How to multiply fractions?

How to multiply fractions?

Today with the math teacher, you started a new topic: multiplication between fractions and simplification on the cross. You seemed to have understood what the teacher had explained in class, but you realized that you did not know how to carry out the assigned exercises when you returned home. Do not worry. With a bit of effort and ten minutes, you will understand how to multiply fractions and what the simplification is on the cross. In this article, we read about How to multiply fractions?

After learning how multiplications are performed, we will see how the inverse fraction to another fraction is obtained. In this way, you will have all the knowledge to know how to perform a division between fractions and the power of a bit. But let’s go in order.


Let’s start immediately with a numerical example, but first, it is better to make a brief introduction.

The prof will indeed have explained to you that the multiplication sign can be written both with a for (x) and with a dot (•). It would be better to get used to using the drop, and I’ll tell you why. Moving forward, perhaps already at the end of the seventh grade, you will study the equations. In addition to numbers, letters such as a, b, c, x, and y are also used in the equations. So you run the risk of mistaking the letter x for the x sign of the multiplication. For this reason, from now on, to write the character of the expansion, we will use the dot (•), which in our case must be placed at the same height as the fraction line.


Let’s start with the first example.

Looking at the example, you have most likely already got an idea of ​​how to do a multiplication between fractions. To find the numerator, you need to multiply the numerators together. To find the denominator, you need to bear the denominators together.

The operations we are going to perform are:

3 5 = 15 (numerator) and 7 4 = 28 (denominator)

The result we were looking for is 15 out of 28 ( fifteen twenty-eighths ). Since the effect is already reduced to a minimum, we have concluded if you do not remember what it means to reduce a fraction to the minimum terms.


Let’s take another example to see if we can multiply fractions and then correctly state the rule. Also, in this case, the result we have found is a fraction that is already reduced to the minimum terms. So we ended the exercise.

We state the rule correctly:

“The result of multiplication between fractions is a fraction that has the product of the numerators as its numerator and the development of the denominators as its denominator.

This is another way to describe in words what we did with the numbers in our two examples.


Let’s continue with another exercise:

The operations we need to perform are:

To find the numerator 7 · 5 = 35 ;

And to find the denominator 11 · 6 = 66. So our result will be:

As well as for the multiplications between natural numbers. The commutative property also holds for accumulations between fractions. That is, by changing the order of the factors, the product does not vary.

It is not possible to reduce to a minimum. The exercise is over. (Remember that what you are learning in this article will also be helpful to you when studying the power of a fraction .)


Even if the fractions to multiply are more than 2, the procedure is the same. Let’s see an example:

We need to multiply the numerators together:

And then, we multiply the denominators together:

Another way to proceed could be to apply the associative property of multiplication. First, the first two fractions are multiplied together, and then the result obtained is multiplied by the third fraction.

We have to perform a multiplication between two fractions, which we now know how to act.

Numerator by numerator, i.e. 9 7 = 63

Denominator for denominator 10 8 = 80

Of course, it doesn’t matter which procedure you choose to follow. The result must always be the same for both systems.


Let’s continue with another example that will allow us to understand the multiplication between fractions and the simplification on the cross.

To perform this multiplication between fractions, we have two ways:

  1. We can follow the procedure that we have learned to know (numerator by numerator and denominator by the denominator):

At this point, however, we must be careful. We are not done. We must reduce to a minimum. It is possible to use different reduction factors. The final result must still be the same.

But we’re not done yet. It is still possible to simplify.

We’re done now. It is no longer possible to simplify. The result we were looking for is 1 in 10, which can also be read a tenth.

  1. The second way is to simplify on the cross. We have already seen what it means to simplify a fraction. Remember: simplifying a fraction means dividing the numerator and denominator of the fraction by the same number. Cross simplification is a very similar procedure. Only it involves two fractions. Let’s apply the simplification on the cross in the example just performed and try to understand better.

We started with this product:

We need to understand if dividing the numerator of the first fraction (2) and the second fraction’s denominator (4) by the same number. It is possible we can divide them by 2. It is written like this:

Similarly, we must try to understand if it is possible to divide the denominator of the first fraction (15) and the numerator of the second fraction (3) by the same number. The operation is possible. We can divide them by 3. It is written like this:

We can no longer simplify. What we need to do now is multiply the numerator of the first fraction (1) by the numerator of the second fraction (1):

1 1 = 1

And then multiply the denominator of the first fraction (5) by the denominator of the second fraction (2):

5 2 = 10

The result we get is the following:

We got 1 out of 10 (which can be read even a tenth), the same result we obtained with the first method.

I know what you are thinking. You think that you do not like this method of simplification on the cross and that you prefer the first method. It is understandable, but it will be better to know how to apply the simplification in a cross when you multiply four fractions. Otherwise, you will find yourself working with vast numbers. And we don’t like big numbers because they are challenging to manage and handle.

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