Percents
Definition: A percent is another way of showing
a fraction whose denominator is 100. Percent
means parts per hundred. The word percent
comes from the Latin phrase per centum,
which means each | hundred. In mathematics,
we use the symbol % for percent.
Percents
Population of China: 1,321,851,888 (July 2007 est.)
----------- out of ----------Population of the world: 6,602,224,175
It’s hard to grasp the relationship when China’s
population is written as a fraction of world population.
But turn it into a percent….
Almost exactly 20%
Just about 20 out of every one hundred people in
the world lives in China.
Percents
• This proportion is the key to solving percent
problems. You should memorize it.
part %

total 100
Percents
part %

total 100
1 50

2 100
• Let’s say that 4 out of 16 people in this class
absolutely love math. We could represent
that as a ratio 4 to 16 or 4 . If we want to
16
know what percentage of people surveyed
love math, we look for an
part %

equivalent fraction with a

total 100
denominator of 100.
4
?

16 100
• To solve any basic percent problem we use the
same steps:
1. Write two fractions bars with = between, and
write 100 as the second fraction’s
denominator
2. Fill in the information we have according to
the part % model.

total 100
3. Multiply along the diagonal whatever
direction we have two numbers (not the ?)
In this case – 4 x 100 = 400
4
?

16 100
4. Divide the answer from
step 4 by the remaining number (in this case
16)
400/16 = 25

Percents
• GED percent problems will give you two out of
the 3 necessary pieces of information. (Note
that the 100 on the bottom right doesn’t
change)
part %

total 100
Example 1 – Finding the part
• What is 20% of 300?
• Step 1 – 
100
• Step 2 – we know the percent and the total.
We’re
trying to find the part, so

?
20

300 100
Example 1 – Finding the part
• Step 4 –
?
20

300 100
– Cross multiply  20 x 300 = 6000

• Step 5 –
– divide by the remaining number 6000/100 = 60
20% of 300 is 60
Example 2 – Finding the total
• 18 is 15% of what number?
• Step 1 – 
100
• Step 2 – we know the part and the percent.
We’re
trying to find the total, so

18 15

? 100
Example 2 – Finding the total
• Step 4 –
18 15

? 100
– Cross multiply  18 x 100 = 1800

• Step 5 –
– divide by the remaining number 1800/15= 120
15% of 120 is 18
Example 3 – Finding the percent
• 70 is what percent of 800?
• Step 1 – 
100
• Step 2 – we know the part and the total.
We’re
trying to find the percent, so

70
?

800 100
Example 3 – Finding the percent
• Step 3–
70
?

800 100
– Cross multiply  70 x 100 = 7000

• Step 4 –
– divide by the remaining number 7000/800 = 8.75
70 is 8.75% of 800
You try:
• 50 is what percent of 250?
• What is 30% of 500?
• 18 is 6% of what number?
(press pause)


You try:
• 50 is what percent of 250?


100
50
?

250 100
 (50 x 100)/250 = 20
• What is 30% of 500?


100
?
30
 500  100
 (30x 500)/100 = 150
• 18 is 6% of what number?


100
18
6

 ? 100
 (18 x 100)/6 = 300
Percents
• Some problems using percents are a little
more complicated.
– Markup
– Discount
– Tax
– Percent Change
Percents
Mark-up
Fred Meyer buys potted palms from a local
grower for $3.50 each. They sell them to the
public at a 90% markup
part %

What is 90% markup?
total 100
?
90

3.50 100
90 x 3.50 = 315
 ÷ 100 = 3.15
315
Percents
• Mark-up
Fred Meyer buys potted palms from a local
grower for $3.50 each. They sell them to the
public at a 90% markup
• Markup is $3.15 – this is added to the original
cost of the plant to reach the sale price.
• $3.50 + $3.15 = $6.65
Percents
• Discount – Fred Meyer is having a 20% off sale
on potted palms. How much are the plants
now?
• They are selling for $6.65
• We need to find 20% of $6.65
Percents
• Discount – Fred Meyer is having a 20% off sale
on potted palms. How much are the plants
now?
• They are selling for $6.65
• We need to find 20% of $6.65
part %

total 100
?
20

6.65 100

Percents
?
20

6.65 100
20 x 6.65 = 133
133 ÷ 100 = 1.33
The discount is $1.33, so the price is now
6.65 – 1.33 = 5.32
Sale price: $5.32
Percents
• Tax – If Washington State sales tax is 7% and
you buy a potted palm at the sale price, how
much will you pay at the register?
Percents
• Tax – If Washington State sales tax is 7% and
you buy a potted palm at the sale price, how
much will you pay at the register?
• We need to find 7% of 5.32
part %

total 100

?
7

5.32 100
Percents
?
7

5.32 100
7 x 5.32 = 37.24
 37.24 ÷ 100 = .3724
(since we’re talking about money we round to
the nearest cent - .37)
Percents
• The price of the plant was $5.32 and the tax is
37¢, so we need to add the tax to the price to
get the final total:
• 5.32 + .37 = 5.69
• The total price at the register is $5.69
Percents
• Percent Change Problems – amount of
change becomes part, original becomes total.
amount _ change %

original
100
Percents
• % Increase
• James used to make $8.50/hr. His boss gave
him a raise, and now he makes $8.84/hr.
What percent raise did James get?
Percents
• Percent Increase
• James used to make $8.50/hr. His boss gave
him a raise, and now he makes $8.84/hr.
What percent raise did James get?
• The original was 8.50, and the amount it
changed by is 8.84 – 8.50 = .34
amount _ change %

original
100
.34 x 100 = 34
34 ÷ 8.5 = 4

James received a 4% raise.
.34
?

8.50 100
Percents
• Percent Decrease
• A cookbook was reduced from $20 to $15.
What percent off was the book?
amount _ change %

original
100
5
?

20 100

Percents
5
?

20 100
5 x 100 = 500
500 ÷ 20 = 25

The book was 25% off – The price had been
decreased by 25%
Percents
• Try the practice on pages 130 – 133 of the
book.
• Do GED Practice pages 15 – 17 and submit
your answers using the answer sheet on BB.