Multiply a Fraction by a Whole Number
When you multiply a fraction by a whole number, you are taking that fraction several times. A good way to think about it is:
- (\frac{a}{b} \times n) means (n) copies of (\frac{a}{b}).
Method
- Multiply the numerator by the whole number.
Keep the denominator the same.
- Simplify the result if possible.
- If the answer is an improper fraction, you may also rewrite it as a mixed number if that helps, but keep the form requested.
Example idea
If you have (\frac{2}{5} \times 3), multiply 2 by 3 to get 6, so the result is (\frac{6}{5}). This can be simplified only if numerator and denominator share a factor; here they do not.
Check your work
- Make sure only the numerator changed.
- See whether the fraction can be reduced by dividing top and bottom by the same number.
- You can estimate: multiplying by a whole number should make the fraction larger, unless the fraction is already very small.
Tip
If the whole number is on the left, (n \times \frac{a}{b}), the process is the same.