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A Step-by-Step Guide to Dividing Fractions With Whole Numbers

boy dividing fractions with whole numbers while laying on the grass

The process of dividing fractions with whole numbers is different than what it seems. Even though you are dividing whole numbers, the most effective way to solve these kinds of math problems is to use a multiplication sign. Let's explain why.

How Division of Fractions Work

Before explaining why dividing fractions with whole numbers requires you to multiply fractions, let’s learn how to divide fractions. Any time you are asked to divide fractions, you have to flip or invert the fraction. Here's an example:

dividing fractions with whole numbers example

As you can see, dividing the first fraction by the second fraction of one-half is actually the same thing as multiplying the numerator (the top part of the fraction) by 2.

The result is an improper fraction, which means the numerator is larger than the denominator (the bottom number of the fraction.) This improper fraction can also be converted into a mixed number:

dividing fractions with whole numbers: improper fraction

So 6/5 and 1 1/5 are equivalent fractions. Use this fractions worksheet to learn how to turn improper fractions into mixed fractions.

Dividing Fractions With Whole Numbers: A Step-by-Step Guide

Now that we know how multiplying and dividing fractions work, let's learn how to divide whole numbers by fractions.

dividing fractions with whole numbers

Anytime a whole number is the divisor of a fraction, you are further dividing this fraction into multiple equal parts. Let's break this process down step by step:

1. Inverse the the Whole Number

To start, you must convert the whole number into a fraction by inversing it. This means that the value of 1 will become the numerator and the whole number will become the denominator. A fraction with a numerator value of 1 is called a unit fraction.

inverse the whole number

2. Multiply the Fractions

You will now multiply the numerators and denominators.

multiply the fractions

3. Simplify the Fraction

Find the lowest common denominator, the smallest number that both numbers can be divided by. In this case, the number is 3.

simplify the fraction

Why Is Dividing Fraction With Whole Numbers Important?

When you enter 5th grade and 6th grade math, you start exploring math worksheets and word problems that involve adding and subtracting fractions. This prepares you for middle school math, where you start multiplying and dividing fractions with whole numbers.

Building a strong fraction foundation helps you with more complex fractional concepts that you'll learn in high school math.

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