Dividing a Fraction by a Whole Number
Updated on February 8, 2026
Welcome to another exciting journey into the world of math with Brighterly! This time, we’ll be exploring how to divide a fraction by a whole number, a skill you will use countless times in the classroom and in real life.
If you are new to fractions, any action with them, including dividing fractions by whole numbers, may seem like uncharted territory, which can feel a little daunting. However, fractions are actually quite simple, and by the end of the article, we promise you’ll make sense of them.
In this article, we will go into how fractions are divided by whole numbers step by step, understand mixed and improper fractions, and solve some fun exercises. Let’s start!
Dividing fractions with whole numbers: Introduction
At its fundamental level, when you divide fraction by whole number, what you do is you break the fractional part into even smaller pieces. A fraction represents a part of a whole, and when divided by a whole number, it becomes an even smaller part of that whole.
So, when you divide a fraction like 1/2 by 2, what you do is split half into two equal parts, which will get you quarters (1/4).
In mathematics, another method on how to divide fractions with whole numbers is through multiplication. More specifically, you multiply the fraction by the reciprocal of the whole number. Reciprocal is the “flipped” version of a number, e.g., the reciprocal of 5 is 1/5. So, if you want to divide 1/2 by 2, you can also multiply it by 1/2 instead: 1/2 × 1/2 = 1/4.
Steps of dividing fractions with whole numbers
Let’s now look at how dividing fractions with whole numbers without calculator works step by step. We’ll look at two processes, each of which has three steps.
For the first method, you simply need to take the denominator of your fraction and multiply it by your whole number. If your fraction is 1/5, and you need to divide it by 3, what you do is:
1/5 ÷ 3 = 1/(5×3) = 1/15
The second method is known as Keep-Change-Flip, and it’s the one where we use a reciprocal. It’s a three-step process.
- Step 1: Keep the fraction as it is. Don’t change it.
- Step 2: Flip your whole number to its reciprocal.
- Step 3: Multiply the two fractions you have now.
Here is how it will look in practice:
2/3 ÷ 4 = 2/3 x 1/4 = 2/12, which we can simplify to 1/6.
It’s quite a simple and straightforward process, and with a bit of practice, you’ll grasp it quite quickly.
How to divide a mixed fraction by a whole number?
Fractions aren’t always smaller than one. Often, fractions can contain whole numbers, and this is what in math we call mixed fractions. For example, 3 1/2 is a mixed fraction. Similar to simple fractions, dividing mixed fractions with whole numbers is an important math skill, so let’s see how it’s done.
Luckily, the process isn’t that much different. What mixed fractions do is add one extra preparatory step to the process when you need to turn them into improper fractions.
To do this, you multiply your whole number part by the denominator, then add the result to the numerator. This new number becomes your numerator, while the denominator stays the same.
For example, if you are dividing 3 1/2 by 2, you would first convert the fraction, like so:
3 1/2 = (3×2)+1/2 = 7/2
Then, you will do the division as we discussed earlier:
7/2 ÷ 2 = 7/(2×2) = 7/4, which can be simplified back into a mixed fraction 1 3/4.
Mixed fractions and improper fractions
We mentioned the term mixed and improper fractions earlier, but what are those, exactly? Well, it’s quite simple.
Mixed fractions are the fractions that contain a whole number, like the 3 1/2 example we solved earlier.
Improper fractions are the “top-heavy” fractions that have a numerator larger than the denominator. In our earlier example on how to divide fractions by whole numbers, we turned 3 1/2 mixed fraction into the 7/2 improper fraction. Improper fractions are great, as during the math class, they can make solving the problems a lot easier. Once you have a confusing-looking whole number, you need to work with it; simply turning it into an improper fraction makes dealing with it much easier.
How to divide whole numbers by a fraction?
So far, we talked about dividing fractions by a whole number. Now, let’s reverse the scenario and look at how to divide whole numbers by fractions, because it’s something you will come across.
Imagine you need to calculate how many 1/4 cup scoops of ice cream are in 3 whole cups of ice cream. How would you approach this? The answer is, with the same Keep-Change-Flip technique we learned earlier!
On the first step, there is one small difference. You keep the whole number, but you visualize it differently. Instead of 3, you would write 3/1, as a fraction over 1.
Next up, you again change the division sign by multiplication.
Lastly, you flip the fraction you had (in this case, the 1/4) to its reciprocal, getting a 4/1.
You then multiply the numbers you have, like this: 3/1 x 4/1 = 12. There are 12 1/4 cups in 3 full cups.
When you are dividing whole numbers by fractions, you will notice that the answer will almost always get larger. This may be confusing at first, but it’s quite logical if you think about it. If you take 2 apples and cut them into 8 slices each, you will have 16 slices.
Dividing fractions with whole numbers worksheet
If you want to practice fraction divided by whole number and the other way around, with structured exercises, while also having fun, make sure to check out our Dividing Fractions By Whole Numbers Worksheets and Dividing Whole Numbers By Fractions Worksheets. These worksheets come as free PDFs, and are filled with a wide range of tasks that will help what you have just learned to stick.
Solved examples
Solved math problem 1
Use the Keep-Change-Flip method to solve 4/7 ÷ 2.
Solution: Keep 4/7 as it is. Then, change the division sign to multiplication, and flip 2 to its reciprocal. Here’s how it will look:
4/7 x 1/2 = 4/14, which we can simplify to 2/7.
| The answer is 2/7 |
Solved math problem 2
How would you turn 4 1/6 into an improper fraction?
Solution: To turn a mixed fraction into an improper fraction, we multiply the whole number by the denominator, then add the numerator. This new number becomes the numerator, with the denominator staying the same. Here’s how: 4 1/6 = (4×6) + 1/6 = 25/6
| The answer is 25/6 |
Solved math problem 3
How can you divide 5 by 1/2?
Solution: We can use the same Keep-Change-Flip method. We keep 5, but visualize it differently, as a fraction 5/1. We change the division sign to the multiplication sign, and take the reciprocal of the fraction. Here’s the solution: 5 ÷ 1/2 = 5/1 x 2/1 = 10/1 = 10. There are 10 halves in 5.
| The answer is 10. |
Practice problems
Math problem 1. How do we call a fraction that contains both a whole number and a fraction?
Math problem 2: You have 3/4 pizza left, and want to share it between 3 people. Which part of a pizza will each person get?
Math problem 3: Solve the problem 5/8 ÷ 10 and simplify your answer.
Frequently Asked Questions
When dividing fractions with whole numbers?
You need to divide a fraction by a whole number whenever you need to split the fraction into even smaller, equal pieces. This is something you’ll do a lot in math class, but will also come across in real life, when you need to, say, split a leftover cake among your friends.
How do you divide a fraction by a whole number?
There are several ways of dividing fractions without calculator with whole numbers, but the most common one is the Keep-Change-Flip method. With this method, you keep the fraction exactly as it is, change the division sign to a multiplication sign, and flip the whole number to its reciprocal.
Why it’s important to divide fractions by whole numbers?
Knowing how to divide fractions by whole numbers and vice versa is an important and very commonly used math topic. It bridges the gap between early math and more advanced algebra, and is a skill you will use often in more advanced math classes.
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