Grade 6 Math Worksheets: Multiplying fractions (denominators 2-25 ... - Free Printable

Problem: Multiplying Fractions (Denominators 2-25)

The task is to solve the multiplication of fractions for each problem listed in the worksheet. Below, I will solve each problem step by step.

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Step-by-Step Solutions

#### 1. \( \frac{7}{8} \times \frac{30}{31} \)

- Multiply the numerators: \( 7 \times 30 = 210 \)
- Multiply the denominators: \( 8 \times 31 = 248 \)
- Result: \( \frac{210}{248} \)

- Simplify the fraction:
- Find the greatest common divisor (GCD) of 210 and 248.
- GCD(210, 248) = 2
- Divide both numerator and denominator by 2:
\[
\frac{210 \div 2}{248 \div 2} = \frac{105}{124}
\]

- Final Answer: \( \frac{105}{124} \)

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#### 2. \( \frac{5}{12} \times \frac{7}{16} \)

- Multiply the numerators: \( 5 \times 7 = 35 \)
- Multiply the denominators: \( 12 \times 16 = 192 \)
- Result: \( \frac{35}{192} \)

- Simplify the fraction:
- The GCD of 35 and 192 is 1 (they are coprime).
- The fraction is already in simplest form.

- Final Answer: \( \frac{35}{192} \)

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#### 3. \( \frac{5}{9} \times \frac{1}{19} \)

- Multiply the numerators: \( 5 \times 1 = 5 \)
- Multiply the denominators: \( 9 \times 19 = 171 \)
- Result: \( \frac{5}{171} \)

- Simplify the fraction:
- The GCD of 5 and 171 is 1 (they are coprime).
- The fraction is already in simplest form.

- Final Answer: \( \frac{5}{171} \)

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#### 4. \( \frac{8}{21} \times \frac{10}{11} \)

- Multiply the numerators: \( 8 \times 10 = 80 \)
- Multiply the denominators: \( 21 \times 11 = 231 \)
- Result: \( \frac{80}{231} \)

- Simplify the fraction:
- The GCD of 80 and 231 is 1 (they are coprime).
- The fraction is already in simplest form.

- Final Answer: \( \frac{80}{231} \)

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#### 5. \( \frac{12}{15} \times \frac{6}{16} \)

- Multiply the numerators: \( 12 \times 6 = 72 \)
- Multiply the denominators: \( 15 \times 16 = 240 \)
- Result: \( \frac{72}{240} \)

- Simplify the fraction:
- Find the GCD of 72 and 240.
- GCD(72, 240) = 24
- Divide both numerator and denominator by 24:
\[
\frac{72 \div 24}{240 \div 24} = \frac{3}{10}
\]

- Final Answer: \( \frac{3}{10} \)

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#### 6. \( \frac{4}{20} \times \frac{4}{15} \)

- Multiply the numerators: \( 4 \times 4 = 16 \)
- Multiply the denominators: \( 20 \times 15 = 300 \)
- Result: \( \frac{16}{300} \)

- Simplify the fraction:
- Find the GCD of 16 and 300.
- GCD(16, 300) = 4
- Divide both numerator and denominator by 4:
\[
\frac{16 \div 4}{300 \div 4} = \frac{4}{75}
\]

- Final Answer: \( \frac{4}{75} \)

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#### 7. \( \frac{1}{5} \times \frac{13}{14} \)

- Multiply the numerators: \( 1 \times 13 = 13 \)
- Multiply the denominators: \( 5 \times 14 = 70 \)
- Result: \( \frac{13}{70} \)

- Simplify the fraction:
- The GCD of 13 and 70 is 1 (they are coprime).
- The fraction is already in simplest form.

- Final Answer: \( \frac{13}{70} \)

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#### 8. \( \frac{6}{14} \times \frac{5}{7} \)

- Multiply the numerators: \( 6 \times 5 = 30 \)
- Multiply the denominators: \( 14 \times 7 = 98 \)
- Result: \( \frac{30}{98} \)

- Simplify the fraction:
- Find the GCD of 30 and 98.
- GCD(30, 98) = 2
- Divide both numerator and denominator by 2:
\[
\frac{30 \div 2}{98 \div 2} = \frac{15}{49}
\]

- Final Answer: \( \frac{15}{49} \)

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#### 9. \( \frac{9}{10} \times \frac{6}{17} \)

- Multiply the numerators: \( 9 \times 6 = 54 \)
- Multiply the denominators: \( 10 \times 17 = 170 \)
- Result: \( \frac{54}{170} \)

- Simplify the fraction:
- Find the GCD of 54 and 170.
- GCD(54, 170) = 2
- Divide both numerator and denominator by 2:
\[
\frac{54 \div 2}{170 \div 2} = \frac{27}{85}
\]

- Final Answer: \( \frac{27}{85} \)

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#### 10. \( \frac{1}{6} \times \frac{1}{19} \)

- Multiply the numerators: \( 1 \times 1 = 1 \)
- Multiply the denominators: \( 6 \times 19 = 114 \)
- Result: \( \frac{1}{114} \)

- Simplify the fraction:
- The GCD of 1 and 114 is 1 (the fraction is already in simplest form).

- Final Answer: \( \frac{1}{114} \)

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Final Answers

1. \( \frac{105}{124} \)
2. \( \frac{35}{192} \)
3. \( \frac{5}{171} \)
4. \( \frac{80}{231} \)
5. \( \frac{3}{10} \)
6. \( \frac{4}{75} \)
7. \( \frac{13}{70} \)
8. \( \frac{15}{49} \)
9. \( \frac{27}{85} \)
10. \( \frac{1}{114} \)

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Boxed Final Answer

\[
\boxed{
\begin{aligned}
1. & \ \frac{105}{124} \\
2. & \ \frac{35}{192} \\
3. & \ \frac{5}{171} \\
4. & \ \frac{80}{231} \\
5. & \ \frac{3}{10} \\
6. & \ \frac{4}{75} \\
7. & \ \frac{13}{70} \\
8. & \ \frac{15}{49} \\
9. & \ \frac{27}{85} \\
10. & \ \frac{1}{114}
\end{aligned}
}
\]