How to Multiply Fractions with a Whole Number
Multiplying fractions with a whole number can be a straightforward process if you understand the basic principles of fraction multiplication. In this article, we will explore the steps involved in multiplying a fraction by a whole number and provide you with some practical examples to help you grasp the concept.
Understanding the Basics
Before we dive into the multiplication process, it’s essential to understand that a whole number can be expressed as a fraction with a denominator of 1. For instance, the whole number 3 can be written as 3/1. This representation allows us to multiply fractions with whole numbers using the same rules as when multiplying two fractions.
Step-by-Step Guide
To multiply a fraction by a whole number, follow these steps:
1. Write the fraction next to the whole number, with a multiplication sign between them. For example, 2/3 x 4.
2. Treat the whole number as a fraction with a denominator of 1. In our example, this would be 4/1.
3. Multiply the numerators of the two fractions together. In our example, this is 2 x 4 = 8.
4. Multiply the denominators of the two fractions together. In our example, this is 3 x 1 = 3.
5. Write the product of the numerators over the product of the denominators. In our example, this is 8/3.
Example 1: Multiplying a Proper Fraction by a Whole Number
Let’s consider the fraction 1/2 multiplied by the whole number 5. Using the steps outlined above, we can solve the problem as follows:
1. Write the fraction next to the whole number: 1/2 x 5.
2. Treat the whole number as a fraction with a denominator of 1: 1/2 x 5/1.
3. Multiply the numerators: 1 x 5 = 5.
4. Multiply the denominators: 2 x 1 = 2.
5. Write the product of the numerators over the product of the denominators: 5/2.
So, 1/2 multiplied by 5 is equal to 5/2.
Example 2: Multiplying an Improper Fraction by a Whole Number
Now, let’s consider the improper fraction 3/4 multiplied by the whole number 2. We can solve this problem using the same steps:
1. Write the fraction next to the whole number: 3/4 x 2.
2. Treat the whole number as a fraction with a denominator of 1: 3/4 x 2/1.
3. Multiply the numerators: 3 x 2 = 6.
4. Multiply the denominators: 4 x 1 = 4.
5. Write the product of the numerators over the product of the denominators: 6/4.
However, we can simplify the fraction 6/4 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 3/2.
So, 3/4 multiplied by 2 is equal to 3/2.
Conclusion
Multiplying fractions with a whole number is a simple process that involves converting the whole number into a fraction, multiplying the numerators, and multiplying the denominators. By following the steps outlined in this article, you can quickly and accurately multiply fractions with whole numbers.
