Question

There are 20 girls and 15 boys in a class. What is the ratio of the number of girls to the number of boys?

Answer 1

Hint: Here, we will divide the number of girls with the number of boys. Then we will convert the obtained fraction in the simplest form that the fraction could be in to find the required ratio.

Complete step-by-step answer:
We are given that the number of boys is 15 and the number of girls are 20.
We know that the ratio is computed by dividing the number of girls with the number of boys.
Using the above values to find the ratio, we get
\[ \Rightarrow \dfrac{{20}}{{15}}\]
But we know that the above fraction is not in the simplest form that the fraction could be in.
Dividing the numerator and denominator with 5 of the above fraction, we get
\[
   \Rightarrow \dfrac{{20 \div 5}}{{15 \div 5}} \\
   \Rightarrow \dfrac{4}{3} \\
 \]
Since the numerator is 4 and denominator is 3, the above fraction cannot be simplified further.
Therefore, the answer in its simplest form is \[4:3\].

Note: We know that a rational number is a number that can expressed as the quotient or fraction of two integers, that is, \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q\] is not equal to zero. We need to know that the rational numbers are closed under addition, multiplication and division, but not closed under subtraction. So we can divide the numerator and denominator by the same number and it won’t affect the fraction. We will not divide the numerator and denominator with different numbers as it will lead to wrong answers.