Question

How can you express 45% as a fraction?

Answer 1

Hint:
In this question, we need to express a percentage as a fractional form. Percentage expression tells the ratio out of 100. So, 45% implies 45 parts out of 100. In order to express 45% as a fraction, we need to need to divide the particular percentage by hundred.

Complete step by step solution:
We know that a percentage signifies parts out of hundred. So, we need to express it as a fraction with the percentage value as numerator and the 100 as the denominator. Then we need to simplify the fractional value to the minimum feasible value by expressing the numerator and denominator as the product of its factors and cancelling the common factors.
45% = 45 parts out of 100
So, 45% can be expressed in the form of fraction as:
\[45\% \]= \[\dfrac{{45}}{{100}}\] = \[\dfrac{{5 \times 9}}{{5 \times 20}}\]
Both the numerator and denominator have 5 as the common factor.
 \[45\% \]=\[\dfrac{{\not{5} \times 9}}{{\not{5} \times 20}}\] = \[\dfrac{9}{{20}}\] (dividing the numerator and denominator by 5)
The above obtained fractional value \[\dfrac{9}{{20}}\] can no longer be reduced. So, the fractional value of 45 % is \[\dfrac{9}{{20}}\]. The fractional value \[\dfrac{9}{{20}}\] also signifies the same quantity as 45%.

Hence the fractional representation of 45% is \[\dfrac{9}{{20}}\].

Note:
Any form of percentage can be expressed in the fractional form by dividing it by 100.The obtained fraction may or may not be reduced further. If the fractional value can be reduced it must be reduced to the least fractional value by breaking the numerator and denominator into factors and then cancelling the common factors of both.