percents definition: a percent is another way of showing a fraction whose denominator is 100....

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’spopulation 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 inthe 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

2=50

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 . If we want to know what percentage of people surveyed love math, we look for an equivalent fraction with a

denominator of 100.

€

4

16

€

part

total=%

1004

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 model.

€

part

total=%

100

3. Multiply along the diagonal whatever direction we have two numbers (not the ?)

In this case – 4 x 100 = 400

4. Divide the answer fromstep 4 by the remaining number (in this case 16)

400/16 = 25

€

4

16=?

100

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 –

• Step 2 – we know the percent and the total. We’re trying to find the part, so€

=100

€

?

300=20

100

Example 1 – Finding the part

• Step 4 –

– Cross multiply 20 x 300 = 6000

• Step 5 – – divide by the remaining number 6000/100 = 60

20% of 300 is 60

€

?

300=20

100

Example 2 – Finding the total

• 18 is 15% of what number?• Step 1 –

• Step 2 – we know the part and the percent. We’re trying to find the total, so€

=100

€

18

?=15

100

Example 2 – Finding the total

• Step 4 –

– Cross multiply 18 x 100 = 1800

• Step 5 – – divide by the remaining number 1800/15= 120

15% of 120 is 18

€

18

?=15

100

Example 3 – Finding the percent

• 70 is what percent of 800?• Step 1 –

• Step 2 – we know the part and the total. We’re trying to find the percent, so€

=100

€

70

800=?

100

Example 3 – Finding the percent

• Step 3–

– Cross multiply 70 x 100 = 7000

• Step 4 – – divide by the remaining number 7000/800 = 8.75

70 is 8.75% of 800

€

70

800=?

100

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?

(50 x 100)/250 = 20

• What is 30% of 500?

(30x 500)/100 = 150

• 18 is 6% of what number?

(18 x 100)/6 = 300

€

=100

€

=100

€

=100

€

50

250=?

100

€

?

500=30

100

€

18

?=6

100

Percents

• Some problems using percents are a little more complicated.– Markup– Discount– Tax– Percent Change

PercentsMark-up

Fred Meyer buys potted palms from a local grower for $3.50 each. They sell them to the public at a 90% markupWhat is 90% markup?

90 x 3.50 = 315

315 ÷ 100 = 3.15

€

part

total=%

100

€

?

3.50=90

100

Percents

• Mark-upFred 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

€

?

6.65=20

100

Percents

20 x 6.65 = 133133 ÷ 100 = 1.33

The discount is $1.33, so the price is now 6.65 – 1.33 = 5.32Sale price: $5.32

€

?

6.65=20

100

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

€

?

5.32=7

100

Percents

7 x 5.32 = 37.2437.24 ÷ 100 = .3724 (since we’re talking about money we round to

the nearest cent - .37)

€

?

5.32=7

100

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

.34 x 100 = 3434 ÷ 8.5 = 4

James received a 4% raise.

€

amount _change

original=%

100

€

.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 x 100 = 500500 ÷ 20 = 25

The book was 25% off – The price had been decreased by 25%

€

5

20=?

100

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.