THE fraction division, although it seems to be a complicated operation, it is something very simple to solve. It is important to remember that, to solve this operation, it is necessary that we remember how the fraction multiplication.
Read too: Addition and subtraction of fractions
Here, we will dedicate ourselves to explaining step by step how to make a division between two or more fractions. Also, let's understand from graphics the fraction division algorithm.
How to do a fraction division
In order to perform the operation of dividing fractions, it is necessary to understand the operation of multiplication between fractions. To multiply two or more fractions, just multiply numerator with numerator and then denominator with denominator. See the following example:
Now we need to understand the idea of dividing a fraction and a integer. To do this, we will show you how to graph a fraction.
Our goal is to divide the fraction ½ by 4. We know that a half represents something whole divided into two parts, that is, each part will be 1 divided by 2, so:
Note that we try to divide each of the 2 parts (½) into 4 parts. Note that if we look at the number of parts formed in relation to the entire rectangle, we will have 8 parts, so each part will be represented by 1/8. Look the following picture:
So the result of dividing 1/2 by 4 is equal to a 1/8.
See that when we split the rectangle that was divided into 2 parts into 4, that is, we divide the fraction 1/2 by 4, we get the 1/8 fraction. Therefore, performing this division operation is the same as performing the following multiplication:
In order to facilitate the calculation of fraction division, we can adopt this idea by making the following generalization:
To divide between fractions, just keep the first fraction and multiply it by the inverse of the second.
Example:
a) Let's divide the 2/3 fraction by the 5/6 fraction:
b) Determine the quotient between the numbers one hundredth and one thousandth.
How to represent a division of fractions
We can represent the division of fractions in two ways.
The first and most common way is:
We can represent a division of fractions also in the following way:
Read too: Problems involving fractional numbers
solved exercises
question 1 - Determine the result of the following division:
Solution:
According to the algorithm, we should keep the first fraction and multiply by the inverse of the second fraction, like this:
question 2 – Graphically represent the following division:
Solution:
To perform the graphical representation of this division of fractions, we must represent the fraction 1/8 and count how many parts gave in relation to the fraction one ½. Look:
Notice that when we look at fraction a 1/8 in relation to fraction a ½, we have 4 parts of a 1/8 within a 1/2. Thus,
by Robson Luiz
Maths teacher
Source: Brazil School - https://brasilescola.uol.com.br/matematica/divisao-com-fracoes.htm