Question

How do you write 282% as a fraction, mixed number, or whole number in simplest form?

Answer 1

Hint: Here, in this question we are given the number in percent. We need to find the fraction of that number. So we will convert percent into fraction by removing the % sign. After that, we will change the number into mixed form from the improper form. Now we will reduce it into the simplest form. After that, we will change the number into mixed form from the improper form.

Complete step by step answer:
Let’s solve the question now.
As we know that there are 3 forms in which fractions can be written: proper, improper and mixed. In proper fraction, the numerator is smaller than the denominator. For example: $\dfrac{21}{235},\dfrac{12}{27}$ etc. is improper, the numerators are greater than the denominator. For example: $\dfrac{23}{5},\dfrac{45}{14}$ etc. And the last one is mixed which is totally different from improper and proper fraction. It is represented by a whole number and a fraction. They are represented together but are not in multiplication. For example: In $2\dfrac{3}{5}$, 2 is a whole number whereas $\dfrac{3}{5}$ is a fractional part.
As per question, we are given 282%. If we remove the % sign, the 100 will be placed in the denominator. So it will be converted into fraction:
$\Rightarrow 282\%\Leftrightarrow \dfrac{282}{100}$
First step is done. Second is to reduce into the simplest form. Divide both numerator and denominator by the lowest common factor i.e. 2:
$\Rightarrow \dfrac{141}{50}$
Further, it cannot be reduced because there are no common factors left for 141 and 50. So this will be the reduced form. Now we will be moving on the mixed form. As the fraction is in improper form, we will divide 141 by 50 to convert it in mixed form. The quotient will become the whole number and the fractional part will be $\dfrac{remainder}{divisor}$.
$50\overset{2}{\overline{\left){\begin{align}
  & 141 \\
 & 100 \\
 & \overline{041} \\
\end{align}}\right.}}$
So the mixed form will be: $2\dfrac{41}{50}$.
The whole number will be 2 and the fractional part will be $\dfrac{41}{50}$.

Note: We learnt how to convert the improper form into mixed form but you also need to know how a fraction can be converted from mixed to improper form. For this conversion, let’s take an example like if we want to convert $3\dfrac{4}{5}$ into improper, then first multiply 3 by 5 then the result of this multiplication will be added to the numerator. So it will be: $3\times 5+4=19$. So the fraction will be $\dfrac{19}{5}$.