CALCULATING PERCENTAGES
WARNING: There are two prerequisites for learning about percents: knowledge of
decimals and fractions.
There is a series of questions listed below. In order for you to continue,
you should answer yes to all of them. If you are unsure of any of these points,
click on the appropriate question for a review.
CALCULATING PERCENTS
By now you know how to take a percent of a number, you're ready to get your raise
and go on a shopping spree at the neighborhood mall.
But what if you knew that you paid $45.50 for an item that usually cost $36.40,
and wanted to know
what percent was deducted from the original price.
And what if a bill jumped from $156 to $177.84.
Angrily you might want to yell, “MY BILL WENT UP BY __%”
In both of these cases you need to actually calculate a percentage.
We’ll get back to these questions in section two of this page,
but first let’s get a little hardware.
Remember our formula
BASE * PERCENT = AMOUNT
The BASE is again the number (or object) that we are working on. It constitutes 100%
Each PERCENT is 1/100 of the base.
What if you knew the base the amount figures, and you needed to calculate the percent.
In other words “what percent of __ is __?”
Well the percent is the amount divided by the base (i.e. percent=amount/base)
Now you may be saying “that’s all good in theory, but let’s see you actually do it!”
Okay have it your way.
What percent of 46 is 34.5?
Well 46 is our base, which when multiplied by some percent will yield the end figure 34.5.
To calculate the percent first divide 34.5 by 46.
34.5 / 46 = 0.75
Now multiply this decimal by 100 to get a percent
0.75 = 75%
Thus 75% of 46 is 34.5 (i.e 46 * 0.75 = 34.5)
Want to see it again. All right
What percent of 240 is 6?
Again, we will divide our amount by our base figure, convert this fraction to a decimal, and finally change it to a percent.
Well 6 / 240 = 1 / 40 = 0.025
Multiplying by 100 we get 2.5%
2.5% of 240 is 6 (i.e. 240 * 0.025 = 6)
I'll show you one more problem. This one about a restaurant.
On a busy Saturday night a restaurant sold 16,000 dinners.
It was determined that 10,000 of these dinners were chicken.
What percentage of the customers ordered chicken?
This problem could be stated as "what percent of 16000 is 10000?"
Well 10000/16000 = 10/16 = 5/8 = 0.625.
Multiplying this by 100 we get 62.5
So 62.5% of the 16,000 dinners were for chicken. (i.e. 16,000 * .0625 = 10,000)
Now after a few exercises we’ll get back to the sale and bill questions
posed at the beginning of this section.
Compute the percent in each of the problems.
In each problem give your answer as a decimal.
Exercise 1
A baseball team played 160 games, of which they won 120. What percent of the games did they win?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next section
Exercise 2
A test has 20 questions. You answered 18 of the questions correctly.
What percent did you answer correctly?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next section
Exercise 3
On a Monday the library circulated 125,000 books. Of these 85,000 were fiction.
What was the percent of fiction books circulated on Monday?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next section
Exercise 4
1,600,000 people voted in the last election.
The winning candidate received 1,040,000 votes.
What percent of the electorate voted for him?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next section
Exercise 5
There are 20 members of city council. When a bill was passed 17 of them voted for it.
What percent of the council members voted for the bill?
Go to the top of this page
Go to the percent home page
Go to the next section
CALCULATING PERCENTS WHILE INCREASING OR DECREASING
What if you knew that you paid $45.50 for an item that usually cost $36.40 and wanted to know what percent
was deducted from the original price.
And what if a bill jumped from $156 to $177.84. Angrily you might want to yell, “MY BILL WENT UP BY __%”
Let’s look at these problems one at a time.
First the sale problem
What if you knew that you paid $45.50 for an item that usually cost $36.40 and wanted to know what percent was deducted from the original price.
Well we know the starting figure for this product was $45.50 and it was reduced to $36.40.
But before actually computing the percent involved we have to know
“exactly how much was discounted from the original price.”
By a simple subtraction we get $9.10 (45.50 - 36.40 = 9.10).
Now the question becomes what percent of 45.50 is 9.10.
Using the hardware developed in the above section 9.10 / 45.50 = 0.20 = 20%.
Thus 20% was discounted off the original price of $45.50 to arrive at the sale price of $36.40 (A 20% off sale isn’t so great-you could have done better than that)
Now let’s get to that bill.
A bill jumped from $156 to $177.84. Angrily you might want to yell, “MY BILL WENT UP BY __%”
Well the bill increased by 177.84 - 156 = 21.84
Now what percent of 156 is 21.84?
21.84 / 156 = 0.14 = 14%
Your can yell, “MY BILL WENT UP BY 14%”
I’ll show you two more examples, but that’s it until our next page when we
start looking at percents larger than 100.
Your business is prospering. In the last month your profits went from $5000 to $7250.
What was the percent increase?
The actual increase in profit was 7250 - 5000 = 2250.
What percent of 5000 is 2250?
2250 / 5000 = 45 / 100 = 45%
Your business improved by 45%. Keep up the good job.
To make things even better, your supplier has slightly reduced their prices.
Their price dropped from $350 to $343. What is percent decrease?
In this case the actual decrease is 350 - 343 = 7.
What percent of 350 is 7?
7 / 350 = 1/50 = 0.02 = 2%
Your supplier reduced their price by 2%
Now I have graciously supplied a few exercises for you to do.
We’ll continue our discussion of percents on the next page.
In each of the exercises listed below, you'll be asked to calculate a percentage
after either an increase or descrease has occured.
To help you along, there will be two steps to each problem.
First take the calculate the actual change (increase of decrease).(Step 1)
And then calculate the percentage.(Step 2).
In each problem give your answer as a decimal.
In order for the computer to check your answer, please do not include any commas.
So if your answer was 23,456 then you would enter it as 23456.
Exercise 1
At the library they had a banner year. Last year the number of books curculated went from
13.4 million to
18.09 million. What was the percent increase?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next page
Exercise 2
You saved some money by going to a sale. You paid $39.60 for an item that usually
sells for $66.
What percent was discounted from the original price?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next page
Exercise 3
Your telephone bill went from $123.50 to $135.85. What was the percent increase?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next page
Exercise 4
Your credit card situation is improving. Last month you had $2450 on the card and now
you have $2401 still owed on the card.
What is the percentage decrease?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next page
Exercise 5
3.5 million people saw a movie on it's opening weekend.
2.94 million saw it the following weekend.
What was the percentage decrease?
Go to the top of this page
Go to the percent home page
Go to the next problem.
Go to the next page
Exercise 6
Your salary has gone from $23,100 to $24,255. What percent raise did you receive?
Go to the top of this page
Go to the percent home page
Go to the next page
