Question

How do you write $275\mathrm{\%}$ into fractions?

Answer 1

Hint: Here, we are required to write the given percentage into fractions. Thus, we will use the steps of conversion and simply write the percentage sign as a fraction. Then, we will divide the numerator and the denominator by their highest common factor such that we get the simplest form of the fraction. We will find that the fraction is an improper fraction thus, we can express the given percentage either as an improper fraction or mixed fraction. Thus, this will be our required answer.

Complete step-by-step answer:
In order to answer this question, we should know what a percentage is.
‘Percentage’ means ‘per 100’ or we can say that percentage is that number which can be expressed as a fraction of 100 or by just using the $\mathrm{\%}$ sign.
Now, in this question, it is asked to convert $275\mathrm{\%}$ into fractions
We can write the percentage sign, i.e. $\mathrm{\%}$ as ${\displaystyle \frac{1}{100}}$.
Hence, we will write $275\mathrm{\%}$ as:
$275\mathrm{\%}={\displaystyle \frac{275}{100}}$
Now, since we are required to convert this fraction in the simplest possible form.
Thus, we will try to reduce this by the HCF of the numerator and the denominator.
Now, we can write:
$275=5\times 5\times 11$
$100=5\times 5\times 4$
Therefore, clearly the highest common factor, HCF of 275 and 100 is $5\times 5=25$
Hence, we will divide the numerator and denominator by 25.
$\Rightarrow 275\mathrm{\%}={\displaystyle \frac{{\displaystyle \frac{275}{25}}}{{\displaystyle \frac{100}{25}}}}={\displaystyle \frac{11}{4}}$
As we can see, the numerator is greater than the denominator; hence, this is an improper fraction.
Now, we can express this improper fraction as a mixed fraction.
$\Rightarrow 275\mathrm{\%}={\displaystyle \frac{11}{4}}=2{\displaystyle \frac{3}{4}}$

Hence, we can write $275\mathrm{\%}$ into fractions as ${\displaystyle \frac{11}{4}}$ or $2{\displaystyle \frac{3}{4}}$.

Therefore, this is the required answer.

Note: A mixed fraction is a number that contains both the whole number and the proper fraction; whereas an improper fraction is a fraction where the numerator is greater than the denominator hence, it is called an ‘improper’ fraction. When we convert a mixed fraction into an improper fraction or vice-versa, their values remain the same and only the way of writing those numbers is different.