How To Multiply Fractions By Whole Numbers

Fraction Multiplication Rule:

\[ \text{Result} = \frac{\text{Whole Number} \times \text{Numerator}}{\text{Denominator}} \]

Result:

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1. What Is Fraction Multiplication?

Multiplying a fraction by a whole number is a fundamental arithmetic operation that scales the fraction by the whole number amount. It's commonly used in recipes, measurements, and scaling problems.

2. How To Multiply Fractions By Whole Numbers

The basic rule for multiplying a fraction by a whole number:

\[ \frac{a}{b} \times c = \frac{a \times c}{b} \]

Where:

\( \frac{a}{b} \) — The original fraction
\( c \) — The whole number
Numerator is multiplied by the whole number
Denominator remains unchanged

Explanation: Multiplying a fraction by a whole number is equivalent to adding the fraction to itself multiple times.

3. Practical Examples

Example 1: \( \frac{3}{4} \times 5 = \frac{15}{4} = 3\frac{3}{4} \)
Example 2: \( \frac{2}{5} \times 3 = \frac{6}{5} = 1\frac{1}{5} \)

4. Common Mistakes

Mistake 1: Multiplying both numerator and denominator by the whole number.
Mistake 2: Forgetting to simplify the resulting fraction.
Mistake 3: Converting to improper fractions unnecessarily.

5. Frequently Asked Questions (FAQ)

Q1: Can the result be a whole number?
A: Yes, if the denominator divides evenly into the new numerator (e.g., \( \frac{3}{4} \times 4 = 3 \)).

Q2: What if the whole number is zero?
A: The result will always be zero (e.g., \( \frac{5}{8} \times 0 = 0 \)).

Q3: How is this different from multiplying two fractions?
A: When multiplying two fractions, you multiply both numerators and denominators. With whole numbers, the denominator stays the same.

Q4: Should I convert mixed numbers first?
A: Yes, convert mixed numbers to improper fractions before multiplying.

Q5: How does this relate to division?
A: Multiplying by a whole number is the same as dividing by its reciprocal (e.g., \( \times 5 = \div \frac{1}{5} \)).