Math 010: Percents (Ch. 8)

Math 010: Percent (Ch. 8)November 20, 2013When do we use percents?

What do we know about percents?

What does percent mean?Watch: http://www.khanacademy.org/math/arithmetic/decimals/percent_tutorial/v/describing-the-meaning-of-percent

Per means out of or divided by

Cent means one hundred

So percent literally means out of 100 or divided by 100

Converting percents to fractionsConverting fractions to percentsDecimals PercentsTo convert a decimal to a percent, move the decimal point two places to the right and add the % sign.

Example: 0.56 = 56%

1 = 100%

1.5 = 150%

4 = 400%Percents DecimalsTo convert a percent to a decimal, remove the % sign and move the decimal point two places to the left.Example: 25% = 0.25100% = 1Sales increased 400% this year! means that sales increased by 4 times last years amount, because 400% = 4.

Fractions, decimals, percents

Check your understandinghttp://www.polleverywhere.com/multiple_choice_polls/mpM1npuC8GrWp2O

Correct answer: 8/10,000

Eight hundredths of a percent means 0.08 divided by 100, which is 0.0008 or eight ten-thousandths

Think about itWhat is 5% of 100?

% means out of 100, so 5% of 100 is 5.

What is 5% of 200?

5 out of each 100 5 2 = 10

What is 5% of 300?

5 3 = 15

You can use this method with any multiple of 100.

8.2 The Basic Percent EquationPercent Base = Amount

Base is the quantity we are drawing from

Base quantity usually comes after the word of or out of

Example: What is 25% of 800?

Percent = 25%

Base = 800

Amount = unknown = xWhat is 25% of 800?Percent Base = Amount

25% 800 = x

Need to convert the percent to a decimal

0.25 800 = 200

So 25% of 800 is 200.

Does that make sense?

25% is one-fourth.

200 is one-fourth of 800.20 is what percent of 32?

Percent Base = Amount

Percent is unknown

Base is 32

Amount is 20

x 32 = 20

Divide each side by 32

x = 20 32

x = 0.625

Need to convert to a percent

20 is 62.5% of 32.

Work on Problems #9-14 in assigned groups of 3. Answers to #9-14 on worksheet9)40% of 30 is 12.

10)60% of 500 is 300.

11)8 is 25% of 32.

12)24 is 12% of 200.

13)58.5% of 50 grams is 29.25 grams.

14)29 students is 20% of 145 students.8.3 Percent Increase & DecreaseGiven original amount and new amount

Need to find amount increase/decrease before finding percent increase/decrease

Use the same formula: Percent Base = Amount

To find percent increase or decrease, use the original amount as your base.

Example #2The price of an item increases from $15 to $18. Find the percent increase.

Amount increase = $3

Base = $15 (original price)

Percent = unknown

Percent Base = Amount

x $15 = $3

Divide each side by $15

x = 0.2 = 20%

Work on Problems #3-8 in your groups.Answers to #3-83) Amount decrease = $10, Base = $48 $10 $48 = 0.208 = 20.8%

4) Amount increase = 0.7 mi/gal, Base = 17.5 mi/gal 0.7 17.5 = 0.04 = 4%

5) Amount increase = $4032, Base = $2498 $4032 $2498 = 1.61 = 161%

6) Percent decrease = 45% = 0.45, Base = 1200 Amount increase = (0.45)(1200) = 540; New number = 1200 540 = 660

7) Percent decrease = 25% = 0.25, Base = $16.50 Amount decrease = (0.25)($16.50) = $4.125 New price = $16.50 - $4.125 = $12.375 $12.38 (the store gets half a cent)

8) Percent increase = 20% = 0.2, Base = $47.25 Amount increase = (0.2)($47.25) = $9.45 Bill total = $47.25 + $9.45 = $56.70

Quiz Answer on a separate sheet of paper.

1.) Write 0.08% as a decimal and as a fraction.

2.) Write one-fifth as a decimal and as a percent.

3.) If a quantity doubles, what is the percent increase?