If you have wondered how to multiply fractions, we tell you that it is an extremely simple procedure, it only takes a few steps that we will talk about later; Let’s first look a little bit about fractions as such.
History of Fractional Numbers
As is known, the first numbers they built were those that we call natural, those that are used to count quantities, which, as the name itself says, are natural, by nature, for example: twenty people, five horses, three houses, thirty pencils, two butterflies, forty bells, three mules, five dolls, among others; this then served the ancients to count the cattle they owned, the members that made up the family and of course for the goods they had and exchanged.
As time went by, they realized that not only the natural numbers were needed but also something else, for example there was half an orange, a quarter of an apple or a pumpkin and a half, and in this way the rationals arose. The Egyptians and the Mesopotamians already worked and used some simple fractions such as 1/5, 1/3, 1/2, among others, they generally had the number ONE as the denominator and very occasionally they used others such as 2/5, but the most common was the formula 1/x.
Thus, then, we can say that apparently the Egyptians were the ones who made use of fractions for the first time, of course they were only those of the form known as 1/x, that is, the one obtained as a combination of themselves, which means that the Egyptians used the fractions that had the number ONE as the numerator and the numbers TWO, THREE, FOUR, FIVE as the denominator, although sometimes they did use fractions such as ¾ or 2/3, but it was not common, thus achieving be able to do various fractional calculations.
We can say that in the Moscow and Rhind papyri, as well as in the rosette stone, we find fractional records, these may be one of the oldest, or it is thought that even the oldest; both are from the Egyptians and their culture.
So the ancients worked with rationales that were really fractional, since as its name indicates, the fractional ones help us to understand the fractionalizations of some object which is known. Well, the work as such of the rationals, as we have been explained from the formula a/b where a and b come to be natural and b comes to be different from zero; It was given to this culture much later, around the year 1500.
The Babylonians, for their part, also developed a fairly efficient system of fractional notations, which allowed them to establish approximations of the decimal type, which were truly surprising. The evolution and simplification of the method used in the fractions allowed the origin of new mathematical operations, which helped the same mathematics that would come later (centuries later) and its community, because thanks to this excellent calculations could already be made between the which we find, for example, a square root.
For the Babylonians it was somewhat easy to get their approximations that turned out to be quite accurate; for in their calculations they proceeded to use fractional notations; this civilization had the best notation for fractions until the renaissance came along.
Ancient China must also be highlighted here, because that fact occurred right there where it is already required that in a division of fractions there be a reduction of these to a common denominator.
The ancient Chinese knew quite well the different operations of ordinary fractions, reaching the point that they could, in this context, perfectly find what we know as the lowest common denominator of fractions; These in turn adopted some tricks with decimals in order to speed up the process of fractions and their manipulation a little.
The Greeks were not left behind either and we must also mention them, since they stood out widely in geometry and in constructions that used it, in the latter they represented their lengths with rational numbers.
Concept of a fraction
If we already want to know what the concept of a fraction is, it is the one that gives us an idea that is intuitive, that helps us to divide the totality of something into completely equal parts; For example, when we talk about the time, we are talking about fractions, look what we say, an hour and a quarter or a quarter of an hour, half an hour, among others; We can say that we have eaten half of a cake, or we are going to add gasoline and we only want to fill up to half the tank. Since you may be wondering, if the ¾ of an hour is not the same as the ¾ of a cake, but its calculation is the same, then what we do is divide the totality of either an hour or a cake in 4 exactly equal parts and then taking 3 of those parts.
The fraction is represented mathematically speaking, by some numbers that are written on others, and these are separated by a horizontal line that receives the name of fraction or fractional line, the number above the line is called the numerator and the one below denominator.
How to multiply fractions?
Now let’s look at how fractional numbers are multiplied.
Step one
Multiply the two numbers above, these are called nominators.
step two
Multiply the two numbers below, these are called denominators.
Step three
Simplify the number you have left.
Let’s look at an example
When you start to write the fractions math problem you should see that the numerators are well aligned with their respective denominators, as we show in the following images.
Step one
We will multiply the numbers above, the nominators
4/5 X 5/3 = 4 X 5 = 20 then we have that 20 is the nominator that gives us the result.
In this case, the numerators are 4 and 5, which is why they are the ones you must multiply to then obtain the result of 20.
Let’s look at the illustration below
S=tep two
4/5 X 5/3 = 5 X 3 =15, then we have that 15 is the denominator that gives us the result
The denominators in this case are 5 and 3, so they are the ones you must multiply to obtain the number 15.
As in the following illustration
Step three
So we have a result like this 20/15, that is, it has given us a nominator and a new denominator.
Step four
We already have a result but this does not end here, at this point we need to simplify it, for that we must find something called GCD which has the meaning of Greatest Common Division that occurs between the numerator and the denominator; For this we look for the largest number by which each one can be divided, so then if we have the number 20 and we have 5 we would apply dividing it by 5, since we can divide 10 by 5 which will give us 4 and we can divide 15 by 5 which will give us 3, note that it cannot be divided by 2 because it would give us a decimal number in 15, nor by 3 because the same would happen in 20, by 4 it would happen in 15, but by 5 we get the result both the nominator and the denominator in natural numbers. So we have that the GCD of the nominator 20 and of the nominator 15 is the number 5 and when we simplify the fraction we should have 4/3 and that’s it, so you get the result of a multiplication of fractions.
In simpler words, before simplifying you must divide both the numerator and the denominator by a whole number, and it must be the largest possible in both.
Another method to multiply fractions
There is another method that consists of simplifying before we do the respective multiplication.
Step one
Likewise, the numerator must be aligned with the denominator.
step two
You will have to simplify the first fraction in the same way that we taught before, looking for the largest number by which the numerator and denominator can be divided.
Step three
Take the second fraction and do the same, simplify it by finding the largest number by which you can divide both the numerator and denominator.
Step four
Multiply the numbers that you have left after simplifying the fraction you want to multiply, as we had already taught the numerators and then the denominators, and thus you will obtain the answer; Since you simplified before multiplying, you will not have to do it with the result returned, but that will be the end; You should still review the result because if it can be simplified you should do so.
Notes to keep in mind when multiplying fractions.
- We recommend the first method, it is easier
- Simplified fractions must continue simplifying until they reach a fraction that is already irreducible, that is, it cannot be simplified.
- If you are going to multiply a fraction by a whole number, you must take the latter as the nominator and put the number 1 as the denominator, and you can now do the multiplication just as we teach you in this article.