__Objective:__

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

__Converting Percentages to Fraction____s __

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**:

Answer = 75%

**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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