Question

Convert the following ratio into percentage: ${\displaystyle \frac{22}{30}}$?

Answer 1

Hint: In this question, we have to convert the given ratio into percentage. To convert into percent, the ratio will be multiplied by 100%. Before that, this ratio has to be reduced in the simplest form. The ratio is already given in the form of a fraction.

Complete step by step solution:
Now, let’s begin to solve the question.
Ratio is the value which can be written with the symbol ‘:’ or can be denoted in the form of a fraction. For example: if we are given 4:3, it can also be expressed as ${\displaystyle \frac{4}{3}}$. Here also in the given question, ${\displaystyle \frac{22}{30}}$
Is not only the ratio but can also be called as a fraction. We have to convert the given ratio in to percentage. For that, we have to multiply the given ratio with ${\displaystyle \frac{100}{100}}$. 100 in the denominator is used to express a percentage with a % symbol. That means we have to multiply the given ratio with 100%. The result we obtain will also be expressed with this symbol.
$\Rightarrow {\displaystyle \frac{22}{30}}\times 100\mathrm{\%}$
Now, the next step is to reduce the terms and obtain the value in the simplest form. First cancel the zero from numerator and denominator:
$\Rightarrow {\displaystyle \frac{22}{3}}\times 10\mathrm{\%}$
As we can see, the terms will not get reduced anymore, so we will multiply and divide with 3:
$\Rightarrow {\displaystyle \frac{220\mathrm{\%}}{3}}$
$3\stackrel{73.3}{\overline{)\begin{array}{rl}& 220\\ & 21\\ & \stackrel{―}{010}\\ & 9\\ & \stackrel{―}{10}\\ & 9\\ & \stackrel{―}{1}\end{array}}}$
So the answer will be 73.3%.

Note: We used long division above for dividing the terms. If we are expressing any number in the form of a percentage, then the% symbol has to be written with it otherwise you will not get any marks. We haven’t reduced ${\displaystyle \frac{22}{30}}$ above before multiplying it with 100% because it would have increased the calculations. To make calculations easy, the above steps are performed.