Multiplying Fractions & Mixed Numbers Worksheet

Problem: Multiplying Fractions & Mixed Numbers

The task is to multiply the given fractions and mixed numbers, simplify the results, and write them in simplest form. Mixed numbers should be converted to improper fractions before performing the multiplication.

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Solution:

#### 1. $\frac{1}{6} \times \frac{5}{9}$

- Multiply the numerators: $1 \times 5 = 5$
- Multiply the denominators: $6 \times 9 = 54$
- Result: $\frac{5}{54}$

Answer: $\boxed{\frac{5}{54}}$

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#### 2. $\frac{2}{5} \times \frac{7}{8}$

- Multiply the numerators: $2 \times 7 = 14$
- Multiply the denominators: $5 \times 8 = 40$
- Simplify $\frac{14}{40}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
$$

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

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#### 3. $\frac{6}{7} \times \frac{2}{9}$

- Multiply the numerators: $6 \times 2 = 12$
- Multiply the denominators: $7 \times 9 = 63$
- Simplify $\frac{12}{63}$ by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{12 \div 3}{63 \div 3} = \frac{4}{21}
$$

Answer: $\boxed{\frac{4}{21}}$

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#### 4. $18 \times \frac{5}{6}$

- Convert $18$ to a fraction: $18 = \frac{18}{1}$
- Multiply the numerators: $18 \times 5 = 90$
- Multiply the denominators: $1 \times 6 = 6$
- Simplify $\frac{90}{6}$ by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{90 \div 6}{6 \div 6} = 15
$$

Answer: $\boxed{15}$

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#### 5. $\frac{5}{24} \times \frac{8}{15}$

- Multiply the numerators: $5 \times 8 = 40$
- Multiply the denominators: $24 \times 15 = 360$
- Simplify $\frac{40}{360}$ by dividing both numerator and denominator by their GCD, which is 40:
$$
\frac{40 \div 40}{360 \div 40} = \frac{1}{9}
$$

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

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#### 6. $\frac{16}{7} \times \frac{21}{8}$

- Multiply the numerators: $16 \times 21 = 336$
- Multiply the denominators: $7 \times 8 = 56$
- Simplify $\frac{336}{56}$ by dividing both numerator and denominator by their GCD, which is 56:
$$
\frac{336 \div 56}{56 \div 56} = 6
$$

Answer: $\boxed{6}$

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#### 7. $2 \frac{11}{12} \times \frac{2}{5}$

- Convert $2 \frac{11}{12}$ to an improper fraction:
$$
2 \frac{11}{12} = \frac{(2 \times 12) + 11}{12} = \frac{24 + 11}{12} = \frac{35}{12}
$$
- Multiply the numerators: $35 \times 2 = 70$
- Multiply the denominators: $12 \times 5 = 60$
- Simplify $\frac{70}{60}$ by dividing both numerator and denominator by their GCD, which is 10:
$$
\frac{70 \div 10}{60 \div 10} = \frac{7}{6}
$$

Answer: $\boxed{\frac{7}{6}}$

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#### 8. $1 \frac{3}{4} \times \frac{20}{21}$

- Convert $1 \frac{3}{4}$ to an improper fraction:
$$
1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
$$
- Multiply the numerators: $7 \times 20 = 140$
- Multiply the denominators: $4 \times 21 = 84$
- Simplify $\frac{140}{84}$ by dividing both numerator and denominator by their GCD, which is 28:
$$
\frac{140 \div 28}{84 \div 28} = \frac{5}{3}
$$

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

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#### 9. $4 \frac{9}{10} \times 1 \frac{1}{7}$

- Convert $4 \frac{9}{10}$ to an improper fraction:
$$
4 \frac{9}{10} = \frac{(4 \times 10) + 9}{10} = \frac{40 + 9}{10} = \frac{49}{10}
$$
- Convert $1 \frac{1}{7}$ to an improper fraction:
$$
1 \frac{1}{7} = \frac{(1 \times 7) + 1}{7} = \frac{7 + 1}{7} = \frac{8}{7}
$$
- Multiply the numerators: $49 \times 8 = 392$
- Multiply the denominators: $10 \times 7 = 70$
- Simplify $\frac{392}{70}$ by dividing both numerator and denominator by their GCD, which is 14:
$$
\frac{392 \div 14}{70 \div 14} = \frac{28}{5}
$$

Answer: $\boxed{\frac{28}{5}}$

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#### 10. $8 \frac{1}{3} \times 4 \frac{1}{2}$

- Convert $8 \frac{1}{3}$ to an improper fraction:
$$
8 \frac{1}{3} = \frac{(8 \times 3) + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}
$$
- Convert $4 \frac{1}{2}$ to an improper fraction:
$$
4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}
$$
- Multiply the numerators: $25 \times 9 = 225$
- Multiply the denominators: $3 \times 2 = 6$
- Simplify $\frac{225}{6}$ by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{225 \div 3}{6 \div 3} = \frac{75}{2}
$$

Answer: $\boxed{\frac{75}{2}}$

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Final Answers:

1. $\boxed{\frac{5}{54}}$
2. $\boxed{\frac{7}{20}}$
3. $\boxed{\frac{4}{21}}$
4. $\boxed{15}$
5. $\boxed{\frac{1}{9}}$
6. $\boxed{6}$
7. $\boxed{\frac{7}{6}}$
8. $\boxed{\frac{5}{3}}$
9. $\boxed{\frac{28}{5}}$
10. $\boxed{\frac{75}{2}}$