Multiplying Fractions with Cross Cancelling Worksheet | Free ... - Free Printable

Problem: Solving Multiplication of Fractions with Cross-Cancelling

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

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#### 1) \( \frac{3}{8} \times \frac{7}{9} \)

- Step 1: Multiply the numerators: \( 3 \times 7 = 21 \).
- Step 2: Multiply the denominators: \( 8 \times 9 = 72 \).
- Step 3: Simplify the fraction \( \frac{21}{72} \):
- The greatest common divisor (GCD) of 21 and 72 is 3.
- Divide both numerator and denominator by 3: \( \frac{21 \div 3}{72 \div 3} = \frac{7}{24} \).

Answer: \( \frac{7}{24} \)

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#### 2) \( \frac{2}{5} \times \frac{5}{7} \)

- Step 1: Multiply the numerators: \( 2 \times 5 = 10 \).
- Step 2: Multiply the denominators: \( 5 \times 7 = 35 \).
- Step 3: Simplify the fraction \( \frac{10}{35} \):
- The GCD of 10 and 35 is 5.
- Divide both numerator and denominator by 5: \( \frac{10 \div 5}{35 \div 5} = \frac{2}{7} \).

Answer: \( \frac{2}{7} \)

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#### 3) \( \frac{3}{5} \times \frac{1}{3} \)

- Step 1: Multiply the numerators: \( 3 \times 1 = 3 \).
- Step 2: Multiply the denominators: \( 5 \times 3 = 15 \).
- Step 3: Simplify the fraction \( \frac{3}{15} \):
- The GCD of 3 and 15 is 3.
- Divide both numerator and denominator by 3: \( \frac{3 \div 3}{15 \div 3} = \frac{1}{5} \).

Answer: \( \frac{1}{5} \)

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#### 4) \( \frac{3}{4} \times \frac{2}{7} \)

- Step 1: Multiply the numerators: \( 3 \times 2 = 6 \).
- Step 2: Multiply the denominators: \( 4 \times 7 = 28 \).
- Step 3: Simplify the fraction \( \frac{6}{28} \):
- The GCD of 6 and 28 is 2.
- Divide both numerator and denominator by 2: \( \frac{6 \div 2}{28 \div 2} = \frac{3}{14} \).

Answer: \( \frac{3}{14} \)

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#### 5) \( \frac{2}{3} \times \frac{1}{2} \)

- Step 1: Multiply the numerators: \( 2 \times 1 = 2 \).
- Step 2: Multiply the denominators: \( 3 \times 2 = 6 \).
- Step 3: Simplify the fraction \( \frac{2}{6} \):
- The GCD of 2 and 6 is 2.
- Divide both numerator and denominator by 2: \( \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \).

Answer: \( \frac{1}{3} \)

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#### 6) \( \frac{7}{8} \times \frac{2}{5} \)

- Step 1: Multiply the numerators: \( 7 \times 2 = 14 \).
- Step 2: Multiply the denominators: \( 8 \times 5 = 40 \).
- Step 3: Simplify the fraction \( \frac{14}{40} \):
- The 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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#### 7) \( \frac{6}{7} \times \frac{7}{10} \)

- Step 1: Multiply the numerators: \( 6 \times 7 = 42 \).
- Step 2: Multiply the denominators: \( 7 \times 10 = 70 \).
- Step 3: Simplify the fraction \( \frac{42}{70} \):
- The GCD of 42 and 70 is 14.
- Divide both numerator and denominator by 14: \( \frac{42 \div 14}{70 \div 14} = \frac{3}{5} \).

Answer: \( \frac{3}{5} \)

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#### 8) \( \frac{2}{9} \times \frac{3}{8} \)

- Step 1: Multiply the numerators: \( 2 \times 3 = 6 \).
- Step 2: Multiply the denominators: \( 9 \times 8 = 72 \).
- Step 3: Simplify the fraction \( \frac{6}{72} \):
- The GCD of 6 and 72 is 6.
- Divide both numerator and denominator by 6: \( \frac{6 \div 6}{72 \div 6} = \frac{1}{12} \).

Answer: \( \frac{1}{12} \)

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#### 9) \( \frac{3}{4} \times \frac{4}{9} \)

- Step 1: Multiply the numerators: \( 3 \times 4 = 12 \).
- Step 2: Multiply the denominators: \( 4 \times 9 = 36 \).
- Step 3: Simplify the fraction \( \frac{12}{36} \):
- The GCD of 12 and 36 is 12.
- Divide both numerator and denominator by 12: \( \frac{12 \div 12}{36 \div 12} = \frac{1}{3} \).

Answer: \( \frac{1}{3} \)

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#### 10) \( \frac{2}{50} \times \frac{5}{18} \)

- Step 1: Multiply the numerators: \( 2 \times 5 = 10 \).
- Step 2: Multiply the denominators: \( 50 \times 18 = 900 \).
- Step 3: Simplify the fraction \( \frac{10}{900} \):
- The GCD of 10 and 900 is 10.
- Divide both numerator and denominator by 10: \( \frac{10 \div 10}{900 \div 10} = \frac{1}{90} \).

