Question

What is 65 percent of 160?

Answer 1

Hint: First of all understand the meaning of ‘percentage’. Assume that 65 percent of 160 is equal to x. Now, convert 65% into fraction by dividing it with 100 and removing the percentage sign. Take the product of this fraction with 160 and equate it with x to form a linear equation in x. Solve for the value of x to get the answer.

Complete step-by-step solution:
Here we have been asked to find the value of 65 percent of 160. First let us understand the meaning of the term ‘percentage’.
In mathematics, percentage represents a number or ratio as a fraction of 100. For example: if we say 72% of the total number of mangoes in the shop are rotten that means if there are 100 mangoes then 72 of them are rotten and the rest 28 are not rotten. To change a percentage into fraction we divide the given number by 100 and remove the percentage sign.
Now let us come to the question. We have been asked to determine the value of 65% of 160. First we need to change 65% into its fractional form. So removing the percentage sign and dividing with 100 we have,
$\Rightarrow 65\mathrm{\%}={\displaystyle \frac{65}{100}}$
Now the term ‘of’ means multiplication in mathematics, so we have,
$\Rightarrow {\displaystyle \frac{65}{100}}\times 160=x$
Cancelling the common factors we get,
$$\therefore x=104$$
Hence, 65% of 160 is 104.

Note: You must remember the interconversion rules of fractions, decimals and percentages. Note that percentage is dimensionless, i.e. it has no unit and is a pure number. The reason is that it is a ratio of the same quantities having same units which is multiplied with 100. Remember different terms used in mathematics like ‘of’ or ‘times’ means product and ‘by’ means division.