Dividing a Fraction by a Whole Number
Created on Dec 20, 2023
Updated on January 8, 2024
Welcome to another exciting journey into the realm of mathematics with Brighterly, your trusted companion for making math simpler and more fun! Today, we’ll be exploring the captivating world of dividing fractions by whole numbers. At first glance, fractions can seem like uncharted territory filled with unfamiliar terms and daunting operations. However, with the Brighterly approach, you’ll soon find that these concepts are as easy and intuitive as slicing an apple or sharing a pizza.
Our journey will lead us through understanding the principles and processes of division involving fractions and whole numbers, with examples and practice problems to ensure you’re thoroughly versed. Plus, you’ll uncover how multiplication ties into the whole process (hint: division is similar to multiplying by the reciprocal). So, ready your mathematical compass and let Brighterly guide you through this thrilling expedition.
Dividing Fractions with Whole Numbers: Introduction
The world of mathematics can be daunting and confusing at times. One such area where students often find challenges is when it comes to dividing fractions by whole numbers. However, once you understand the principles, the process becomes significantly easier. Just like you would slice an apple into parts, dividing fractions is about determining how many of these slices you have. Here’s a fun fact: Dividing is actually the same as multiplying by the reciprocal! That means when you’re dividing a fraction by a whole number, you’re essentially multiplying the fraction by the inverse of the whole number. This might sound a bit complicated now, but stick with us – it’ll make a lot more sense once we walk through the steps together!
Steps of Dividing Fractions with Whole Numbers

Reciprocal of the Whole Number: The first step is to take the reciprocal of the whole number. But wait, what is a reciprocal? It’s quite simple! The reciprocal of a whole number is just 1 divided by that number. For example, the reciprocal of 5 is 1/5.

Multiplication: After finding the reciprocal, you multiply this by the original fraction. This can be done simply by multiplying the numerators (the top number in the fraction) and then the denominators (the bottom number).

Simplify: The last step involves simplifying the fraction, if necessary. To do this, you find the greatest common factor (GCF) of the numerator and the denominator and divide both by it.
How to Divide a Mixed Fraction by a Whole Number?
Let’s take a step further into the mathematics labyrinth and talk about mixed fractions. A mixed fraction is a whole number and a fraction combined, like 2 1/2. The process of dividing a mixed fraction by a whole number involves an extra step at the beginning: turning the mixed fraction into an improper fraction.
Mixed Fractions and Improper Fractions
You’re probably wondering, “What on earth is an improper fraction?” Don’t worry; it’s not as improper as it sounds! An improper fraction is simply a fraction where the numerator is greater than the denominator. For example, 5/3 is an improper fraction. You can convert a mixed fraction to an improper fraction by multiplying the whole number by the denominator of the fraction, then adding the numerator.
How to Divide Whole Numbers by a Fraction?
Now that we’ve covered dividing a fraction by a whole number, you may be wondering, “What if we need to divide a whole number by a fraction?” Well, you’re in luck! The process is very similar. Just as before, you find the reciprocal of the fraction (this time it’s the fraction, not the whole number) and then multiply.
Solved Examples
Ready to see these steps in action? Here are some solved examples:

Dividing a Fraction by a Whole Number: Divide 2/3 by 4.

Dividing a Mixed Fraction by a Whole Number: Divide 3 1/2 by 5.
Practice Problems
Practice makes perfect! Try solving these problems:

Divide 3/4 by 6.

Divide 4 1/2 by 7.
Conclusion
Congratulations! You’ve successfully navigated through the labyrinth of dividing fractions and whole numbers. By now, you should be feeling more confident and capable in tackling these problems. Remember, with the Brighterly approach, learning mathematics is less about rote memorization and more about understanding concepts intuitively.
We encourage you to continue exploring and practicing, as each step enhances your mathematical proficiency and critical thinking skills. Brighterly is here to guide and support you throughout this fascinating journey of discovery. Thank you for choosing Brighterly – your brightness makes us shine!
Frequently Asked Questions
What is a reciprocal and how do I find it?
The reciprocal of a number is simply 1 divided by that number. So, the reciprocal of a whole number like 5 would be 1/5. If you’re dealing with a fraction, like 2/3, the reciprocal would be the fraction flipped, or 3/2.
How do I convert a mixed fraction to an improper fraction?
You can convert a mixed fraction to an improper fraction by multiplying the whole number by the denominator of the fraction, then adding the numerator. For instance, to convert 2 1/2 to an improper fraction, you’d multiply 2 (the whole number) by 2 (the denominator), then add 1 (the numerator). This would give you 5/2.
What is the process for dividing a whole number by a fraction?
It’s quite similar to dividing a fraction by a whole number. You find the reciprocal of the fraction (by flipping it), and then multiply the whole number by this reciprocal.