Even students who love maths tend to struggle with fractions. It is one of those topics that kids just can’t seem to get their heads around. However, once you know how to do them, and they are properly explained to you, it becomes clear that they are actually one of the simplest concepts to grasp in maths.
Dividing fractions by fractions is especially important to understand because it has real-life applications. When students get frustrated and they do not understand certain things in maths, their main complaint is that they are never going to use it in the real world anyway. Well, we are here to tell you that you will definitely be using fractions in your real life, whether you like it or not.
That is why we are here to teach you this essential life skill. Not only will knowing how to divide fractions help you to complete that math problem in your homework or ace your next test, it will also help you throughout your life as you encounter it everywhere you go.
How do you divide a fraction by a fraction?
Here are the key steps to divide fractions by fractions:
- Step 1: The first thing you are going to need to do is turn the second fraction upside down. You need to take the second fraction and put the denominator (the bottom number) on top and the numerator (the top number) on the bottom. Essentially, you need to just flip the second fraction around.
- Step 2: Next, you need to treat the problem like a multiplication problem and multiply the two fractions together. In order to do this, all you need to do is multiply the numerators together and that will give you the numerator for your answer and multiply the denominators together and that will give you the denominator for your answer.
- Step 3: The final step might not always be needed, but if you can, you should simplify the fraction. You can find out if your answer is simplifiable by seeing if there are any numbers that can be divided into both the numerator and denominator. If there is, go ahead and divide both sides of your fraction by this number and the numbers you get will be your final answer.
Dividing fractions by fractions example
In order to help you visualize the above steps in the form of an actual equation, here is an example to show you how it works in practice:
½ ÷ ⅙
- Step 1: The first thing you are going to need to do is flip the second fraction around. Once you have done this, you will be left with the equation below:
½ ÷ 6/1
- Step 2: Now you just treat this like you would a usual multiplication problem and multiply the numerators together, which will give you 6, and then multiply the denominators together, which will be 2.
Therefore your answer will be 6/2.
- Step 3: The final step is to simplify the fraction. In this case, the highest common factor is 2, and you can see that 2 goes into 6 3 times, meaning your final answer will be 3.
How do you divide fractions and whole numbers?
Now that you have hopefully mastered the standard division of fractions by fractions, we will move on to dividing fractions by whole numbers. Dividing fractions by whole numbers is no harder, it just requires a different approach.
All you need to do is place the whole number with the denominator and multiply them together. This will give you the new denominator. The numerator stays the same, and that is it, you have your answer. Again, as with any fraction problems, if you can simplify the answer, simplify the answer.
Dividing fractions and whole numbers example
Q. ½ ÷ 3
The first thing you need to do here is place the 3 with the 2 as the denominator and multiply them together. This will give you your new denominator. Therefore, your new denominator is 6 as 3 x 2 = 6.
Then simply keep your numerator in place to give yourself the answer of ⅙.
How to divide mixed fractions
Now that you have the hang of these two types of problems, we are going to take it up a notch and divide mixed fractions. These might seem more daunting and more difficult than the previous two, but they are actually fairly simple and easy to get the hang of.
- Step 1: The first thing you need to do is turn the mixed numbers into improper fractions, which is actually the only additional step that is any different from the things we have already done. To turn a mixed number to an improper fraction, all you need to do is multiply the denominator by the whole number and add the numerator to that number. This new number that you reach will be your new numerator. The denominator stays the same.
- Step 2: Then, you can treat this problem like a usual fraction division problem. You flip the second fraction around and then multiply the numerators and denominators.
- Step 3: The final step, as always, is to simplify the fraction if possible. In this case, it might involve turning it back into a mixed number.
Dividing mixed numbers example
Once again in order to help you visualize the above steps, we have an example for you.
Q. 6 ½ ÷ 2 ¼
- Step 1: Turn the mixed numbers into improper fractions. For the first fraction you multiply the 2 by the 6 and add the 1. Your answer is 13 and this is your new numerator.
For the second fraction, you multiply 2 by 4 and add 1. Your answer is 9 and this is your new numerator. Therefore, your new equation should look like this:
13/2 ÷ 9/4
- Step 2: Next you need to flip the second fraction and then treat it like a multiplication problem. You therefore have:
13/2 x 4/9
And multiply the numerators, which will equal 52
And multiply the denominators will equal 18
- Step 3: Finally simplify the equation, and your final answer should be 28/9.
Need help in maths?
Above, we have covered the basics of dividing fractions. However, there is a lot more to learn when it comes to fractions. Maths syllabuses are vast and varied, meaning there is always something more to learn. If you are struggling in mathematics and need additional help, tutorax is here to help.
Since the pandemic hit, many students have fallen behind in maths and are struggling to catch up. Tutorax provides students with qualified tutors both in-person and online in a variety of subjects. Our team of tutors are dedicated to collaborating with you to discover what learning style you will benefit from most to ensure you can achieve your full academic potential in a seamless manner.