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Percents
What is a Percent?
A percent is a number that represents a ratio (or fraction) with a denominator of 100. So, if you have a
ratio, such as 53 out of 100, you can express it as 53%, which corresponds to 0.53 in decimal notation.
Example of how a percent looks going from percent to fraction to decimal notation:
You can convert a decimal to a percent by multiplying it by 100 (which causes the decimal place to
move two spaces to the right).
Example of decimal notation changing to a percentage:
0.5367 = 53.67 %
A fraction can become a percentage if you first convert it into decimal notation by completing the
specified division. You can then convert the resulting decimal number to a percent as was done
above.
Example of a fraction becoming a percentage:
3/5 = 0.6 = 60%
Percent Word Problems
There are several common types of word problems involving percents. Most of them involve one or
more of the following actions:
1)
2)
3)
4)
5)
Finding what amount is a given percentage of another amount.
Increasing by a percentage.
Decreasing by a percentage.
Finding what percentage an amount represents with respect to another amount.
Finding an amount, given that another amount is a certain percentage of it.
Examples of Percent Word Problems
These examples correspond to the above types of problems. Try answering them yourself. The
solutions are found on the following page.
1)
2)
3)
4)
If you bought 4L of milk and 25% of it is left then how much milk is left (in Liters).
A sweater costs $15 before a 7% sales tax is added. What is the cost after the tax is added?
A pair of shoes costs $35 before a 10% discount is applied. What is the cost after the discount?
If you had 750mL of vodka and now find that there is only 200mL left then what percentage of
the original amount of vodka is left?
5) A mathematics textbook costs $40 after a 15% discount is applied. What was the original price of
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This document last updated: 12/22/2010
Student Academic Learning Services
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the textbook?
Question 1)
The problem is to find what 25% of 4L is, therefore we must multiply:
4 × 0.25 = 1
Therefore, the answer is that 1L of milk is left.
Question 2)
This question is to find what 7% of $15 is, and then add that amount to find the new price.
To do this we must first multiply, like question 1, and then add the 7% to the old price:
$15 × 0.07 = $1.05

$15 + $1.05 = $16.05
Therefore, the final answer is $16.05.
An alternate solution to this problem is to find 107% of 35, as this is the same as adding 7% to
the original 100% of the price. Check that you get the same answer by multiplying 35 by .07.
Question 3)
Here you must find out what 10% of $35 is, and then subtract it to find the new price.
Similar to question 2, we first multiply, but then we subtract the 10% discount from the old
price.
$35 × 0.1 = $3.50 
$35 - $3.50 = $31.50
Therefore, the final answer is $31.50.
An alternate solution to this problem is to find 90% of 35, as this is the same as subtracting
10%. Check that you get the same answer by multiplying 35 by 0.9.
Question 4)
This question is asking what 200mL / 750mL is as a percentage. Do the division that is
specified in the question, and then multiply by 100 in order to find the percentage:
(rounding to the nearest 100th)
0.27 × 100 = 27%
Therefore, 27% of the vodka is left over.
Question 5)
The question is the reverse to what we have solved in Question 3. Knowing the final price,
we can set up an equation to solve for the answer. A discount of 15% means the final price is
85% of the original price. With “x” being the original price, our equation will look like:
0.85x = 40 solve for x by dividing both sides by 0.85 (or 85%)
x = 40 / 0.85
x = 47.06 (rounding off to the nearest 100th)
Therefore, the final answer is that the textbook was originally $47.06.
www.durhamcollege.ca/sals
Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010