Question

Convert each part of the ratio to percentage
a) 3 : 1
b) 2 : 3 : 5
c) 1 : 4

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:
a 🡪 $\left( {\dfrac{a}{{a + b}} \times 100} \right)\% $ or
b 🡪$\left( {\dfrac{b}{{a + b}} \times 100} \right)\% $

Complete step-by-step answer:
a) Given ratio 3 : 1
Total parts = 3 + 1
                     = 4
Percentage of 3 using (1) :
\[\left( {\dfrac{3}{4} \times 100} \right)\% \]
= ( 3 X 25 ) %
= 75 %
Percentage of 1 using (1) :
\[\left( {\dfrac{1}{4} \times 100} \right)\% \]
= ( 1 X 25 ) %
= 25 %

b) Given ratio 2 : 3 : 5
Total parts = 2 + 3 + 5
                     = 10
Percentage of 2 using (1) :
\[\left( {\dfrac{2}{{10}} \times 100} \right)\% \]
= ( 2 X 10 ) %
= 20 %
Percentage of 3 using (1) :
\[\left( {\dfrac{3}{{10}} \times 100} \right)\% \]
= ( 3 X 10 ) %
= 30 %
Percentage of 5 using (1) :
\[\left( {\dfrac{5}{{10}} \times 100} \right)\% \]
= ( 5 X 10 ) %
= 50 %



c) Given ratio 1 : 4
Total parts = 1 + 4
                     = 5
Percentage of 1 using (1) :
\[\left( {\dfrac{1}{5} \times 100} \right)\% \]
= ( 1 X 25 ) %
= 25 %
Percentage of 4 using (1) :
\[\left( {\dfrac{4}{5} \times 100} \right)\% \]
= ( 4 X 20 ) %
= 80 %

Note: 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