Question

What percent of 180 is 45?

Answer 1

Hint: Assume that x percent of 180 is 45. Now, convert x percent into fraction by dividing x with 100. Multiply this obtained fraction with 180 and equate it with 45. Form a linear equation in x and solve it for the value of x to get the answer.

Complete step by step answer:
Here we have been provided with two numbers: 180 and 45 and we are asked to determine a percentage of 180 that will make 45. But first we need to understand the meaning of the term percentage.
In mathematics, percentage represents a number or ratio as a fraction of 100. For example: if we write 60% then we mean 60 parts of something in its 100 parts. To change a percentage into fraction we divide the given percentage by 100 and remove the percentage sign.
Now let us come to the question. We are asked to determine the percentage of 180 that will be equal to 45. So, let us assume $x\mathrm{\%}$ of 180 is 45. Here $x\mathrm{\%}$ means x parts in a total of 100 parts. So, converting $x\mathrm{\%}$ into fraction we get,
$\Rightarrow x\mathrm{\%}={\displaystyle \frac{x}{100}}$
According to the question we must have,
$\Rightarrow {\displaystyle \frac{x}{100}}\times 180=45$
Solving the above equation for the value of x we get,
$$\Rightarrow x={\displaystyle \frac{45\times 100}{180}}$$
Cancelling the common factors and simplifying the relation we get,
$$\therefore x=25$$

Hence, 25% of 180 is 45.

Note: You must remember the basic definition of percentage to solve the above question. Note that if we have to convert a decimal or fraction into the percentage then we multiply it with 100 and include a percentage sign. Since percentage is a fraction multiplied with 100, so it is dimensionless in nature. It means percentage has no units and is a pure number.