Question

The ratio 5:4 expressed as percent equals:
(a) 12.5 %
(b) 40 %
(c) 80 %
(d) 125 %

Answer 1

Hint: Consider the ratio given in the question. Convert it into a fraction that is \[a:b=\dfrac{a}{b}\]. Now convert this fraction in percent, multiply it by 100 and simplify it and use % sign in it to get the required answer.

Complete step-by-step answer:
In this question, we have to convert 5 : 4 into a percentage. Before proceeding with this question, let us see what percent means in Mathematics. Basically, Percent implies for every hundred or it is a number or ratio expressed as a fraction of 100 and the sign % is read as a percentage and x % is read as x percent. In other words, a fraction with denominator 100 is called a percent. For example, 20 % means \[\dfrac{20}{100}\] (i.e. 20 parts from 100). This can also be written as 0.2. Conversely, 0.2 or \[\dfrac{2}{10}\] means \[0.2\times 100=20\]%.
To convert a fraction or decimal to a percentage, multiply by 100 that is,
Percentage % = (Fraction) \[\times \]100
Now, let us consider our question. Here, we have to convert the ratio of 5:4 into percent. We know to convert a ratio or fraction into a percentage, we need to multiply it by 100, so we get,
\[\text{Percent}=\left[ \left( \text{Fraction} \right)\times 100 \right]\text{ }\!\!\%\!\!\text{ }\]
We know that,
\[5:4=\dfrac{5}{4}\]
So, by substituting the value of the fraction as \[\dfrac{5}{4}\] as given in the question in the above equation, we get,
\[\begin{align}
  & \text{Percent}=\dfrac{5}{4}\times 100\text{ }\!\!\%\!\!\text{ } \\
 & \text{Percent}=\dfrac{500}{4}\text{ }\!\!\%\!\!\text{ } \\
 & \text{Percent}=125\text{ }\!\!\%\!\!\text{ } \\
\end{align}\]
So, we can express 5 : 4 as 125 %.

Note: In this question, many students get confused about whether they should multiply the fraction by 100 or divide the fraction by 100. So, they must note that if we have to convert the fraction into percent, we have to multiply the fraction by 100 and if we have to convert the percent into a fraction, we have to divide the percent by 100. Also, students must understand the physical significance of percentage as it is widely used in many areas. For example, discounts in shops, bank interest rates, and almost all financial aspects of everyday life use percentages in them.