How to Multiply a Fraction by a Whole Number?

To multiply a fraction by a whole number, follow these steps:

1. Write the whole number as a fraction: Express the whole number as a fraction with a denominator of 1. This doesn't change the value of the whole number. For example, if you have the whole number 5, you can write it as 5/1.

2. Multiply the numerators: Multiply the numerator of the fraction by the numerator of the whole number (which is the whole number itself).

3. Multiply the denominators: Multiply the denominator of the fraction by the denominator of the whole number (which is always 1).

4. Simplify: Simplify the resulting fraction, if possible. This might involve reducing the fraction to its lowest terms or converting an improper fraction (where the numerator is greater than the denominator) to a mixed number.

Here's a table summarizing the process:

Step	Description	Example (Multiplying 1/2 by 4)
1. Whole Number as Fraction	Write the whole number as a fraction with a denominator of 1.	4 = 4/1
2. Multiply Numerators	Multiply the top numbers (numerators).	1 x 4 = 4
3. Multiply Denominators	Multiply the bottom numbers (denominators).	2 x 1 = 2
4. Simplify	Reduce the fraction to its simplest form, or convert to a mixed number if it's an improper fraction (numerator > denominator).	4/2 = 2

Example

Let's multiply 1/3 by the whole number 6:

1. Write the whole number as a fraction: 6 becomes 6/1.

2. Multiply the numerators: 1 x 6 = 6

3. Multiply the denominators: 3 x 1 = 3

4. Simplify: 6/3 = 2

Therefore, 1/3 multiplied by 6 equals 2.

Another Example: Improper Fractions and Mixed Numbers

What if we multiply 2/3 by 5?

1. 5 becomes 5/1.

2. 2 x 5 = 10

3. 3 x 1 = 3

4. We get 10/3. This is an improper fraction. To convert it to a mixed number, we divide 10 by 3. 3 goes into 10 three times (3 x 3 = 9) with a remainder of 1. Therefore, 10/3 = 3 1/3.