Percentages
In a nutshell
Percentages are used very often in the real world as they are very easy to interpret and understand. It is important to know how to find one quantity as a percentage of another as well as how to find percentages of a quantity.
Interpreting percentages
The percent symbol (%) means "out of 100". So, 35% literally means "35 out of 100". Another way of writing this is 10035, or 0.35.
Finding percentages of a number
A common problem is to find percentages of a number. To approach these questions, use the fraction interpretation of the percentage symbol. It is also helpful to read the word "of" as "times".
Example 1
What is 35% of 160?
Write the percentage symbol as 100 and the "of" as the multiplication symbol:
35% of 160 =10035×160
Put this into a calculator:
10035×160=56
35% of 160 is 56.
However, if you don't have a calculator you can follow this method:
35% of 160=10035×160 =10035×1160 =1005600=56
Expressing one number as a percentage of another
You may be asked to compare one number as a percentage of another number. To do this, first write what you want to find as a fraction. Then, convert it to a decimal, and then convert it to a percentage.
Example 2
A quiz has 60 questions. If I answered 54 questions correctly, what percentage of questions did I get correct?
First, find the relevant fraction:
I answered 54 questions correct out of 60 questions in total.
So, the relevant fraction is 6054.
To convert this to a percentage, first convert it to a decimal:
6054=54÷60=0.9
Now, convert the decimal to a percentage:
0.9=(0.9×100)%=90%
I answered 90% of questions correctly.
Note: In this example, you also could have simplified the fraction to 109. Using your common conversions, you should know that 109=90%.