Answer: \( \frac{1}{90} \)

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#### 11) \( \frac{9}{24} \times \frac{6}{90} \)

- Step 1: Multiply the numerators: \( 9 \times 6 = 54 \).
- Step 2: Multiply the denominators: \( 24 \times 90 = 2160 \).
- Step 3: Simplify the fraction \( \frac{54}{2160} \):
- The GCD of 54 and 2160 is 54.
- Divide both numerator and denominator by 54: \( \frac{54 \div 54}{2160 \div 54} = \frac{1}{40} \).

Answer: \( \frac{1}{40} \)

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#### 12) \( \frac{2}{45} \times \frac{9}{20} \)

- Step 1: Multiply the numerators: \( 2 \times 9 = 18 \).
- Step 2: Multiply the denominators: \( 45 \times 20 = 900 \).
- Step 3: Simplify the fraction \( \frac{18}{900} \):
- The GCD of 18 and 900 is 18.
- Divide both numerator and denominator by 18: \( \frac{18 \div 18}{900 \div 18} = \frac{1}{50} \).

Answer: \( \frac{1}{50} \)

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#### 13) \( \frac{5}{6} \times \frac{8}{7} \)

- Step 1: Multiply the numerators: \( 5 \times 8 = 40 \).
- Step 2: Multiply the denominators: \( 6 \times 7 = 42 \).
- Step 3: Simplify the fraction \( \frac{40}{42} \):
- The GCD of 40 and 42 is 2.
- Divide both numerator and denominator by 2: \( \frac{40 \div 2}{42 \div 2} = \frac{20}{21} \).

Answer: \( \frac{20}{21} \)

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#### 14) \( 2 \frac{1}{2} \times \frac{1}{10} \)

- Step 1: Convert the mixed number \( 2 \frac{1}{2} \) to an improper fraction:
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} \).
- Step 2: Multiply the fractions: \( \frac{5}{2} \times \frac{1}{10} \).
- Numerator: \( 5 \times 1 = 5 \).
- Denominator: \( 2 \times 10 = 20 \).
- Step 3: Simplify the fraction \( \frac{5}{20} \):
- The GCD of 5 and 20 is 5.
- Divide both numerator and denominator by 5: \( \frac{5 \div 5}{20 \div 5} = \frac{1}{4} \).

Answer: \( \frac{1}{4} \)

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#### 15) \( \frac{3}{2} \times \frac{5}{6} \)

- Step 1: Multiply the numerators: \( 3 \times 5 = 15 \).
- Step 2: Multiply the denominators: \( 2 \times 6 = 12 \).
- Step 3: Simplify the fraction \( \frac{15}{12} \):
- The GCD of 15 and 12 is 3.
- Divide both numerator and denominator by 3: \( \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \).

Answer: \( \frac{5}{4} \)

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#### 16) \( 2 \frac{4}{7} \times \frac{1}{10} \)

- Step 1: Convert the mixed number \( 2 \frac{4}{7} \) to an improper fraction:
- \( 2 \frac{4}{7} = \frac{2 \times 7 + 4}{7} = \frac{18}{7} \).
- Step 2: Multiply the fractions: \( \frac{18}{7} \times \frac{1}{10} \).
- Numerator: \( 18 \times 1 = 18 \).
- Denominator: \( 7 \times 10 = 70 \).
- Step 3: Simplify the fraction \( \frac{18}{70} \):
- The GCD of 18 and 70 is 2.
- Divide both numerator and denominator by 2: \( \frac{18 \div 2}{70 \div 2} = \frac{9}{35} \).

Answer: \( \frac{9}{35} \)

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#### 17) \( \frac{7}{9} \times \frac{15}{4} \)

- Step 1: Multiply the numerators: \( 7 \times 15 = 105 \).
- Step 2: Multiply the denominators: \( 9 \times 4 = 36 \).
- Step 3: Simplify the fraction \( \frac{105}{36} \):
- The GCD of 105 and 36 is 3.
- Divide both numerator and denominator by 3: \( \frac{105 \div 3}{36 \div 3} = \frac{35}{12} \).

Answer: \( \frac{35}{12} \)

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#### 18) \( \frac{5}{2} \times 3 \frac{3}{5} \)

- Step 1: Convert the mixed number \( 3 \frac{3}{5} \) to an improper fraction:
- \( 3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5} \).
- Step 2: Multiply the fractions: \( \frac{5}{2} \times \frac{18}{5} \).
- Numerator: \( 5 \times 18 = 90 \).
- Denominator: \( 2 \times 5 = 10 \).
- Step 3: Simplify the fraction \( \frac{90}{10} \):
- The GCD of 90 and 10 is 10.
- Divide both numerator and denominator by 10: \( \frac{90 \div 10}{10 \div 10} = 9 \).

Answer: \( 9 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \frac{7}{24} \\
2) & \frac{2}{7} \\
3) & \frac{1}{5} \\
4) & \frac{3}{14} \\
5) & \frac{1}{3} \\
6) & \frac{7}{20} \\
7) & \frac{3}{5} \\
8) & \frac{1}{12} \\
9) & \frac{1}{3} \\
10) & \frac{1}{90} \\
11) & \frac{1}{40} \\
12) & \frac{1}{50} \\
13) & \frac{20}{21} \\
14) & \frac{1}{4} \\
15) & \frac{5}{4} \\
16) & \frac{9}{35} \\
17) & \frac{35}{12} \\
18) & 9 \\
\end{array}
}
\]