The rule for multiplying a fraction by an integer is simple: multiply the numerator of the fraction by the integer, and keep the denominator the same.
Here's a more detailed breakdown:
- Multiply the Numerator: Take the integer (whole number) and multiply it by the numerator (the top number) of the fraction.
- Keep the Denominator: The denominator (the bottom number) of the fraction remains unchanged.
- Simplify: If possible, simplify the resulting fraction to its lowest terms.
Formula:
Integer × (Numerator / Denominator) = (Integer × Numerator) / Denominator
Example:
Let's say you want to multiply 3 by the fraction 2/5.
- Multiply the Numerator: 3 × 2 = 6
- Keep the Denominator: The denominator remains 5.
- Result: 3 × (2/5) = 6/5
The answer is 6/5, which can also be expressed as the mixed number 1 1/5.
Why This Works
An integer can be thought of as a fraction with a denominator of 1. For example, 3 is the same as 3/1. Multiplying fractions involves multiplying the numerators and multiplying the denominators. So, 3 × (2/5) is the same as (3/1) × (2/5) = (3 × 2) / (1 × 5) = 6/5. Because the integer's denominator is always 1, it doesn't change the original fraction's denominator when multiplying.
Example Table:
| Integer | Fraction | Multiplication | Result (Unsimplified) | Result (Simplified) |
|---|---|---|---|---|
| 4 | 1/3 | 4 × (1/3) | 4/3 | 1 1/3 |
| 2 | 3/4 | 2 × (3/4) | 6/4 | 3/2 or 1 1/2 |
| 5 | 2/7 | 5 × (2/7) | 10/7 | 1 3/7 |
Multiplying fractions by integers is a fundamental arithmetic operation. By following the simple rule of multiplying the numerator and keeping the denominator, you can easily perform these calculations.
