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