Question

The value of $ \dfrac{5}{{20}} $ of $ 100 $ is equal to:

Answer 1

Hint: “Of” means “a part of”. Means you have to calculate the $ \left( {\dfrac{5}{{20}}} \right)th $ part of $ 100 $ . “Of” represents multiplication in mathematics. So, multiply $ \dfrac{5}{{20}} $ with $ 100 $ to get the answer. While multiplying them, keep in mind, the rules of multiplying a fraction with an integer.

Complete step-by-step answer:
We can use the same concept in percentage as well. For example, $ 20\% $ of $ 50 $ can be written as $ \dfrac{{20}}{{100}} \times 50 $
In this question, we need to know that “Of” is multiplication. You might get confused as why would “Of” represent multiplication when we already have a symbol to represent multiplication? The answer for this question is, though mathematically, “Of” represents multiplication. But in theory, it represents a part of a given number. For example, “ $ n $ of $ B $ ” means $ {n^{th}} $ part of $ B $ . In the operations with more than one symbol, “Of” is given the first priority. Then brackets. Then division, multiplication and so on.
“Of” represents multiplication in mathematics. So we can write,
 $ \Rightarrow \dfrac{5}{{20}} $ of $ 100 = \dfrac{5}{{20}} \times 100 $
 $ \dfrac{5}{{20}} \times 5 \times 20 $
By cancelling the common terms, we can write
 $ = 5 \times 5 $
 $ = 25 $
Therefore, $ \dfrac{5}{{20}} $ of $ 100 $ is equal to $ 25 $

Note: If we know that $ \dfrac{5}{{20}} $ of $ 100 $ represents $ \left( {\dfrac{5}{{20}}} \right)th $ part of $ 100 $ , then this question becomes very easy. The alternate method to solve this question will be. We know that, $ \dfrac{5}{{20}} = \dfrac{1}{4} $ . So $ \left( {\dfrac{5}{{20}}} \right)th $ part of $ 100 $ is actually the $ \left( {\dfrac{1}{4}} \right)th $ part of $ 100 $ . And we know that $ 100 $ can be separated into 4 parts of 25 each. Therefore, without making any difficult calculations, we can write $ \dfrac{5}{{20}} $ of $ 100 = 25 $ .