2 percents

TENNESSEE ADULT EDUCATION

PERCENTS

LESSON 2

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

WHAT IS PERCENT?

It’s the number of parts out of 100.

25% means 25 parts out of 100

WHEN SOLVING PERCENT PROBLEMS, YOU WILL BE SOLVING FOR ONE OF THESE THREE PARTS.

Example: 25% of 100 is 25.

Percent Whole Part

25% OF THE PIZZA

Does 25% = 25?

No.

There are not 25 pizzas.

25% is 25 slices out of 100 total.

BEFORE SOLVING PERCENT PROBLEMS, IT IS NECESSARY TO CHANGE THE PERCENT TO A DECIMAL.When given the percent, always move the decimal 2

places to the left.

For example: 13% = .13

Let’s practice changing the following percents to decimals.

1.62% = _____ 2. 122% = _____ 3. 2% = _____

0 0 0 1 3 0

ThousandthsHundredths

Tenths

Hundreds

Tens

Ones

decimal

.

AT THE END OF PROBLEMS, YOU MAY NEED TO CHANGE FROM A DECIMAL BACK INTO A PERCENT.When you have a decimal, always move the decimal 2

places to the right to make a percent.

For example: .6 = 60%

Let’s practice changing the following percents to decimals.

1. .33 = _____ 2. .6 = _____ 3. .03 = _____

0 0 0 6 0 0

ThousandthsHundredths

Tenths

Hundreds

Tens

Ones

decimal

.

WHEN SOLVING PERCENT PROBLEMS, YOU WILL BE SOLVING FOR ONE OF THESE THREE PARTS.

Example: 25% of 200 is 50.

Percent Whole Part

In other words:

•When given the PART, you must divide.

•When given the WHOLE and the PERCENT, you must multiply.

Part

Whole Percent

÷

X

One way to solve percent problems is to use the Percent Pyramid. The pyramid will explain what operation is necessary to solve the problem.

WholeFollows the word “of”

Original

Principal

Beginning

Overall

Total

PartFollows the word “is”

Discounted Price

Interest

Down Payment

Amount Paid

Taxes

Tips

The following charts provide key words that will help identify what each number represents in a word problem.

GUIDED PRACTICE

Part

Whole Percent

÷

X

What is 20% of 30?

Example: 25% of 200 is 50.

Percent Whole Part

Percent Whole

.2 X 30 =

GUIDED PRACTICE

Part

Whole Percent

÷

X

What is 40% of 300?

Example: 25% of 200 is 50.

Percent Whole Part

Percent Whole

.4 X 300 =

GUIDED PRACTICE

Part

Whole Percent

÷

X

What is 25% of 300?

Example: 25% of 200 is 50.

Percent Whole Part

Percent Whole

.25 X 300 =

GUIDED PRACTICE

Part

Whole Percent

÷

X

What % of 300 is 30?

Example: 25% of 200 is 50.

Percent Whole Part

Whole Part

30 ÷ 300 =

GUIDED PRACTICE

Part

Whole Percent

÷

X

What % of 100 is 50?

Example: 25% of 200 is 50.

Percent Whole Part

Whole Part

50 ÷ 100 =

GUIDED PRACTICE

Part

Whole Percent

÷

X

20 is what percent of 100.

Example: 25% of 200 is 50.

Percent Whole Part

Part Whole

20 ÷ 100 =

GUIDED PRACTICE

1.30% of 90 = ______

2.25% of 180 = ______

3.What % of 30 is 6?

4.$12 is what percent of $48?

5.14 is 20% of what number?

6.20% of what number is 34?

Part

Whole Percent

÷

X

Directions: Solve each problem using the Percent Pyramid.

Draw out the pyramid for each problem.

GUIDED PRACTICE

1.30% of 90 = __27__

2.25% of 180 = __45__

3.What % of 30 is 6? 20%

4.$12 is what percent of $48? 25%

5.14 is 20% of what number? 70

6.20% of what number is 34? 170

Part

Whole Percent

÷

X

Directions: Solve each problem using the Percent Pyramid.

Draw out the pyramid for each problem.

STEPS FOR SOLVING PERCENT WORD STEPS FOR SOLVING PERCENT WORD PROBLEMS.PROBLEMS.

1. Read the problem.

2. Determine what the numbers represent.a. Is the number the: Part, Whole, or Percentb. This will also help determine what the problem wants to

know.

3. Using the percent pyramid, determine what operation is necessary to solve the problem.

4. Solve.

5. Ask, “Does this answer make sense?”There may be another step. BE CAREFUL!

STEP 1: READ THE PROBLEM.

