Whether you are a math genius or find the presence of numbers terrifying, fractions can often cause problems for a lot of students. However, getting the hang of fractions is not only essential to help you get 100% on that test you have coming up next week, it is actually one of those things that you learn in maths that have direct uses in your everyday life, and you won’t always have a calculator to multiply fractions so it helps to know all the basics.
For example, if you go to the store and see that there is a sale for ½ off, you are going to have to use fractions to calculate the new price of the things you want to buy. You are inevitably going to encounter fractions outside of the classroom, so you are going to want to have a solid grasp on how to deal with them.
3 simple steps to multiply fractions
1. Multiply the numerators
The first thing you need to do when multiplying fractions is to multiply the numerators. The numerators are the numbers on top of the fractions. The answer that you get will create the numerator for your answer.
2. Multiply the denominator
The second thing you need to do is multiply the denominators. The denominators are the numbers on the bottom of the fraction. The number that you get is going to create the denominator number for your answer.
3. Simplify the answer
In some cases, the answer that you get after the first two steps will be the final answer because the numerator and denominator cannot be further divided by the same number to make them smaller numbers.
Examples
A fraction that cannot be simplified
First, we will multiply fractions with whole numbers when the answer cannot be simplified any further.
Q. ⅔ X ⅓
- Step 1: The first thing you need to do is multiply the numerators. In order to do this in this case, all you need to do is multiply 2 by 1, which equals 2.
- Step 2: The second thing you need to do is multiply the denominators. In order to do this, all you need to do is multiply 3 by 3, which equals 9.
- Step 3: Finally, you put these numbers together in the appropriate position on the fraction, which will give you the answer 2/9. There are no numbers that can be divided into both 2 and 9, so this is your final answer as it cannot be simplified any further.
A fraction that can be simplified
Now, we will go over an example where the answer can be simplified. Although there is an extra step involved, it is no more difficult than the previous example we just completed.
Q. 2/8 x 2/4
- Step 1: Again, the first thing you need to do is multiply the numerators together. In order to do this, you need to multiply 2 by 2, which gives you 4.
- Step 2: The next thing you need to do is multiply in denominators. In order to do this, you need to multiply 8 by 4, which gives you 32.
- Step 3: Your answer is 4/32. Although technically this answer is correct, there is a much simpler way in which you can say 4/32. All you need to do is decipher what is the highest number that both of these numbers can be divided by. In this case, 4 is the biggest number they can both be divided by. You therefore divide both the numerator and denominator by 4 to give you the simplified version of this fraction. Your final answer for this multiplication question should be ⅛.
Multiplying fractions with mixed numbers
Multiply fractions with whole numbers and mixed numbers is slightly different. It is important that you know how to complete both types of multiplications as they are both likely to appear in your life at some point.
- Step 1: The first thing you need to do when multiplying any kind of mixed numbers is to turn the mixed number into an improper fraction. In order to do this, you need to multiply the denominator with the whole number and add the numerator. The number that you get will be your new numerator. Your denominator will remain the same as it was when in a mixed number.
- Step 2: The next step is to simplify if possible. This goes across both numbers. Therefore, if you can divide a number in the first fraction and the second fraction by 2, go ahead and divide those two numbers, they do not need to be within the same fraction.
- Step 3: You then need to do as you would a normal problem and multiply the numerators together and the denominators together.
- Step 4: The final step is to simplify the fraction and turn it back into a mixed number if that is possible.
Example of multiplying fractions with mixed numbers
Although it might have been difficult to follow the above instructions, we have this example for you below so you can see these types of problems in action.
Q. 6 ⅔ X 3 3/11
- Step 1: The first thing you need to do is create improper numbers, which is done as follows.
- 6 x 3 + 2 = 20 ——> 20/3
- 11 x 3 + 3 = 36 ——-> 36/11
- Step 2: Next, you simplify the numbers as Both 3 and 36 can be divided by 3, you divide these numbers by three, so your new problems looks like this:
20/1 x 12/11
- Step 3: You then multiply the numerators and denominators together, which gives you:
240/11
- Step 4: Turn the number back into a mixed number. In order to do this, you divide 240 by 11 and the remainder number becomes the numerator. Therefore, your final answer is:
21 9/11
Need help in maths?
Whilst we have covered the basics of multiplying fractions, there is a lot more to learn, such as multiplying fractions with different denominators, multiplying fractions with variables, subtracting fractions and dividing fractions. If you have difficulty with any of these concepts or other concepts related to mathematics, tutoring sessions can help you.
Tutorax offers not only in-person tutoring, but also online tutoring so that you can choose the solution that best adapts to the needs and learning style of your child. Our aim is to provide your child with the capabilities and tools needed to access their full potential and achieve academic success.