Question

How do you convert ratio $3:1$ to a percentage?

Answer 1

Hint: Percentage of each part of ratio can be calculated by dividing each part by the total parts multiplied by 100. If $a:b$ is the ratio parts then their percentage is given as
Total parts $ = a + b$, and for each part:
$\left( {\dfrac{a}{{a + b}} \times 100} \right)\% {\text{ }}......{\text{(i)}}$
or $\left( {\dfrac{b}{{a + b}} \times 100} \right)\% {\text{ }}......{\text{(ii)}}$

Complete step by step solution:
Given ratio $3:1$
Total parts $ = 3 + 1 = 4$
Percentage of 3 using (i):
$\left( {\dfrac{3}{4} \times 100} \right)\% $
$ = \left( {3 \times 25} \right)\% $
$ = 75\% $
Percentage of 1 using (ii):
$\left( {\dfrac{1}{4} \times 100} \right)\% $
$ = \left( {1 \times 25} \right)\% $
$ = 25\% $
Final solution: Hence, the ratio $3:1$ to a percentage is $75\% :25\% $.

Note:
i. The ratio is first converted to fraction and the fraction is then converted to percentage by multiplying with 100. Percentage is used to compare various quantities and in literal terms it means per 100.
ii. Ratio: If the values of two quantities A and B are $4$ and $6$ respectively, then we say that they are in the ratio $4:6$ (read as “four is to six”). Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part or parts, one quantity is of the other. The ratio of two quantities “$a$” and “$b$” is represented as $a:b$ and is read as “$a$ is to $b$”. Here, “$a$” is called antecedent, “$b$” is the consequent. Since the ratio expresses the number of times one quantity contains the other, it’s an abstract quantity.
iii. Percentage: “Percent” implies “for every hundred”. This concept is developed to make the comparison of fractions easier by equalising the denominators of all fractions to hundred.
Percentage can also be represented as decimal fractions. In such a case it is effectively equivalent to the proportion of the original quantity.