When Meyer bought a new stove, he made a $146 down payment. If the down payment is 25% of the purchase price, what is the cost of the stove?

When Meyer bought a new stove, he made a $146 down payment. If the down payment is 25% of the purchase price, what is the cost of the stove?

Look back at the key words provided earlier in the PowerPoint.

What does down payment represent?

The Part

•$146 is a down payment, therefore, it is only PART of the purchase price and will be placed in the top section of the pyramid.

•25 is the percent because it has the % sign; the percent is placed in the bottom right corner of the pyramid.

Step 2: Determine what the numbers represent.

• $146 was the part.

Step 3: Draw the percent pyramid, and fill it in.

X

÷

percentwhole

part

$146

• The percent was also given. 25%

25%

The pyramid indicates division is the operation needed to solve the problem.

HINT: Don’t forget to change the percent to a decimal!

STEP 4 : SOLVING THE PROBLEM

Set up the division:

.25 146

Looks like: 25 14600.

Change the decimal to a whole number by moving the decimal back to the right.

If you change the outside number, you have to move the inside number the same number of spaces. Then add zeros to cover the empty spaces.

STEP 4: SOLVING PROBLEMDivide:

25 $14600.

- 125

52

21 0

8

200

4

-

100

4

100

0

STEP 5: READ THE PROBLEM AGAIN.

What does the question want to know?

The price of the stove.

Is $584 a reasonable price for a stove?

YES

When Meyer bought a new stove, he made a $146 down payment. If the down payment is 25% of the purchase price, what is the cost of the stove?

Step 1: Read the problem!

Step 2: Determine what the numbers stand for.

$39.50 was the total cost = whole

20 % = is the percent

Guided Practice:

Our meal was $39.50, but we got a 20% discount because our food was late. What did our meal cost after the discount?

Step 3: Draw and fill in the triangle.

?

$39.50 20%

Notice that you have both numbers on the bottom of the triangle. When this happens, you simply multiply.

STEP 4: SOLVE THE PROBLEM.

Hint: When solving by hand, you must change the percent to a decimal by moving the decimal two places to the left.

$39.50

x .20

7.9000

* Count the number of decimal places in the problem and move the decimal that many places.

STEP 5: DOES THE ANSWER MAKE SENSE?

Always make sure you answered the question.

You must subtract the $7.90 from the original cost to find what you will pay for the meal.

$39.50

- 7.90

$31.60 is the amount paid.

• Is $7.90 a reasonable answer.• No, if you were given a 20% discount, $7.90 is more

than half off the price. This does not make sense.

15400

44,000 ?

1. During the November special election in Blaine, only 15,400 voters went to the ballot box. If 44,000 registered voters live in Blaine, what percent of the registered voters cast their votes?

35%

Step 2: 15,400 is part of the voters; 44,000 is the total number of voters which makes it the whole.

Step 3: Use the pyramid to determine what operation to use.

44,000 ) 15400.00·3

13200 0

2200 00

5

2200 00

HINT: Don’t forget to change the decimal to a percent.

Step 4:

2. Julia had her car windshield replaced at a cost of $250. After a $25 deductible is applied, her insurance company will pay 80 percent of the remaining balance. In dollars, how much will the insurance company pay?

$180

Step 2: $250 is the total cost; $25 is the deductible; and 80 is the percent the insurance company will pay. Be careful! $250 is not the whole because the 80 is the percent off the remaining balance after the deductible; therefore, the $250 is extra information. Find the whole by subtracting the deductible.

$250 – $25 = $225

$225 80 %

Step 3: Fill out pyramid.

Step 4: Solve.

$225x .8018000

Don’t forget the decimal. There are 2 decimal places.

3. Mr. and Mrs. Potato Head bought a house five years ago for 95,000. Since then, the value of their home has increased 2%. In dollars, what is the value of their home now?

$96,900

Step 2: 95,000 is the original amount; 2 is the percent.

Step 3: Fill out pyramid.

95,000 2%

Step 4: Solve.

95,000 x .021900.00

Step 5: Does $1900.00 make sense for the price of a home?

No, Add the increase back to the original cost of the home. 1,900

95,000+1,900

4. Mr. Buzz took Mr. Woody out for dinner. The cost of their meal was $32.00. If Mr. Buzz wishes to leave a 15% tip, how much money should he leave for a tip?

$4.80

Step 2: $32.00 is the original amount; 15 is the percent off the original amount.

Step 3: Fill out pyramid.

Step 4: Solve.

$32.00 15%

$32 x.15 160 320 480 HINT: Don’t forget

the decimal.

Step 5: Is $4.80 a reasonable amount to leave for a tip? YES