Question

There are 90 boys and 70 girls on the school field. How do you write down the ratio of boys to girls in its simplest form?

Answer 1

To write the given data in ratio of number of boys to girls, write the number of number of boys in the numerator of the fraction and number of girls in the denominator of the fraction. And in order to simplify the fraction, find the HCF (Highest Common Factor) between numerator and denominator and then divide both of them with the HCF to get the simplest form.

Complete step by step solution:
In order to write ratio of boys to girls in its simplest form where number of boys is 90 and number of girls is 70, we will first write down the ratio as follows
$90:70$
Now we know that the ratio of two number $a:b$ can be written in fractional form as $\dfrac{a}{b}$
So writing the above ratio in its fractional form as follows
$90:70 = \dfrac{{90}}{{70}}$
Now we will simplify the fraction by finding the highest common factor between numerator and denominator by writing the factors
$90 = 2 \times 3 \times 3 \times 5 \\\ 70 = 2 \times 5 \times 7 \\\$
We can clearly see in the factors of the numerator and denominator that $2 \times 5 = 10$ is the HCF.
Dividing numerator and denominator with $10$
$\dfrac{{90 \div 10}}{{70 \div 10}} = \dfrac{9}{7}$
Now converting fraction into ratio form $\dfrac{9}{7} = 9:7$
$\therefore 9:7$ is the required ratio of boys to girls in its simplest form.

Note: We have converted the ratio into fractional form, so that we can take out their HCF and write them in simplest form as asked in the question. Simplest form of a ratio or a fraction means that the numerator and denominator will no more have any common factors except one.