Multiplying Fractions Questions and Answers (teacher made) - Free Printable

Problem: Multiplying Fractions & Whole Numbers

The task involves multiplying fractions and whole numbers, simplifying the results, and expressing mixed fractions with a space between the whole number and the fraction. Let's solve each problem step by step.

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#### 1. $\frac{1}{6} \times \frac{5}{9}$
- Step 1: Multiply the numerators: $1 \times 5 = 5$.
- Step 2: Multiply the denominators: $6 \times 9 = 54$.
- Step 3: Write the result as a fraction: $\frac{5}{54}$.
- Step 4: Simplify (if possible). The fraction $\frac{5}{54}$ is already in simplest form.

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

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#### 2. $\frac{2}{5} \times \frac{7}{8}$
- Step 1: Multiply the numerators: $2 \times 7 = 14$.
- Step 2: Multiply the denominators: $5 \times 8 = 40$.
- Step 3: Write the result as a fraction: $\frac{14}{40}$.
- Step 4: Simplify. The greatest common divisor (GCD) of 14 and 40 is 2. Divide both numerator and denominator by 2:
$$
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
$$

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

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#### 3. $\frac{6}{7} \text{ of } \frac{2}{9}$
- "Of" means multiplication. So, this is equivalent to $\frac{6}{7} \times \frac{2}{9}$.
- Step 1: Multiply the numerators: $6 \times 2 = 12$.
- Step 2: Multiply the denominators: $7 \times 9 = 63$.
- Step 3: Write the result as a fraction: $\frac{12}{63}$.
- Step 4: Simplify. The GCD of 12 and 63 is 3. Divide both numerator and denominator by 3:
$$
\frac{12 \div 3}{63 \div 3} = \frac{4}{21}
$$

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

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#### 4. $18 \times \frac{5}{6}$
- Step 1: Treat 18 as a fraction: $18 = \frac{18}{1}$.
- Step 2: Multiply the numerators: $18 \times 5 = 90$.
- Step 3: Multiply the denominators: $1 \times 6 = 6$.
- Step 4: Write the result as a fraction: $\frac{90}{6}$.
- Step 5: Simplify. Divide both numerator and denominator by their GCD, which is 6:
$$
\frac{90 \div 6}{6 \div 6} = 15
$$

Answer: $15$

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#### 5. $5 \times \frac{8}{15}$
- Step 1: Treat 5 as a fraction: $5 = \frac{5}{1}$.
- Step 2: Multiply the numerators: $5 \times 8 = 40$.
- Step 3: Multiply the denominators: $1 \times 15 = 15$.
- Step 4: Write the result as a fraction: $\frac{40}{15}$.
- Step 5: Simplify. The GCD of 40 and 15 is 5. Divide both numerator and denominator by 5:
$$
\frac{40 \div 5}{15 \div 5} = \frac{8}{3}
$$
- Step 6: Convert to a mixed number:
$$
\frac{8}{3} = 2 \frac{2}{3}
$$

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

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#### 6. $\frac{2}{9} \text{ of } 7$
- "Of" means multiplication. So, this is equivalent to $\frac{2}{9} \times 7$.
- Step 1: Treat 7 as a fraction: $7 = \frac{7}{1}$.
- Step 2: Multiply the numerators: $2 \times 7 = 14$.
- Step 3: Multiply the denominators: $9 \times 1 = 9$.
- Step 4: Write the result as a fraction: $\frac{14}{9}$.
- Step 5: Convert to a mixed number:
$$
\frac{14}{9} = 1 \frac{5}{9}
$$

Answer: $1 \frac{5}{9}$

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#### 7. $2 \frac{11}{12} \times \frac{2}{5}$
- Step 1: Convert the mixed number to an improper fraction:
$$
2 \frac{11}{12} = \frac{(2 \times 12) + 11}{12} = \frac{24 + 11}{12} = \frac{35}{12}
$$
- Step 2: Multiply the fractions: $\frac{35}{12} \times \frac{2}{5}$.
- Step 3: Multiply the numerators: $35 \times 2 = 70$.
- Step 4: Multiply the denominators: $12 \times 5 = 60$.
- Step 5: Write the result as a fraction: $\frac{70}{60}$.
- Step 6: Simplify. The GCD of 70 and 60 is 10. Divide both numerator and denominator by 10:
$$
\frac{70 \div 10}{60 \div 10} = \frac{7}{6}
$$
- Step 7: Convert to a mixed number:
$$
\frac{7}{6} = 1 \frac{1}{6}
$$

Answer: $1 \frac{1}{6}$

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#### 8. $1 \frac{3}{4} \times \frac{20}{21}$
- Step 1: Convert the mixed number to an improper fraction:
$$
1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
$$
- Step 2: Multiply the fractions: $\frac{7}{4} \times \frac{20}{21}$.
- Step 3: Multiply the numerators: $7 \times 20 = 140$.
- Step 4: Multiply the denominators: $4 \times 21 = 84$.
- Step 5: Write the result as a fraction: $\frac{140}{84}$.
- Step 6: Simplify. The GCD of 140 and 84 is 28. Divide both numerator and denominator by 28:
$$
\frac{140 \div 28}{84 \div 28} = \frac{5}{3}
$$
- Step 7: Convert to a mixed number:
$$
\frac{5}{3} = 1 \frac{2}{3}
$$

Answer: $1 \frac{2}{3}$

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#### 9. $4 \frac{9}{10} \times 1 \frac{1}{7}$
- Step 1: Convert both mixed numbers to improper fractions:
$$
4 \frac{9}{10} = \frac{(4 \times 10) + 9}{10} = \frac{40 + 9}{10} = \frac{49}{10}
$$
$$
1 \frac{1}{7} = \frac{(1 \times 7) + 1}{7} = \frac{7 + 1}{7} = \frac{8}{7}
$$
- Step 2: Multiply the fractions: $\frac{49}{10} \times \frac{8}{7}$.
- Step 3: Multiply the numerators: $49 \times 8 = 392$.
- Step 4: Multiply the denominators: $10 \times 7 = 70$.
- Step 5: Write the result as a fraction: $\frac{392}{70}$.
- Step 6: Simplify. The GCD of 392 and 70 is 14. Divide both numerator and denominator by 14:
$$
\frac{392 \div 14}{70 \div 14} = \frac{28}{5}
$$
- Step 7: Convert to a mixed number:
$$
\frac{28}{5} = 5 \frac{3}{5}
$$

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

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#### 10. $2 \frac{1}{3} \text{ of } 3 \frac{1}{2}$
- "Of" means multiplication. So, this is equivalent to $2 \frac{1}{3} \times 3 \frac{1}{2}$.
- Step 1: Convert both mixed numbers to improper fractions:
$$
2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}
$$
$$
3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
$$
- Step 2: Multiply the fractions: $\frac{7}{3} \times \frac{7}{2}$.
- Step 3: Multiply the numerators: $7 \times 7 = 49$.
- Step 4: Multiply the denominators: $3 \times 2 = 6$.
- Step 5: Write the result as a fraction: $\frac{49}{6}$.
- Step 6: Convert to a mixed number:
$$
\frac{49}{6} = 8 \frac{1}{6}
$$

Answer: $8 \frac{1}{6}$

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Final Answers:

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

$$
\boxed{\frac{5}{54}, \frac{7}{20}, \frac{4}{21}, 15, 2 \frac{2}{3}, 1 \frac{5}{9}, 1 \frac{1}{6}, 1 \frac{2}{3}, 5 \frac{3}{5}, 8 \frac{1}{6}}
$$