Question

Reduce to standard form: $\dfrac{{36}}{{ - 24}}$ .

Answer 1

Hint: In this question we have to write the given fraction in to its simplest form. So first we will find the HCF of the given number. After that we will divide the common factor in the numerator and denominator. This kind of dividing process is also called reducing the terms by common factors.

Complete step-by-step solution:
Here we have been given the fraction $\dfrac{{36}}{{ - 24}}$ .
As we know that a factor is a number that divides the given number without any number or we can say that it is the divisor of the number. For example, the factors of $8$are $1,8,2,4$ .
This number completely divides the number $8$ .
So we will first write down all the factors of the numerator and denominator of the fraction. After that we will find the HCF of both these numbers.
So the factors of $36$ are
$1,2,3,4,6,9,12,36$
Now the factors of $24$ are
$1,2,3,4,6,12,24$
So the highest factors in both the numbers is
$12$ .
Now we will divide the numerator and denominator by $12$ to get the standard form i.e.
$\dfrac{{\dfrac{{36}}{{12}}}}{{\dfrac{{ - 24}}{{12}}}}$
It gives us value $\dfrac{3}{{ - 2}}$ .
Hence the required answer is $\dfrac{{ - 3}}{2}$ .

Note: We can check if the fraction is in simplest form or not i.e. there is only one factor that is common between the numerator and denominator which is $1$ . We should note that the simplest form means that the fraction or ratio is not divisible further. We can also write the above fraction in decimal and percentage.
The decimal form of $\dfrac{{ - 3}}{2}$ is
 $ - 1.5$
and the percentage form of $\dfrac{{ - 3}}{2}$ is $ - 150\% $.