How To Divide Fractions – A Complete Guide
When you complete the math sections on the SAT or the ACT, you are going to need to know how to add, subtract, multiply, and divide fractions.
There will likely be a couple of questions where you will have to divide fractions within a limited amount of time, meaning that you’ll need to know what fractions are and how to divide them with ease.
Considering you only have 75 seconds per question for the Math (No Calculator) section, and 87 seconds per question for the Math (Calculator) section on the SAT, and 1 minute per question on the ACT Math section, it is essential that you are able to divide fractions quickly.
Fortunately, learning how to divide fractions is just as easy as learning how to multiply fractions. All you need to do is complete four simple steps, and you’ll be able to divide fractions efficiently and effectively.
This guide will explain everything you need to know about fractions and detail the four steps you’ll need to know to divide them.
What are fractions?
Fractions are a representation of parts of a whole. For example, if you eat half of a pizza, you have eaten a fraction of the whole pizza. If you eat a third of a pie, you have consumed a fraction of the pie. In both cases, not only have you devoured a fraction of the food, but you have left a fraction remaining.
When you see fractions, like ½ or ⅚ , these numbers are representing how much of the whole is remaining.
For example, if you have consumed half of a pizza, you have eaten ½ of the pizza, and there is still ½ of the pizza remaining. If you have eaten a third of a pie, you have consumed ⅓ of the pie, and there is ⅔ of the pie remaining.
Fractions always have a numerator and denominator.
The numerator is the number on the top half of a fraction, and it represents how much of the whole has not been used. The denominator is the number beneath the line of a fraction, and it represents the whole.
For instance, if you take a look at the fraction below, the numerator is 5 and the denominator is 6.
This means that there are 5 parts remaining out of the 6 total parts that used to comprise the whole. Let’s say we were talking about a pizza. The fraction ⅚ would mean that there are 5 slices remaining of a pizza that was originally cut into 6 slices.
Without understanding numerators and denominators and what they’re meant to represent, it will be difficult for you to divide fractions.
Make sure you understand how fractions represent what is remaining from a whole before you move on to the next section.
Once you feel comfortable with fractions in general, you’ll have all the tools you need to divide fractions on the SAT and ACT Math sections.
While dividing fractions may sound complicated, it only requires four steps:
1. Find the reciprocal
The first thing you need to do when dividing fractions is to find what is called the reciprocal of the second fraction. This is always the fraction you are trying to divide by in an equation.
So if you are trying to figure out the answer to ½ divided by ⅙ , you will need to find the reciprocal of ⅙.
To find the reciprocal of a fraction, you just need to turn that fraction upside down. In this way, ⅙ becomes 6/1.
Now that you have the reciprocal, you can move on to your next step.
2. Multiply the numerators
The second step is to multiply the two numerators (remember you are using the first fraction and the reciprocal). If you’re having trouble remembering how to multiply fractions in general, check out our guide.
However, since you are only multiplying the numerators for this step, it shouldn’t be too challenging.
For the example above, you will multiply 1 and 6, which will give you 6.
3. Multiply the denominators
Now that you have a new numerator, you will need to create a new denominator, too.
This means that you need to multiply the two denominators (the one for the first fraction and the one for the reciprocal you created earlier).
For the example above where you are dividing ½ by ⅙ , you would multiply 2 (the denominator of fraction 1) and 1 (the denominator of the reciprocal of ⅙), which would give you 2.
1x62x1 = 62
Now, you have successfully divided your fraction! There is only one last step for you to take care of to reduce your fraction, and you will have your final answer.
4. Simplify your fraction
When possible, reduce your fraction to the smallest possible fraction or number that still represents the same amount of the whole.
This is called simplifying your fraction.
In order to simplify a fraction, you often just need to divide the numerator by the denominator.
In the example above, 6 divided by 2 is 3, which means that 3 will be your final answer.
If you can complete the steps above, you will be able to divide fractions without any struggle.
Try using these steps with a few examples (don’t worry, I’ll share the answers with you below so that you can check your work.)
- Divide ⅘ and ¼
- Divide ¾ and ⅚
- Divide ½ and ⅗
When you’re finished, check your work below. You should have the following answers:
- Answer= 315 . After finishing steps 1-3, you should end up with 165, which can be simplified to 315
- Answer =910 . After finishing steps 1-3, you should have 910, which cannot be simplified any further.
- Answer = 56. After finishing steps 1-3, you should have 56, which cannot be simplified any further.
If you were able to get the correct answers for these questions, you are on the right track to doing well on the SAT and ACT Math sections.
Multiplying mixed fractions
Occasionally, you will see mixed fractions on the SAT or the ACT.
Mixed fractions have a whole number with a fraction.
For example, 2 ⅔ is a mixed fraction.
When multiplying mixed fractions, you need to convert the mixed fraction into an ordinary fraction first.
To do this, you need to follow a couple of steps:
1. Multiply the whole number by the denominator
In the example 2 ⅔ above, you would multiply 2 and 3, which is 6.
2. Add your answer from step 1 to the numerator
For the example above, you would add 6 to 2 to make the new numerator 8. This would make your new fraction look like this:
3. Use this new fraction to divide
If you were asked to divide 2 ⅔ and ⅓ , for example you would first convert 2 ⅔ to 8/3, and then you can use the steps mentioned earlier to divide this fraction by ½. Your answer for this example, by the way, should be 8.
Learning SAT and ACT Math tips
If you want to learn about adding, subtracting, or dividing fractions, you should consider attending an ACT or SAT prep course or working with a private math tutor.
When you have such a short amount of time to answer math questions, it can be easy to feel overwhelmed and even forget some of the steps required to divide fractions.
When you work with a private math tutor, you can gain extra practice and learn tips that will help remember the steps above and alleviate the pressure you’ll feel when taking the test.
If you know how to divide fractions, but you’re struggling with other math concepts, a prep course will be beneficial. With a prep course, you’ll learn all the strategies you’ll need to know to answer the math questions on the test without hesitation.
Learn more about how you can improve your SAT or ACT scores with f Prep Expert’s private math tutors or taking a prep course today when you visit our website.