Multiplying Fractions with Cross Cancelling Worksheet Download - Free Printable

Problem: Multiplying Fractions with Cross-Cancelling

The task involves solving each multiplication problem of fractions and expressing the answers as improper fractions if necessary. We will solve each problem step by step, using cross-cancelling to simplify the process.

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Step-by-Step Solutions

#### 1. $\frac{1}{6} \times \frac{4}{5}$
- Multiply numerators: $1 \times 4 = 4$
- Multiply denominators: $6 \times 5 = 30$
- Result: $\frac{4}{30}$
- Simplify by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{4 \div 2}{30 \div 2} = \frac{2}{15}
$$
- Answer: $\frac{2}{15}$

#### 2. $\frac{1}{2} \times \frac{2}{3}$
- Multiply numerators: $1 \times 2 = 2$
- Multiply denominators: $2 \times 3 = 6$
- Result: $\frac{2}{6}$
- Simplify by dividing numerator and denominator by their GCD, which is 2:
$$
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
$$
- Answer: $\frac{1}{3}$

#### 3. $\frac{1}{3} \times \frac{3}{5}$
- Multiply numerators: $1 \times 3 = 3$
- Multiply denominators: $3 \times 5 = 15$
- Result: $\frac{3}{15}$
- Simplify by dividing numerator and denominator by their GCD, which is 3:
$$
\frac{3 \div 3}{15 \div 3} = \frac{1}{5}
$$
- Answer: $\frac{1}{5}$

#### 4. $\frac{4}{5} \times \frac{7}{8}$
- Multiply numerators: $4 \times 7 = 28$
- Multiply denominators: $5 \times 8 = 40$
- Result: $\frac{28}{40}$
- Simplify by dividing numerator and denominator by their GCD, which is 4:
$$
\frac{28 \div 4}{40 \div 4} = \frac{7}{10}
$$
- Answer: $\frac{7}{10}$

#### 5. $\frac{4}{7} \times \frac{1}{8}$
- Multiply numerators: $4 \times 1 = 4$
- Multiply denominators: $7 \times 8 = 56$
- Result: $\frac{4}{56}$
- Simplify by dividing numerator and denominator by their GCD, which is 4:
$$
\frac{4 \div 4}{56 \div 4} = \frac{1}{14}
$$
- Answer: $\frac{1}{14}$

#### 6. $\frac{1}{3} \times \frac{3}{4}$
- Multiply numerators: $1 \times 3 = 3$
- Multiply denominators: $3 \times 4 = 12$
- Result: $\frac{3}{12}$
- Simplify by dividing numerator and denominator by their GCD, which is 3:
$$
\frac{3 \div 3}{12 \div 3} = \frac{1}{4}
$$
- Answer: $\frac{1}{4}$

#### 7. $\frac{3}{7} \times \frac{7}{9}$
- Multiply numerators: $3 \times 7 = 21$
- Multiply denominators: $7 \times 9 = 63$
- Result: $\frac{21}{63}$
- Simplify by dividing numerator and denominator by their GCD, which is 21:
$$
\frac{21 \div 21}{63 \div 21} = \frac{1}{3}
$$
- Answer: $\frac{1}{3}$

#### 8. $\frac{2}{5} \times \frac{5}{6}$
- Multiply numerators: $2 \times 5 = 10$
- Multiply denominators: $5 \times 6 = 30$
- Result: $\frac{10}{30}$
- Simplify by dividing numerator and denominator by their GCD, which is 10:
$$
\frac{10 \div 10}{30 \div 10} = \frac{1}{3}
$$
- Answer: $\frac{1}{3}$

#### 9. $\frac{2}{3} \times \frac{3}{4}$
- Multiply numerators: $2 \times 3 = 6$
- Multiply denominators: $3 \times 4 = 12$
- Result: $\frac{6}{12}$
- Simplify by dividing numerator and denominator by their GCD, which is 6:
$$
\frac{6 \div 6}{12 \div 6} = \frac{1}{2}
$$
- Answer: $\frac{1}{2}$

#### 10. $\frac{5}{54} \times \frac{9}{40}$
- Multiply numerators: $5 \times 9 = 45$
- Multiply denominators: $54 \times 40 = 2160$
- Result: $\frac{45}{2160}$
- Simplify by dividing numerator and denominator by their GCD, which is 45:
$$
\frac{45 \div 45}{2160 \div 45} = \frac{1}{48}
$$
- Answer: $\frac{1}{48}$

#### 11. $\frac{6}{27} \times \frac{3}{42}$
- Multiply numerators: $6 \times 3 = 18$
- Multiply denominators: $27 \times 42 = 1134$
- Result: $\frac{18}{1134}$
- Simplify by dividing numerator and denominator by their GCD, which is 18:
$$
\frac{18 \div 18}{1134 \div 18} = \frac{1}{63}
$$
- Answer: $\frac{1}{63}$

