Question

How do you write \[56\dfrac{1}{4}\% \] as a fraction?

Answer 1

Hint:First we need to observe that in the given problem we have mixed fraction as well a percent. We need to convert the mixed fraction into an improper fraction. Then to remove the percent, we need to divide the obtained improper fraction by 100. After simplifying this we will get the required result.

Complete step by step solution:
Given, \[56\dfrac{1}{4}\% \].

Now we have the mixed fraction, \[56\dfrac{1}{4}\]
\[56\dfrac{1}{4} = \dfrac{{(56 \times 4) + 1}}{4}\]

\[ = \dfrac{{224 + 1}}{4}\]

\[ = \dfrac{{225}}{4}\].

Thus we have an improper fraction \[\dfrac{{225}}{4}\]. We divide this by 100. We get,
\[ = \dfrac{{\left( {\dfrac{{225}}{4}} \right)}}{{100}}\]

Rearranging this we get
\[ = \dfrac{{225}}{{4 \times 100}}\]

Dividing by 25 on the numerator on the denominator we get,
\[ = \dfrac{9}{{4 \times 4}}\]
\[ = \dfrac{9}{{16}}\] is the required fraction.

Additional information:We have a different type of fraction.
 \[ \bullet \]The given fraction is said to be a proper fraction if the numerator is less than the denominator. For example our obtained result \[\dfrac{9}{{16}}\]is a proper fraction.

 \[ \bullet \] The given fraction is said to be an improper fraction if the numerator is greater than the denominator. In the above problem when we convert the mixed fraction we obtained an improper fraction. That is \[\dfrac{{225}}{4}\].

\[ \bullet \] The given two or more fraction is said to be like a fraction if the denominator are the
same. For example \[\dfrac{1}{2},\dfrac{5}{2}\].

Note: If we want to find the percent of a fraction or a decimal we multiply it by 100. If we want to remove the percent we divide it by 100. Mixed fraction is a combination of natural number and fraction. In the given problem we have 56 as the natural number and \[\dfrac{1}{4}\] as a fraction. The obtained fraction is the proper fraction.