If you want to know how to divide fractions, continue reading this article, but before we get into the subject, let’s talk a little about fractions.
Mathematical operations with fractions come from ancient times, it is believed that they exactly come from the Egyptians, since they used them to solve the different mathematical problems that were presented to them daily; They used mathematical operations for the construction of pyramids, to know how they distributed bread and even to study the earth as a planet.
This has been verifiable thanks to evidence such as the Ahmes papyrus; we can say that the fraction arises as a form of measurement and at the same time of distribution; the Egyptians began with these mathematical operations, but really the Indians (India) exactly in the sixth century AD were the ones who instituted the rules of the different fractions. The laws were established by Aryabhata and later in the 7th century by Bramagupta.
Today’s fractional rules were created in the 9th century by the Mhavira and the 12th century by the Bháskara respectively.
So we see that the fractions, or also called broken, originated a long time ago, even Before Christ, they are very remote. Well, they were already known by the Egyptians, the Babylonians and the Greeks and they arise as a need to be able to measure, count and distribute.
The name of fraction is given because Juan de Luna was the one who was in charge, in the twelfth century, of translating into Latin the book of arithmetic written by “Al-Juarizmi”, because when he made this translation, he used the word Fractio to be able to translate AL -KASR Arabic word that means to break or break, hence many call the fractional numbers broken.
Document – Papyrus of Ahmes
We will talk a little about this document since it contains the first evidence of fractional operations.
This document is written as they did in ancient times on a papyrus, it is exactly 6 meters long and three and three centimeters wide; today it continues to be preserved in good condition; in it we find hieratic writings and, of course, content of a mathematical type; The Ahmes Papyrus is also known as the Rhind Papyrus; the chronology of its content is given from 2000 to 1800 BC; and it was written by a scribe named Ahmes around 1650 BC.
This papyrus was found in the 19th century, in the ruins of one of the buildings in Luxor, it was obtained by Henry Rhind, hence it is also known by this name, it was in the year 1858 AD; and since 1865 it is guarded by the British Museum in London. Currently the document is not exposed to the public.
In its content we find exactly eighty-seven mathematical problems, in which basic arithmetic, area calculations, progressions, rules of three, linear type equations, trigonometry, volumes and of course proportional distribution and fractions are linked.
Division of fractions
Now let’s get into the topic of how to divide fractions; Dividing fractions with each other may seem somewhat complicated, but the reality is that it is not, since it is only a question of inverting each fraction, then multiplying and finally simplifying; Continue reading this guide so that you know how to do the process, you will see that it is not difficult at all. There is also the method of multiplying in the form of a cross.
Dividing fractions by cross multiplying
This method is very simple, all you have to do is look at the numerator of the first fraction you have and multiply it by the denominator of the other fraction, so you will have the new denominator, then look at the numerator of the second fraction and multiply it by the denominator of the first fraction and in this way you will have a new denominator, look at the image that we have below.
If we have 4/5 ÷ 5/3 we will have to multiply the nominator 4 of the first fraction by the denominator of the second fraction 3 and we would obtain the numerator 12, 4×3 =12, thus 12 would be the new nominator, then we have multiply the denominator of the first fraction, the number 5, by the denominator of the second fraction, the number five, to thus obtain the new denominator 5×5=25, then the result would be 12/25; Since we don’t have a greatest common factor that we can divide by the two returned numbers, we don’t simplify and leave the result as is.
let’s look at the illustration
Dividing Fractions by Reversing
Another method that we have to be able to divide fractions is to invert the fraction and then multiply; To do this, the first thing you should do is invert the second fraction, so if your second fraction is 4/3, change it to ¾; change the numerator you have for the denominator; once you do this you must multiply but in line, as in the example below.
- So you should leave the first fraction as it is
- Then you must change the division sign to the multiplication sign.
- The second fraction must be inverted by changing the nominator for the denominator, this is called finding the reciprocal.
- Then multiply the numerators that you have left, that is, the numbers that are above in each fraction, in this way you will obtain the nominator of the result.
- Then multiply the remaining denominators, that is, the numbers below the fractions, and thus you will obtain the denominator of the result.
- You will need to simplify the fraction.
let’s look at the illustration
Let’s look at the following example
- 3/4÷ 2/5, you must leave the first fraction as it is, that is, the ¾.
- Then you must change the division sign to the multiplication sign, so 3/4÷ 2/5 must be transformed into ¾ x.
- Later you will have to invert the second fraction to find what we call reciprocal, thus 2/5 remains in 5/2 and thus you must remain with this equation, ¾ x 5/2.
- Next, you multiply the numerators, the numbers that are above, that is, 3 and 5 to obtain the result of 15, which becomes the new nominator (3 x 5 = 15).
- Then you multiply the denominators, that is, the numbers that are below, which are 4 and 2, in order to obtain the new denominator, which would be the number 8 (4 x 2 = 8).
- In this way we obtain that the result of the division of this fraction is 15/8, since we do not have a natural number divisible by the two numbers, this would be a final result.
Note to keep in mind when dividing fractions.
Let’s remember a bit about how to reduce fractions, although we believe that if you are already looking for how to divide them, it is because you already know how to do this.
What you have to do is list the factors of both the numerator and the denominator; the factors are those numbers that when we multiply them together we obtain another number, then the factors are all the numbers that when we multiply them we can obtain the number we need, both from the nominator and from the denominator and that when divided gives an integer.
Start making your list of numbers from least to greatest, you must include the number 1 and the number you want to factor. So for example, let’s list this fraction 30/15
30: 1, 2, 3, 5, 6, 10, 15, 30
10:1, 2, 5, 10
To simplify this then we would have to find the GCD which is the greatest common divisor, that is, the largest number by which both fractions can be divided in this case would be 5, then the simplification of the fraction 30/10 would be 6/2.