# Form 1 Unit 5 Lesson 3 – Converting Percentages To Fractions And Vise Versa

Objective:

At the end of this lesson, the students should be able to convert percentages to fractions and fractions to percentages.

Converting Percentages to Fractions

Here, you use the fact that “percent” means “out of a hundred”.

To convert a percentage to a fraction, follow these steps:

Step 1:  Write down the percentage.

Step 2: If the percentage is not a whole number, then multiply both numerator and denominator by 10 for every number after the decimal point or convert the percent to a decimal and then to a fraction

Step 3: Simplify (or reduce) the fraction.

For instance:

40% = 0.40 = 40/100
Now you can reduce the fraction to its simplest form.

40/100 = 4/10 = 2/5

Most conversions are simple like this, but some require a little extra care. The reason I converted to a decimal first is that the number of decimal places tells me how many zeroes to have underneath. Notice that “0.40” can also be written as “0.4”. Then 0.4 = 4/10 = 2/5, which is the same answer as above. It works out because “0.4” has one decimal place and “10” has one zero. This concept (matching the number of decimal places with the number of zeroes) helps in more complicated problems

Example 1

Change the percentages to fractions.

a) 104%         b) 0.5%

Solution
(Note: 100% = 1, 104% is greater than 1)

Example 2

Change these percentages to fractions.

Solution

Converting Fractions to Percentages

It is easy to convert a fraction to a percentage when the denominator is 100. If a fraction does not have a denominator of 100, in some cases, you can easily convert it to its equivalent fraction with a denominator of 100, and then write the equivalent fraction as a percentage.

In a case where you cannot easily convert the fraction to its equivalent fraction with a denominator of 100, simply multiply the fraction by 100%

Steps to follow:

• Find a number that multiplies the denominator of the fraction to make 100.
• Multiply both numerator and denominator of the fraction by that number.
• Write only the top number with the “%” sign.

Example 1

Convert 3/4 to a percentage.

Solution

• We can multiply 4 by 25 to make 100 (why 25? because 25x 4 is 100)
• Multiply top and bottom by 25.

• Write down 75 with the percent sign:

Note: 16 is not a factor of 100. Simply multiply 3/16 by 100% to change it into percentage.

Method 1

Method 2

Change 3/16  into a decimal using long division, and then multiply by 100%.

3/16 = 3 ÷ 16 =

0.1875 × 100% = 18.75%

Example 3

Last marking period, 15 out of every 100 students in Ms. Jones class achieved a grade A and 3 out of every 20 students in Mr. McNeil’s class achieved a grade A. What percentage of each teacher’s students got an A?

Solution

15% of the students in both classes achieved grade A.

Example 4

One team won 19 out of every 20 games played, and a second team won 7 out of every 8 games played. Which team has a higher percentage of wins?

Solution

Team 1 has a higher percentage of wins.

In example 1 above, we used equivalent fractions to help convert the fraction to a percentage while in example 2; we multiplied the fraction by 100% to change it to a percentage. Another way to do this is to convert each fraction to a decimal, then convert each decimal to a percentage. To convert a fraction to a decimal, divide its numerator by its denominator. Look at the example below to see how this is done.

Example 1

Write each fraction as a percentage: 7/8, 19/20, 3/200

Solution

Summary

To write a fraction as a percentage, we can:

i) Convert it to an equivalent fraction with a denominator of 100.

ii) Multiply the fraction by 100%

iii) Divide its numerator by its denominator, then convert the resulting decimal to a percentage.

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