Math worksheet for practicing operations with mixed numbers and fractions.

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

---

Section 1: Add the mixed numbers

#### Problem 22: $ 4 \frac{7}{8} + 3 \frac{1}{14} $

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}{14} = 3 + \frac{1}{14} = \frac{42}{14} + \frac{1}{14} = \frac{43}{14} $

2. Find a common denominator:
- The denominators are 8 and 14. The least common multiple (LCM) of 8 and 14 is 56.
- Convert each fraction to have a denominator of 56:
- $ \frac{39}{8} = \frac{39 \times 7}{8 \times 7} = \frac{273}{56} $
- $ \frac{43}{14} = \frac{43 \times 4}{14 \times 4} = \frac{172}{56} $

3. Add the fractions:
- $ \frac{273}{56} + \frac{172}{56} = \frac{273 + 172}{56} = \frac{445}{56} $

4. Convert back to a mixed number:
- Divide 445 by 56:
- $ 445 \div 56 = 7 $ remainder $ 53 $
- So, $ \frac{445}{56} = 7 \frac{53}{56} $

Answer:
$$
\boxed{7 \frac{53}{56}}
$$

#### Problem 23: $ 3 \frac{3}{5} + 4 \frac{1}{8} $

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}{8} = 4 + \frac{1}{8} = \frac{32}{8} + \frac{1}{8} = \frac{33}{8} $

2. Find a common denominator:
- The denominators are 5 and 8. The LCM of 5 and 8 is 40.
- Convert each fraction to have a denominator of 40:
- $ \frac{18}{5} = \frac{18 \times 8}{5 \times 8} = \frac{144}{40} $
- $ \frac{33}{8} = \frac{33 \times 5}{8 \times 5} = \frac{165}{40} $

3. Add the fractions:
- $ \frac{144}{40} + \frac{165}{40} = \frac{144 + 165}{40} = \frac{309}{40} $

4. Convert back to a mixed number:
- Divide 309 by 40:
- $ 309 \div 40 = 7 $ remainder $ 29 $
- So, $ \frac{309}{40} = 7 \frac{29}{40} $

Answer:
$$
\boxed{7 \frac{29}{40}}
$$

---

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 LCM of 6 and 3 is 6.
- Convert each fraction to have a denominator of 6:
- $ \frac{5}{6} = \frac{5}{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 LCM of 9 and 5 is 45.
- Convert each fraction to have a denominator of 45:
- $ \frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{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}{15} - \frac{3}{5} $

1. Find a common denominator:
- The denominators are 15 and 5. The LCM of 15 and 5 is 15.
- Convert each fraction to have a denominator of 15:
- $ \frac{13}{15} = \frac{13}{15} $
- $ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} $

2. Subtract the fractions:
- $ \frac{13}{15} - \frac{9}{15} = \frac{13 - 9}{15} = \frac{4}{15} $

Answer:
$$
\boxed{\frac{4}{15}}
$$

---

Section 3: Subtract the mixed numbers

#### Problem 27: $ 5 \frac{1}{3} - 4 \frac{2}{7} $

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}{7} = 4 + \frac{2}{7} = \frac{28}{7} + \frac{2}{7} = \frac{30}{7} $

2. Find a common denominator:
- The denominators are 3 and 7. The LCM of 3 and 7 is 21.
- Convert each fraction to have a denominator of 21:
- $ \frac{16}{3} = \frac{16 \times 7}{3 \times 7} = \frac{112}{21} $
- $ \frac{30}{7} = \frac{30 \times 3}{7 \times 3} = \frac{90}{21} $

3. Subtract the fractions:
- $ \frac{112}{21} - \frac{90}{21} = \frac{112 - 90}{21} = \frac{22}{21} $

4. Convert back to a mixed number:
- Divide 22 by 21:
- $ 22 \div 21 = 1 $ remainder $ 1 $
- So, $ \frac{22}{21} = 1 \frac{1}{21} $

Answer:
$$
\boxed{1 \frac{1}{21}}
$$

#### Problem 28: $ 6 \frac{3}{5} - 5 \frac{3}{8} $

1. Convert mixed numbers to improper fractions:
- $ 6 \frac{3}{5} = 6 + \frac{3}{5} = \frac{30}{5} + \frac{3}{5} = \frac{33}{5} $
- $ 5 \frac{3}{8} = 5 + \frac{3}{8} = \frac{40}{8} + \frac{3}{8} = \frac{43}{8} $

2. Find a common denominator:
- The denominators are 5 and 8. The LCM of 5 and 8 is 40.
- Convert each fraction to have a denominator of 40:
- $ \frac{33}{5} = \frac{33 \times 8}{5 \times 8} = \frac{264}{40} $
- $ \frac{43}{8} = \frac{43 \times 5}{8 \times 5} = \frac{215}{40} $

3. Subtract the fractions:
- $ \frac{264}{40} - \frac{215}{40} = \frac{264 - 215}{40} = \frac{49}{40} $

4. Convert back to a mixed number:
- Divide 49 by 40:
- $ 49 \div 40 = 1 $ remainder $ 9 $
- So, $ \frac{49}{40} = 1 \frac{9}{40} $

Answer:
$$
\boxed{1 \frac{9}{40}}
$$

---

Section 4: Multiply the fractions

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

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

2. Simplify the fraction:
- $ \frac{10}{65} = \frac{2}{13} $

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

#### Problem 31: $ \frac{7}{9} \times \frac{13}{18} $

1. Multiply the numerators and denominators:
- $ \frac{7}{9} \times \frac{13}{18} = \frac{7 \times 13}{9 \times 18} = \frac{91}{162} $

Answer:
$$
\boxed{\frac{91}{162}}
$$

---

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:
- $ \frac{220}{165} = \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:
- $ \frac{48}{60} = \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} $

3. Convert to a mixed number:
- Divide 27 by 20:
- $ 27 \div 20 = 1 $ remainder $ 7 $
- So, $ \frac{27}{20} = 1 \frac{7}{20} $

Answer:
$$
\boxed{1 \frac{7}{20}}
$$

---

Final Answers:

1. $ 4 \frac{7}{8} + 3 \frac{1}{14} = \boxed{7 \frac{53}{56}} $
2. $ 3 \frac{3}{5} + 4 \frac{1}{8} = \boxed{7 \frac{29}{40}} $
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}{15} - \frac{3}{5} = \boxed{\frac{4}{15}} $
6. $ 5 \frac{1}{3} - 4 \frac{2}{7} = \boxed{1 \frac{1}{21}} $
7. $ 6 \frac{3}{5} - 5 \frac{3}{8} = \boxed{1 \frac{9}{40}} $
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}{9} \times \frac{13}{18} = \boxed{\frac{91}{162}} $
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{1 \frac{7}{20}} $