Question

Express $7\dfrac{3}{4}$ as a percent?

Answer 1

Hint: First of all this is a very simple and a very easy problem. This problem deals with calculating the percentages of the given expression. In mathematics, a percentage is a number or a ratio that represents a fraction of 100. It is a dimensionless number. It is a pure number. It has no unit of measurement. One percent is one hundredth of a whole. It can be written as both decimal and a fraction.

Complete step by step solution:
Here the given expression is a mixed fraction which is $7\dfrac{3}{4}$.
Now we have to convert the mixed fraction into an improper fraction which is as shown below:
$ \Rightarrow 7\dfrac{3}{4} = \dfrac{{28 + 3}}{4}$
$\therefore 7\dfrac{3}{4} = \dfrac{{31}}{4}$
We know that the percentages are the values given out of 100.
So in order to find an equivalent fraction with a denominator of 100, as shown below:
So multiply and divide the fraction with 25.
$ \Rightarrow \dfrac{{25 \times 31}}{{25 \times 4}} = \dfrac{{775}}{{100}}$
Here the above obtained expression is a percent.
$ \Rightarrow \dfrac{{775}}{{100}} = 775\% $
Hence the value of the fraction is equal to $775\%$
$\therefore 7\dfrac{3}{4} = 775\% $

Note: Here while solving the whole problem we should understand that whenever we are given a percentage of any number, then we just divide the number by 100. Even when the given percentage is more than 100, we just divide the number by 100. Here given $x\% $, then the value of the given expression is given by : $x\% = \dfrac{x}{{100}}$.