 and 168 is 56.
$$
\frac{112}{168} = \frac{112 \div 56}{168 \div 56} = \frac{2}{3}
$$

Answer:
$$
\boxed{\frac{2}{3}}
$$

---

Section 5: Divide the fractions

#### Problem 32: $ \frac{10}{11} \div \frac{15}{22} $

1. Rewrite division as multiplication by the reciprocal:
$$
\frac{10}{11} \div \frac{15}{22} = \frac{10}{11} \times \frac{22}{15}
$$

2. Multiply the fractions:
$$
\frac{10}{11} \times \frac{22}{15} = \frac{10 \times 22}{11 \times 15} = \frac{220}{165}
$$

3. Simplify the fraction:
- The GCD of 220 and 165 is 55.
$$
\frac{220}{165} = \frac{220 \div 55}{165 \div 55} = \frac{4}{3}
$$

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

---

#### Problem 33: $ \frac{3}{4} \div \frac{15}{16} $

1. Rewrite division as multiplication by the reciprocal:
$$
\frac{3}{4} \div \frac{15}{16} = \frac{3}{4} \times \frac{16}{15}
$$

2. Multiply the fractions:
$$
\frac{3}{4} \times \frac{16}{15} = \frac{3 \times 16}{4 \times 15} = \frac{48}{60}
$$

3. Simplify the fraction:
- The GCD of 48 and 60 is 12.
$$
\frac{48}{60} = \frac{48 \div 12}{60 \div 12} = \frac{4}{5}
$$

Answer:
$$
\boxed{\frac{4}{5}}
$$

---

#### Problem 34: $ \frac{9}{10} \div \frac{2}{3} $

1. Rewrite division as multiplication by the reciprocal:
$$
\frac{9}{10} \div \frac{2}{3} = \frac{9}{10} \times \frac{3}{2}
$$

2. Multiply the fractions:
$$
\frac{9}{10} \times \frac{3}{2} = \frac{9 \times 3}{10 \times 2} = \frac{27}{20}
$$

Answer:
$$
\boxed{\frac{27}{20}}
$$

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Final Answers:

1. $ 4 \frac{7}{8} + 3 \frac{1}{16} = \boxed{7 \frac{15}{16}} $
2. $ 3 \frac{3}{5} + 4 \frac{1}{5} = \boxed{7 \frac{4}{5}} $
3. $ \frac{5}{6} - \frac{1}{3} = \boxed{\frac{1}{2}} $
4. $ \frac{7}{9} - \frac{3}{5} = \boxed{\frac{8}{45}} $
5. $ \frac{13}{17} - \frac{3}{17} = \boxed{\frac{10}{17}} $
6. $ 5 \frac{1}{3} - 4 \frac{2}{3} = \boxed{\frac{2}{3}} $
7. $ 8 \frac{3}{5} - 5 \frac{3}{5} = \boxed{3} $
8. $ \frac{2}{3} \times \frac{1}{8} = \boxed{\frac{1}{12}} $
9. $ \frac{1}{5} \times \frac{10}{13} = \boxed{\frac{2}{13}} $
10. $ \frac{7}{8} \times \frac{16}{21} = \boxed{\frac{2}{3}} $
11. $ \frac{10}{11} \div \frac{15}{22} = \boxed{\frac{4}{3}} $
12. $ \frac{3}{4} \div \frac{15}{16} = \boxed{\frac{4}{5}} $
13. $ \frac{9}{10} \div \frac{2}{3} = \boxed{\frac{27}{20}} $