Fractions and percentages carry the same meaning. For example, 50% of a number is equal to half of that number; 25% of a number is equal to one-fourth of that number and 20% of a number is equal to one-fifth of that number etc.

PERCENTAGE – RATIO EQUIVALENCE

Sometimes it is better to use equivalent fractions in place of actual percentages. For example, to calculate 14.28% of 343, we should not directly use \(\frac{{14.28 \times 343}}{{100}}\), we can use equivalent fractions of 14.28% i.e. \(\frac{1}{7}\). 

Hence the required answer \( = \frac{1}{7} \times 343\) = 49

Example 1: If 28.57% of a number is 36.4, find the number. 

Solution: As we know that 28.57 % = \(\frac{2}{7}\). 

Hence, \(\frac{2}{7}\,\;{\rm{of}}\,\;x = 36.4\,\,{\rm{or}}\,\,x = \frac{7}{2} \times 36.4\, = 7 \times 18.2\,\) = 127.4

Example 2: 123 is what percent of 391?

Solution: Required percentage \(\frac{{123}}{{391}} \times 100\) by approximation 123 is one third that of 391. So if we increase/decrease the numerator by a number \(x\), then the numerator must be increased or decreased by \(3x\). Let us increase 391 by 9 so that it becomes 400 (a round figure) 

Hence \(\frac{{123}}{{391}} = \frac{{123 + 3}}{{391 + 9}} = \frac{{126}}{{400}} = 0.315\)

This calculation is accurate and the method is very short and quick, first we calculate the approximate ratio of the number then making the denominator a round number, we can decrease 391 to 300 and numerator 123 to (123 – 30) = 93 again \(\frac{{93}}{{300}} = 31\% \)