AGENDA 4/19/12

• 1. Review: Ratio/Proportion• 2. Discuss Ratio/Proportion Quiz• 3. Introduction to Percent– The Basics

• 4. The Percent Statement

• NO CLASS MONDAY

PERCENT

• Percent means “out of 100”

• So, if you get 4 out of 5 questions right on a quiz, we generally give a percent to show a grade.

• Percentage is a way of putting numbers in the same terms so no matter what you compare, an understanding can me made.

45=80100

You can see these two fractions are equal, by multiplying diagonally.

400400

Because of this relationship, you can set up a proportion to calculate percentage, find the part, or find the whole.

THE BASICS

• You will need to know how to convert:–A decimal to a fraction (place value)–A fraction to a decimal (division)–A fraction to a percent (division)–A percent to a fraction or decimal

(place value/division)

EXAMPLE

CHANGING A PERCENT TO A DECIMAL

RULE

• 1. Drop the percent sign (%).

• 2. Move the decimal point two places to the LEFT.

45%...Percent Decimal

45%

8%

37 ½ %

250%

0.45

0.08

0.37 ½ or 0.375

2.5

CHANGING A PERCENT TO A FRACTION

RULE• 1. Drop the %

sign.• 2. Write 100 as

the denominator.• 3. Reduce.

EXAMPLE 1• Change 35 % to a

fraction.

•

• Common denominator = 5

CHANGING A MIXED NUMBER PERCENT TO A FRACTION

RULE• 1. Drop the % sign.

• 2. Change to an improper fraction.

• 3. Multiply by • 4. Reduce.

EXAMPLE 3• Change 16 2/3 % to a

fraction.

%

1

2

THE PERCENT STATEMENT

15% of $25 is $3.75Percent

Whole

Part

$3.75 is 15% of $25Part

Percent

Whole

You will be asked to find the part, the percent, or the whole.

𝑖𝑠𝑜𝑓

=%100

FINDING THE PART OF A WHOLE

• Two Strategies:• 1. Turn the percent into a decimal and then

multiply.

• Ex) Find 25% of 12.

• .25 x 12 = 3

• 3 is 25 % of 12.

PROPORTION AND PERCENT

𝑝𝑎𝑟𝑡h𝑤 𝑜𝑙𝑒

=%100 This relationship is ALWAYS TRUE.

𝑝𝑎𝑟𝑡h𝑤 𝑜𝑙𝑒

=%100

Josh got 4 out of 5 questions right on a test. What is his percentage?

45=%100

45=

𝒙100

Step 1: Write a proportion statement.

Step 2: Find the cross products.

𝒙

5 𝑥¿ 400Step 3: Divide by 5 on both sides.

5 5 𝑥=80%4 is the part.

5 is the whole.

We are looking for the %.

FINDING THE PART

• Find 25% of 12.

•Step 1: Set up a proportion.

•Step 2: Cross multiply.

•Step 3: Divide

FINDING THE PART

• Option 1: Change the percent to a decimal, then multiply.

FINDING THE PART• Option 2: Write a

proportion statement.

WORD PROBLEMS (PART)• A state official predicts that 70% of the registered voters in

Montana will vote on election day. If there are 514,000 registered voters in Montana, how many are predicted to vote?

Step 1: Understand the question. “How many registered voters are predicted to vote?”Step 2: What info do you need? Use the % of voters predicted to vote and the number of registered voters.Step 3: Choose the operation. What is 70% of 514,000?

EXAMPLE FROM P 135

• 6. Randi’s property tax bill is increasing by 3% this coming year. She now pays $890 a year in property tax.

• A) By how much is her property tax going to increase?

EXAMPLE FROM P. 135

• 6. Randi’s property tax bill is increasing by 3% this coming year. She now pays $890 a year in property tax.

• B) How much will she pay next year?

FINDING WHAT PERCENT ONE NUMBER IS OF ANOTHER

RULE• 1. First make a

fraction. Put the part (is) over the whole (of) and reduce.

• 2. Change the fraction to a percent.

EXAMPLE 3• 27 is what percent

of 45?

Casio fx-260 Calculator- Example 2

• Use the calculator to find what percent 27 is of 45.

AC1. Press

2. Press 2 7 5

The display should read 60.

÷ SHIFT4

The answer is 60%.

