How To Multiply Fractions – A Complete Guide
Whether you take the SAT or the ACT, you are going to need to be comfortable with multiplying fractions.
You will see many questions that require you to not only understand how fractions work, but also be able to multiply these fractions within a limited amount of time.
On the SAT Math sections, you will have 75 seconds per question for the Math (No Calculator) section, and 87 seconds per question for the Math (Calculator) section. On the ACT Math section, you get 1 minute per question.
This means that you will need to be able to multiply fractions quickly during the test.
While multiplying fractions might seem challenging, this concept is a lot easier to master than it may appear. In fact, you can multiply fractions with just four simple steps.
This guide will help you understand fractions and walk you through the four steps you’ll need to know to multiply fractions.
What are fractions?
Simply put, fractions are part of a whole. For example, if you eat half of a pizza, you have consumed a fraction of the whole pizza.
When you see specific fractions like ¾, ⅚, or ⅞, these fractions are meant to represent how much of a whole has not been “consumed.” In the example above, if you have eaten half of a pizza, you have consumed ½ of the pizza because there are two halves, and you have eaten one of them. This means that there is ½ of the pizza remaining.
Fractions are broken down into numerators and denominators.
Numerators are the numbers at the top half of a fraction, and they represent the amount of the whole that hasn’t been used.
For instance, with the fraction below, the numerator is 7.
The denominator of a number represents the whole or the total. In the above example, the denominator is 8.
Looking at this through the lens of consuming pizza, the fraction ⅞ would mean that there are seven slices of pizza remaining out of a pizza that originally had eight slices.
Once you understand what numerators and denominators represent, it is easier to understand fractions.
If you eat 3 slices of a pie that is cut into four slices, you have ¼ of that pie remaining. If you have a whole number like 1, and you subtract ⅓ from this number, then you have ⅔ remaining (⅔ + ⅓ = 1).
With this knowledge, you’ll have everything you need to be able to multiply fractions when you encounter these types of problems on the SAT or ACT Math sections.
Multiplying fractions requires four steps:
1. Multiply the numerators
The first thing you need to do when multiplying two fractions is to multiply the two numerators.
For example, if you are multiplying ⅔ and ⅞ , you first need to multiply 2 and 7, which will give you 14 for your new numerator.
2. Multiply the denominators
You will then need to multiply the two denominators. In this case you would multiply 3 and 8, which will give you 24 for your new denominator.
3. Create your new fraction
Now that you have a new numerator and a new denominator, you need to create your new fraction. Put your new numerator and denominator into fraction format as I’ve done below.
4. Reduce your fraction
If possible, reduce your fraction to the smallest possible fraction that still represents the same amount of the whole.
Find the greatest common factor of both the numerator and denominator for your new fraction. In this case, you need the greatest common factor of 14 and 24, which is 2.
Once you have this factor, divide both your numerator and your denominator by this factor. In the case of the example above, you have 14 divided by 2, which is 7 for your final numerator, and 24 divided by 2, which is 12 for your final denominator.
This means that after reducing your fraction, your final answer after multiplying ⅔ and ⅞ is 7/12.
By completing the four steps above, you should be able to multiply fractions with ease.
Try using these steps with a few examples (we’ll give you the answers so that you can check your work.)
- Multiply ⅘ and ¼
- Multiply ¾ and ⅚
- Multiply ½ and ⅗
When you’re finished, check your work below. You should have the following answers:
- Answer= ⅕ . After finishing steps 1-3, you should have had 4/20, which can be reduced to ⅕ using the greatest common factor of 4.
- Answer = ⅝ . After finishing steps 1-3, you should have had 15/24, which can be reduced to ⅝ using the greatest common factor of 3.
- Answer = 3/10. After finishing steps 1-3, you should have 3/10, which cannot be reduced.
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, 7 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 7 ⅔ above, you would multiply 7 and 3, which is 21.
2. Add your answer from step 1 to the numerator
For the example above, you would add 21 to 2 to make the new numerator 23. This would make your new fraction look like this:
3. Use this new fraction to multiply
If you were asked to multiply 7 ⅔ and ¼, you would first convert 7 ⅔ to 23/3, and then you can use the steps mentioned earlier to multiply this fraction by ¼ . (You should get 23/12 or 1 11/12, by the way).
Learning SAT and ACT Math tips
If you want to learn about adding, subtracting, or dividing fractions, as well as other math concepts that you will see on the SAT or ACT Math sections, I highly recommend enrolling in an ACT or SAT prep course or working with a private tutor.
Math concepts can be challenging, and with the added pressure of trying to solve these questions within a limited time frame, it can make the math sections seem overwhelming.
When you take a prep course, you will learn all of the math concepts covered on the SAT or ACT, and you will also gain helpful tips and tricks that can help you solve math problems, like ones where you have to multiply fractions, quickly and effectively.
Likewise, private tutors can help you improve your weaknesses when it comes to the math sections of either standardized test.
See how you can improve your SAT score by working with one of Prep Expert’s private math tutors or taking a prep course today when you visit our website.