Grade 6 Math Worksheets: Multiplying fractions by whole numbers ... - Free Printable

Problem: Multiplying Fractions by Whole Numbers

The task involves solving a series of problems where whole numbers are multiplied by fractions, and the results are simplified. Below is the step-by-step solution for each problem.

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#### 1. \( 2 \times \frac{3}{10} \)

- Step 1: Multiply the whole number (2) by the numerator of the fraction (3).
\[
2 \times 3 = 6
\]
- Step 2: Keep the denominator (10) unchanged.
\[
\frac{6}{10}
\]
- Step 3: Simplify the fraction by finding the greatest common divisor (GCD) of 6 and 10, which is 2.
\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]

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

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#### 2. \( 8 \times \frac{4}{5} \)

- Step 1: Multiply the whole number (8) by the numerator of the fraction (4).
\[
8 \times 4 = 32
\]
- Step 2: Keep the denominator (5) unchanged.
\[
\frac{32}{5}
\]
- Step 3: Since 32 and 5 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{32}{5}}\)

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

- Step 1: Multiply the whole number (9) by the numerator of the fraction (3).
\[
9 \times 3 = 27
\]
- Step 2: Keep the denominator (9) unchanged.
\[
\frac{27}{9}
\]
- Step 3: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 9.
\[
\frac{27 \div 9}{9 \div 9} = \frac{3}{1} = 3
\]

Answer: \(\boxed{3}\)

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#### 4. \( 12 \times \frac{2}{11} \)

- Step 1: Multiply the whole number (12) by the numerator of the fraction (2).
\[
12 \times 2 = 24
\]
- Step 2: Keep the denominator (11) unchanged.
\[
\frac{24}{11}
\]
- Step 3: Since 24 and 11 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{24}{11}}\)

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#### 5. \( 3 \times \frac{5}{7} \)

- Step 1: Multiply the whole number (3) by the numerator of the fraction (5).
\[
3 \times 5 = 15
\]
- Step 2: Keep the denominator (7) unchanged.
\[
\frac{15}{7}
\]
- Step 3: Since 15 and 7 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{15}{7}}\)

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

- Step 1: Multiply the whole number (2) by the numerator of the fraction (3).
\[
2 \times 3 = 6
\]
- Step 2: Keep the denominator (5) unchanged.
\[
\frac{6}{5}
\]
- Step 3: Since 6 and 5 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{6}{5}}\)

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#### 7. \( 11 \times \frac{4}{8} \)

- Step 1: First, simplify the fraction \(\frac{4}{8}\). The GCD of 4 and 8 is 4.
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
- Step 2: Now multiply the whole number (11) by the simplified numerator (1).
\[
11 \times 1 = 11
\]
- Step 3: Keep the denominator (2) unchanged.
\[
\frac{11}{2}
\]

Answer: \(\boxed{\frac{11}{2}}\)

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#### 8. \( 10 \times \frac{1}{4} \)

- Step 1: Multiply the whole number (10) by the numerator of the fraction (1).
\[
10 \times 1 = 10
\]
- Step 2: Keep the denominator (4) unchanged.
\[
\frac{10}{4}
\]
- Step 3: Simplify the fraction by finding the GCD of 10 and 4, which is 2.
\[
\frac{10 \div 2}{4 \div 2} = \frac{5}{2}
\]

Answer: \(\boxed{\frac{5}{2}}\)

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#### 9. \( 5 \times \frac{3}{4} \)

- Step 1: Multiply the whole number (5) by the numerator of the fraction (3).
\[
5 \times 3 = 15
\]
- Step 2: Keep the denominator (4) unchanged.
\[
\frac{15}{4}
\]
- Step 3: Since 15 and 4 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{15}{4}}\)

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#### 10. \( 11 \times \frac{2}{7} \)

- Step 1: Multiply the whole number (11) by the numerator of the fraction (2).
\[
11 \times 2 = 22
\]
- Step 2: Keep the denominator (7) unchanged.
\[
\frac{22}{7}
\]
- Step 3: Since 22 and 7 have no common factors other than 1, the fraction is already in its simplest form.

Answer: \(\boxed{\frac{22}{7}}\)

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Final Answers:

1. \(\boxed{\frac{3}{5}}\)
2. \(\boxed{\frac{32}{5}}\)
3. \(\boxed{3}\)
4. \(\boxed{\frac{24}{11}}\)
5. \(\boxed{\frac{15}{7}}\)
6. \(\boxed{\frac{6}{5}}\)
7. \(\boxed{\frac{11}{2}}\)
8. \(\boxed{\frac{5}{2}}\)
9. \(\boxed{\frac{15}{4}}\)
10. \(\boxed{\frac{22}{7}}\)

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Explanation:

To multiply a whole number by a fraction:
1. Multiply the whole number by the numerator of the fraction.
2. Keep the denominator unchanged.
3. Simplify the resulting fraction if possible by dividing both the numerator and the denominator by their greatest common divisor (GCD).

This method ensures accurate and efficient computation for all problems in the worksheet.