Question

How do you express $7\dfrac{3}{4}$ as a percent?

Answer 1

Hint: First, convert the mixed fraction into an improper fraction. Let a fraction be $\dfrac{p}{q}$ where p and q are coprime. If the p, q is not coprime then we have to make them coprime by the elimination of the factors common in both the numerator and denominator. This fraction can be converted into a decimal by making the denominator of the fraction form into multiples of 10. This fraction can be converted into percent form by multiplying its decimal form with 100.

Formula used: When the number is given in fraction, then
Fraction$ \times 100\% $

Complete step-by-step solution:
Now, change the amount from mixed fraction to improper fraction by multiplying the whole number part with the denominator and adding numerator with the resultant,
$ \Rightarrow 7\dfrac{3}{4} = \dfrac{{7 \times 4 + 3}}{4}$
Multiply and add the terms,
$ \Rightarrow 7\dfrac{3}{4} = \dfrac{{31}}{4}$
So, we will start by converting the fraction into a decimal and for this, we will divide the numerator by the denominator, so on applying the above steps we get,
$ \Rightarrow \dfrac{{31}}{4} = 7.75$
Now for getting the percentage we will multiply the decimal by 100 and then we will write the result.
So, on doing the above step, mathematically it can be written as
$ \Rightarrow 7.75 \times 100$
And on solving the multiplication, we will get the value as
$ \Rightarrow 775\% $

Hence, $7\dfrac{3}{4}$ as a percent will be equal to $775\% $.

Note: There is one more formula for finding the percentage and in this, we just need to do the cross multiplication, and on solving it we will get the result. The formula will be
$\dfrac{{{\text{Top of Fraction}}}}{{{\text{Bottom of Fraction}}}} = \dfrac{{{\text{Percent}}}}{{100}}$
And by substituting the values, we will get the equation as
$ \Rightarrow \dfrac{{31}}{4} = \dfrac{{{\text{Percent}}}}{{100}}$
By performing the cross multiplication, the above equation can be written as
$ \Rightarrow 31 \times 100 = {\text{Percent}} \times 4$
Now by taking the constant term to the one side of the equation and solving it we will get the equation as
$ \Rightarrow {\text{Percent}} = \dfrac{{3100}}{4}$
And making the fraction into the simplest form, we get
$ \Rightarrow {\text{Percent}} = 775\% $
Hence, in this way also we can solve this question. Although both are almost the same, yes here we had done the solution directly.