If you’re looking for a simple guide that shows you how to divide fractions, you’re in the right place! In the following article, we’ll walk you through a comprehensive yet simple step by step guide to divide fractions easily! Let’s dive in!
What Are Fractions?
The first thing that you should fully understand before doing division is fractions. As the name suggests, fractions mean a broken part of the whole. So, in mathematical terms, a fraction represents a part of a whole.
In other words, when you say a fraction, you’re describing the number of parts within a certain full number. For instance, one half (1/2), three quarters (3/4), two fifths (2/5).
In the previous case, the first number is called “the dividend”, where the second one is known as “the divisor”.
If you picture the whole fraction as a pizza. In the first example, one half means that you split the pizza into two equal pieces, where each half represents one of these two.
In the 3/4 example, you split the pizza into 4 slices and represent three of them. Lastly, in two fifths, you represent 2 slices of a pizza that’s split into 5 equal parts. It’s very easy to understand once you picture it!
How to Divide Fractions: Step by Step Guide
Here’s a comprehensive guide that shows you everything you need to know about dividing fractions.
Step 1: Know The Basics
Understanding fractions isn’t the only thing that you should know fully before doing fraction division.
To make the most out of this guide, you’ll need to know some important terms that’ll make you follow the guide much easier.
Numerators and Denominators
In a fraction, there are two parts involved. The upper part of the fraction, which is known as “the numerator”, and the lower part of the fraction, which is known as “ the denominator”. To make things easier, we’ll continue using the words top and bottom number of the fraction.
One of the most important things that you need to know before dividing is the reciprocal of a fraction. While the word might sound a bit overwhelming, it’s much simpler than you think!
To put it in the simplest way possible, a reciprocal is the maths term that means the opposite of your fraction.
In other words, it describes what you get when you switch the top (numerator) and bottom (denominator) parts of the fraction.
For example, if you have a fraction 2/3 and you switch the top and bottom parts of the fraction, you’ll get 3/2.
As you can see, 3/2 is the reciprocal of 2/3. On the other hand, 2/3 is the reciprocal of 3/2.
Another interesting fact that you should know about reciprocal is the result of multiplying them. When you multiply any fraction by its own reciprocal, the answer will always be one.
The reason behind that is that you’ll always have the same multiplication problem on top and bottom, so you’ll always end up with a whole fraction, which is equal to one. For example 3/2 x 2/3 = 6/6 = 1.
A whole number means a regular number that’s not in a fraction formula. For example, 5 or 8.
What you need to know is that any whole number is a fraction over 1. This means that 5 = 5/1 and 8 = 8/1.
Division and Multiplication
Another thing that you need to know to understand fraction division is to know that multiplication is the opposite of division.
Different signs of Division
Diving, in general, has a wide variety of signs that express the process.
Among the most common ones is “ ÷ ”. This symbol is used to divide the numbers after it by the one behind it. For example (3 ÷ 5) means that you’re representing 3 parts out of 5 in total.
There are also some popular division signs, such as ” / “. To use it in the previous example, it’ll look like this: 3/5 or ⅗, which are both correct.
It goes without saying that the fraction sign itself is a form of division. This means that “35” also acts as a form of division.
You might ask “what do reciprocals have to do with dividing fractions?”
In fact, using reciprocals can help us make the dividing process a whole lot easier!
Whenever you need to divide anything by a fraction, you can just multiply it by the reciprocal instead!
In the following guide, we’ll show you how you can use this cool trick to solve fraction division problems easily!
Let’s start with the basics and work our way up. First, here’s a simple example that divides one fraction by the other.
For example, 2/3 ÷ 3/5
Step #2: Write Down the First Fraction As it Is
First, you need to start with a blank page to answer the problem. The first step is to write down the first fraction without changing its formula.
In our example, you’ll simply write 2/3.
Step #3: Change the Division Sign to Multiplication Sign
As you already know, there are different division signs that you can find in the problem. The most common one is the one used in the problem above, which is “÷”.
The first step to answer the question is to change this sign with a multiplication sign, which is usually represented as “x”. However, you can also use “ . ” or “ * ”.
By now, the answer should look like that: 2/3 x
Step #4: Find the Reciprocal of the Second Fraction
As you now know, to get the reciprocal of a fraction, you should flip it upside down. In our example, the fraction is 3/5. The reciprocal of 3/5 is 5/3.
After writing down the reciprocal: the problem should look much easier as follows:
2/3 x 5/3
Step #5: Solve the Simple Multiplication Problem
Multiplying a fraction is a much simpler process than division. All you have to do is multiply the top parts (numerators) of the two fractions together.
That’s 2 x 5 = 10
After that, multiply the bottom values (denominators) together.
In the previous example, that’s 3 x 3 = 9
The equation now should look like this:
2/3 x 5/3 = 10/9
Step #6 Simplify the Final Fraction
Since the top value in our case is larger than the bottom value, we can conclude that this fraction is larger than one. So, we need to convert it into a simpler form, which is called a mixed fraction.
A mixed fraction is simply a fraction that also combines a whole number. For instance, 1 1/2.
To determine the value of the whole number, you find how many times the bottom value goes into the upper one. In our case, 9 goes into 10 once. This means that “1” is the whole number used.
To find the rest of the mixed fraction, subtract the top value by the bottom. This also gives “1”. So, you should write the simplified fraction as follows: 1 1/9, which is also equal to 10/9.
Always make sure to simplify the fractions if it can be simplified. If it can’t be simplified, you’re done there!
Step #7: Practice with Larger Numbers (Optional)
You can try out the same step with a larger number. For example 9/17 ÷ 15/19
Once again, you’ll turn in to multiplication like this 9/17 x 19/15= 171/255
You can further simplify this fraction by finding the greatest common factor, which is 3 and dividing both the top and bottom by it. This gives you the final simplified answer of 57/85.
How to Divide Triple or More Fractions?
Now that you know how to divide fractions, let’s kick it up a notch and see what you should do in the case of having more than one fraction to divide.
Let’s say that you have the following problem: 2/3 ÷ 1/7 ÷ 5/6
Here’s how you solve problems with 3 or more fractions.
Step #1: Write Down the First Fraction As it Is
Just like we did in the previous example, you need to write down the first fraction without changing its formula. This takes us to the most important tip to answer multiple fraction division, which is “always keep the first fraction as it is”, as the calculation sequence always moves from left to right.
Step #2: Change all the Division Signs into Multiplication Signs
Even if you have more than one sign of division in the problem, you should turn them all into multiplication symbols.
Your current page should look like this: 2/3 x __ x __
Don’t worry about the blank parts, as we’re going to fill them in the following step.
Step #3: Find the Reciprocal of all the Remaining Fractions
Fortunately, the rule of reciprocal multiplication works with complex forms of division too!
From here, you can simply continue your problem like any other one. Here’s how it goes:
2/3 x 7/1 x 6/5 = 84/15= 28/5= 5 3/5
There you have it. A complete guide that shows you have to divide fractions in a step by step guide. As you can see, the golden rule of reciprocals makes fractional division a much easier process.
To divide fractions you need to always leave the first fraction as it is and multiply it by the reciprocals of the rest. Once you try solving some problems, you’ll realize how simple and fun it can be!