#### 12. $\frac{9}{30} \times \frac{3}{27}$
- Multiply numerators: $9 \times 3 = 27$
- Multiply denominators: $30 \times 27 = 810$
- Result: $\frac{27}{810}$
- Simplify by dividing numerator and denominator by their GCD, which is 27:
$$
\frac{27 \div 27}{810 \div 27} = \frac{1}{30}
$$
- Answer: $\frac{1}{30}$

#### 13. $\frac{5}{2} \times 1\frac{3}{7}$
- Convert mixed number to improper fraction: $1\frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7}$
- Multiply: $\frac{5}{2} \times \frac{10}{7}$
- Multiply numerators: $5 \times 10 = 50$
- Multiply denominators: $2 \times 7 = 14$
- Result: $\frac{50}{14}$
- Simplify by dividing numerator and denominator by their GCD, which is 2:
$$
\frac{50 \div 2}{14 \div 2} = \frac{25}{7}
$$
- Answer: $\frac{25}{7}$

#### 14. $\frac{10}{3} \times 3\frac{1}{4}$
- Convert mixed number to improper fraction: $3\frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4}$
- Multiply: $\frac{10}{3} \times \frac{13}{4}$
- Multiply numerators: $10 \times 13 = 130$
- Multiply denominators: $3 \times 4 = 12$
- Result: $\frac{130}{12}$
- Simplify by dividing numerator and denominator by their GCD, which is 2:
$$
\frac{130 \div 2}{12 \div 2} = \frac{65}{6}
$$
- Answer: $\frac{65}{6}$

#### 15. $\frac{17}{8} \times 2\frac{6}{7}$
- Convert mixed number to improper fraction: $2\frac{6}{7} = \frac{7 \times 2 + 6}{7} = \frac{20}{7}$
- Multiply: $\frac{17}{8} \times \frac{20}{7}$
- Multiply numerators: $17 \times 20 = 340$
- Multiply denominators: $8 \times 7 = 56$
- Result: $\frac{340}{56}$
- Simplify by dividing numerator and denominator by their GCD, which is 4:
$$
\frac{340 \div 4}{56 \div 4} = \frac{85}{14}
$$
- Answer: $\frac{85}{14}$

#### 16. $\frac{11}{8} \times 1\frac{5}{7}$
- Convert mixed number to improper fraction: $1\frac{5}{7} = \frac{7 \times 1 + 5}{7} = \frac{12}{7}$
- Multiply: $\frac{11}{8} \times \frac{12}{7}$
- Multiply numerators: $11 \times 12 = 132$
- Multiply denominators: $8 \times 7 = 56$
- Result: $\frac{132}{56}$
- Simplify by dividing numerator and denominator by their GCD, which is 4:
$$
\frac{132 \div 4}{56 \div 4} = \frac{33}{14}
$$
- Answer: $\frac{33}{14}$

#### 17. $\frac{7}{8} \times \frac{10}{7}$
- Multiply numerators: $7 \times 10 = 70$
- Multiply denominators: $8 \times 7 = 56$
- Result: $\frac{70}{56}$
- Simplify by dividing numerator and denominator by their GCD, which is 14:
$$
\frac{70 \div 14}{56 \div 14} = \frac{5}{4}
$$
- Answer: $\frac{5}{4}$

#### 18. $\frac{10}{9} \times 1\frac{1}{4}$
- Convert mixed number to improper fraction: $1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}$
- Multiply: $\frac{10}{9} \times \frac{5}{4}$
- Multiply numerators: $10 \times 5 = 50$
- Multiply denominators: $9 \times 4 = 36$
- Result: $\frac{50}{36}$
- Simplify by dividing numerator and denominator by their GCD, which is 2:
$$
\frac{50 \div 2}{36 \div 2} = \frac{25}{18}
$$
- Answer: $\frac{25}{18}$

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Final Answers

1. $\frac{2}{15}$
2. $\frac{1}{3}$
3. $\frac{1}{5}$
4. $\frac{7}{10}$
5. $\frac{1}{14}$
6. $\frac{1}{4}$
7. $\frac{1}{3}$
8. $\frac{1}{3}$
9. $\frac{1}{2}$
10. $\frac{1}{48}$
11. $\frac{1}{63}$
12. $\frac{1}{30}$
13. $\frac{25}{7}$
14. $\frac{65}{6}$
15. $\frac{85}{14}$
16. $\frac{33}{14}$
17. $\frac{5}{4}$
18. $\frac{25}{18}$

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Boxed Final Answer

$$
\boxed{
\begin{array}{l}
1. \frac{2}{15} \\
2. \frac{1}{3} \\
3. \frac{1}{5} \\
4. \frac{7}{10} \\
5. \frac{1}{14} \\
6. \frac{1}{4} \\
7. \frac{1}{3} \\
8. \frac{1}{3} \\
9. \frac{1}{2} \\
10. \frac{1}{48} \\
11. \frac{1}{63} \\
12. \frac{1}{30} \\
13. \frac{25}{7} \\
14. \frac{65}{6} \\
15. \frac{85}{14} \\
16. \frac{33}{14} \\
17. \frac{5}{4} \\
18. \frac{25}{18} \\
\end{array}
}
$$