Writing a ratio as a percentage without a calculator

In this lesson, we are given a whole and a part of the whole. We are asked to write the ratio of the part to the whole as a percentage. This calculation is to be done without using a calculator.

The solved examples below help us understand the process of writing a ratio as a percentage.

This year, Mario watched 80 movies. He believed 64 of them were very good. Of the movies, he watched, what percentage did he think were very good?

Solution

Step 1:

The total number 80 goes to the bottom of the ratio and 64 goes to the top of the ratio.

So, the ratio of the good movies to total movies is 64:80 or

$\frac{64}{80}$

Step 2:

Using long division, we reduce the ratio to a decimal

$\frac{64}{80} = 0.8$

Step 3:

This decimal is written as a percent by moving the decimal two places to the right and since there is only one digit 8, we use a placeholder 0 to get 80% as the answer.

So, the percentage of good movies was 80%

Gilbert spent $12 on fruit at the grocery store. He spent a total of $60 at the store. What percentage of the total did he spend on fruit?

Solution

Step 1:

The total amount $60 goes to the bottom of the ratio and $12 goes to the top of the ratio.

So, the ratio of the amount spent on fruits and total amount spent is 12:60 or $\frac{12}{60}$

Step 2:

Using long division, we reduce the ratio to a decimal

$\frac{12}{60} = 0.2$

Step 3:

This decimal 0.2 is written as a percent by moving the decimal two places to the right to get 20%.

So, the percentage of amount spent on fruits is 20%