Mastering the Art of Multiplying Mixed Fractions by Whole Numbers- A Step-by-Step Guide

How do you multiply mixed fractions with a whole number? Multiplying mixed fractions by whole numbers can seem daunting at first, but with a few simple steps, you can easily tackle this mathematical challenge. In this article, we will guide you through the process of multiplying mixed fractions with whole numbers, ensuring that you have a clear understanding of the concept and can apply it confidently in your calculations.

In the following sections, we will cover the following topics:

1. Understanding mixed fractions and whole numbers
2. Converting mixed fractions to improper fractions
3. Multiplying the improper fraction by the whole number
4. Reducing the product to its simplest form
5. Converting the improper fraction back to a mixed number

Let’s begin by understanding what mixed fractions and whole numbers are.

Understanding Mixed Fractions and Whole Numbers

A mixed fraction consists of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where 2 is the whole number and 1/3 is the proper fraction. A whole number, on the other hand, is a number that does not have any fractional part, such as 3, 5, or 10.

Converting Mixed Fractions to Improper Fractions

Before multiplying a mixed fraction by a whole number, you need to convert the mixed fraction into an improper fraction. To do this, follow these steps:

1. Multiply the whole number by the denominator of the proper fraction.
2. Add the result to the numerator of the proper fraction.
3. Write the sum as the numerator of the improper fraction, keeping the denominator the same.

For example, let’s convert the mixed fraction 2 1/3 to an improper fraction:

1. Multiply the whole number (2) by the denominator (3): 2 3 = 6
2. Add the result to the numerator (1): 6 + 1 = 7
3. Write the sum as the numerator of the improper fraction: 7/3

Now that we have the mixed fraction as an improper fraction, we can proceed to multiply it by the whole number.

Multiplying the Improper Fraction by the Whole Number

To multiply an improper fraction by a whole number, simply multiply the numerator of the improper fraction by the whole number. The denominator remains the same.

Continuing with our example, let’s multiply the improper fraction 7/3 by the whole number 5:

1. Multiply the numerator (7) by the whole number (5): 7 5 = 35
2. Write the product as the numerator of the new fraction: 35/3

Reducing the Product to Its Simplest Form

After multiplying the improper fraction by the whole number, you may end up with a fraction that can be reduced to its simplest form. To do this, find the greatest common divisor (GCD) of the numerator and the denominator, and divide both by the GCD.

In our example, the GCD of 35 and 3 is 1, so the fraction 35/3 is already in its simplest form.

Converting the Improper Fraction Back to a Mixed Number

If the product is an improper fraction, you can convert it back to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the proper fraction. The denominator remains the same.

In our example, 35 divided by 3 equals 11 with a remainder of 2. Therefore, the mixed number equivalent of the improper fraction 35/3 is 11 2/3.

By following these steps, you can now multiply mixed fractions with whole numbers with ease. Practice these steps, and you’ll be able to handle similar problems with confidence.