Question

Convert the following ratios to percentages.
(i) \[3:4\]
(ii) \[2:3\]

Answer 1

Hint: First rewrite the ratio into fraction .Once we have rewritten it then round the percentage which we get after multiplying fraction from the ratio with 100.

Formula Used:
\[\dfrac{x}{y}*100{\rm{ }}\% \]

Complete step-by-step answer:
Let’s start with part 1 \[3:4\]
\[3:4\] Means we are dividing 3 with 4 which means Here 3 is numerator and 4 is denominator.
So, we can write it as \[\dfrac{3}{4}\] , so that we can easily write and use it further.
Multiply ratio \[\dfrac{3}{4}\] with 100 to get the percentage of this ratio.
\[\dfrac{3}{4}*100\]
As 3 is not divisible by 4 so divide 100 by 4 and then solve to get a percentage.
\[3*\dfrac{{100}}{4}\]
After dividing 100 by 4. Result is 25, now multiplying that with 3
\[3*25\]
Which is 75 percent.
\[\Rightarrow \dfrac{3}{4}*100 = 3*25 = 75\]
Hence, \[3:4\] is equal to 75 percent.
\[\Rightarrow 3:4 = 75\% \]
Let’s start with part 1 \[2:3\]
\[2:3\] Means we are dividing 3 with 4 which means Here 2 is numerator and 3 is denominator.
So, we can write it as \[\dfrac{2}{3}\] , so that we can easily write and use it further.

Multiply ratio \[\dfrac{2}{3}\] with 100 to get the percentage of this ratio.
\[\dfrac{2}{3}*100\]
As 2 is not divisible by 3 so divide 100 by 3 for easier calculations.
\[2*\dfrac{{100}}{3}\]
After dividing 100 by 3. Result is 33.33, now multiplying that with 2
\[2*33.33\]
Which is 66.66 .
\[\Rightarrow \dfrac{2}{3}*100 = 2*33.33 = 66.66\% \]
Hence, \[3:4\] is equal to 66.66 percent.
\[\Rightarrow 2:3 = 66.66\% \]


Additional Information: For easier calculations we should always divide denominators with 100, it will make dividing easy for us as 100 is divisible by many numbers.

Note: Writing ratio as fraction helps us with dividing and multiplying. Once the fraction is multiplied by 100 we will get the exact percentage of that ratio.