%

• 1. 9 is what percent of 36?

• 7 is what percent of 35?

• 7. The Melino family was on vacation for 12 days. It rained 3 of those days. On what percent of their vacation days did it rain?

Exercise 9, page 160 1-8

FINDING A NUMBER WHEN A PERCENT OF IT IS GIVEN (WHOLE)

RULE• 1. Change the

percent to either a fraction or a decimal.

• 2. Divide the number by that fraction or decimal.

EXAMPLE 1• 20% of what is 9?

Casio fx-260 Calculator- Example 1

• Use the calculator to find 20% of what number is 9.

AC1. Press

2. Press 9 0

The display should read 45.

÷ SHIFT2 %

• 1. 18 is 50% of what number?

• 25% of what number is 30?

• 6. Paul and Jane Bidwell pay $150 a month on their car loan. This is 5% of their monthly income. How much do they make each month?

Exercise 10, p161 1-7

THE PERCENT CIRCLE

P

% x W

•P stands for the Part

•% stands for the Percent

•W stands for the WHOLE

•The horizontal line means divided by.

•The X means multipliedby

The Percent Circle

P

% x W

To Use the Percent Circle:

1. Cover the symbol of the number you are looking for.

2. Do the math shown by the uncovered symbols.

The Percent Circle

P

% x W

What is 50% of 8?

The Percent Circle

P

% x W

4 is 50% of what number?

Finding What Percent One Number is of Another

• To find a percent of a number:

• Step 1: Change the percent to a decimal or a fraction.

• Step 2: Multiply

• What is 62 ½ % of 56?

• Decimal• 62.5 x 56 = 3500

• Move decimal two places to the left.

• 62 ½ % of 56 is 35.

PART

• What is 62 ½ % of 56?• Fraction

• To find a percent of a number:

• Step 1: Change the percent to a decimal or a fraction.

• Step 2: Multiply

Change to a mixed number

Finding What Percent One Number is of Another

Finding What Percent One Number is of Another

• To find the part: • 1. First make a fraction.

Put the part over the whole and reduce.

• 2. Change the fraction to a percent.

• 27 is what percent of 45?

PERCENT

• The Melino family was on vacation for 12 days. It rained 3 of those days. On what percent of their vacation did it rain?

• Write the fraction as

• Change the fraction to percent.

•

Finding What Percent One Number is of Another

Finding a Number When a Percent is Given

• 1. Change the percent to either a fraction or a decimal.

• 2. Divide the number by that fraction or decimal.

• 20% of what number is 9?

• Change to a fraction

WHOLE

REVIEW: THE PERCENT STATEMENT

15% of $25 is $3.75Percent

Whole

Part

$3.75 is 15% of $25Part

Percent

Whole

PRACTICE

• Mrs. Jackson makes a week. She pays $90 a week for food. Money spent for food is what percent of her income?

$450 is her total income.

She spends $90 on food.

$90 is what percent of $450?

𝑖𝑠𝑜𝑓

=%10090450

=𝑥100

450𝑥=9000450 450

𝑥=20%

PRACTICE

• 60% of what number is 45?

• Lois got a 6% commission for selling a house. She sold a house for $120,000. Find the commission.

𝑖𝑠𝑜𝑓

=%10045𝑥

=60100

4500=60𝑥60 60 𝑥=75

𝑖𝑠𝑜𝑓

=%100

𝑥$120,000

=6100

$720 ,000=100 𝑥100 100

𝑥=$7200

THE PERCENT CIRCLE

P

% x W

•P stands for the Part

•% stands for the Percent

•W stands for the WHOLE

•The horizontal line means divided by.

•The X means multipliedby

The Percent Circle

P

% x W

To Use the Percent Circle:

1. Cover the symbol of the number you are looking for.

2. Do the math shown by the uncovered symbols.

The Percent Circle

P

% x W

What is 50% of 8?

The Percent Circle

P

% x W

4 is 50% of what number?

USING THE PERCENT CIRCLE

• Sally wants a new computer that costs $900. She has saved 75% of the price. How much has she saved?

P

% x W

I am looking for the part.

.75 x $900 = $675

USING THE PERCENT CIRCLE

• Bill paid $2 sales tax on a $40 shirt. The tax was what percent of the list price?

P

% x W

I am looking for the percent.

2/40= 1/20=.05

5 %