To multiply a fraction by a whole number, you essentially convert the whole number into a fraction and then multiply the two fractions together. Here's a breakdown:
Steps to Multiply Fractions with Whole Numbers
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Convert the Whole Number to a Fraction: Place the whole number over a denominator of 1. For example, if you have the whole number 5, you would write it as 5/1.
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Multiply the Numerators: Multiply the numerator of the fraction by the numerator of the converted whole number (which is the whole number itself).
- According to the video titled "Multiplying Whole Numbers and Fractions | Math with Mr. J," you multiply straight across the numerators.
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Multiply the Denominators: Multiply the denominator of the fraction by the denominator of the converted whole number (which is 1).
- According to the video titled "Multiplying Whole Numbers and Fractions | Math with Mr. J," you multiply straight across the denominators.
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Simplify the Result: Simplify the resulting fraction, if possible, by dividing both the numerator and denominator by their greatest common factor.
Example
Let's multiply the fraction 1/2 by the whole number 6.
- Convert Whole Number to a Fraction: 6 becomes 6/1.
- Multiply Numerators: 1 (from 1/2) * 6 (from 6/1) = 6
- Multiply Denominators: 2 (from 1/2) * 1 (from 6/1) = 2
- Result: The resulting fraction is 6/2.
- Simplify: 6/2 simplifies to 3 (or 3/1).
Therefore, 1/2 multiplied by 6 is 3.
Table Summarizing the Process
| Step | Description | Example (Multiplying 2/3 by 4) |
|---|---|---|
| 1. Convert Whole Number | Write the whole number as a fraction with a denominator of 1. | 4 becomes 4/1 |
| 2. Multiply Numerators | Multiply the numerators of the two fractions. | 2 * 4 = 8 |
| 3. Multiply Denominators | Multiply the denominators of the two fractions. | 3 * 1 = 3 |
| 4. Resulting Fraction | Write the new fraction with the product of the numerators over the product of the denominators. | 8/3 |
| 5. Simplify (if possible) | Simplify the fraction to its lowest terms or convert to a mixed number if the numerator is greater than the denominator. | 8/3 = 2 2/3 |
