1. Tennessee Adult Education Mathematics Pre-GED
Curriculum 2011
Percents
Lesson 6

2. What is percent?
It is another way to write a part of a whole. It refers to the number of parts out of 100 equal parts.
6% means 6 parts out of 100
In other words:
“Percent” literally means “ per 100”

3. Decimal and percent numbers are used everyday.
For Example: grocery stores and department stores
All items on sale 40% off
Mayo – $2.99
Pickles – $2.49 ea or 2/ $4.00
Olive Oil - $6.49
Shoes – 25% off

4. Percents and money 1 Penny = 1% of a dollar 1 Nickel = 5% of a dollar
$1 dollar is equal to 100 cents or 100%. Coins can be thought of as a percent of a dollar.
1 Penny = 1% of a dollar
1 Nickel = 5% of a dollar
1 Dime = 10% of a dollar
1 Quarter = 25% of a dollar
If Susie found 2 quarters and 3 dimes in her pants pocket, what percent of a dollar does she have?
Practice: = 80
80%

5. What is 100%? 100% stands for one whole object.
Practice:
What percent of the box is shaded?
13 squares out of 100 are shaded.
13%
What percent of the box is not shaded?
87 squares out of 100 are not shaded.
87%
= 100

6. Changing a Percent to a decimal
When solving a percent problem, the percent must be changed to a decimal.
Change to a decimal: 52%

7. Changing a Percent to a decimal
When a percent number is in a problem, take away the percent sign.
52 %
Change the % sign to a decimal point. 52 .

8. 52 . . 52 Next, move the decimal two places to the left.52
52% changed to a decimal becomes:
After the decimal is moved and no digit at the front of the decimal, use a zero (0) as a placeholder. The zero will be to the left of the decimal point.

9. Changing a Decimal to a percent
When finding the percent in a problem, it will be in decimal form and must be changed to a percent.
Where ever the decimal point is in the number, it will be moved two (2) places to the right.

10. Changing a Decimal to a percent
Change to a percent:
0.34
Move the decimal two places to the right.
After the decimal is moved two places to the right, the point is changed back to a percent sign.
34.

11. 34%
Place a % sign at the end of the number.

12. Guided Practice Change to a percent 0.23 = ________ 0.84 = ________
0.02 = ________
Change to a decimal
78% = ________
45% = ________
5% = ________

13. Guided Practice 23% 84% 2% 0.78 0.45 0.05 Change to a percent
0.23 = ________
0.84 = ________
0.02 = ________
Change to a decimal
78% = ________
45% = ________
5% = ________
23%
84% 2%
0.78
0.45
0.05

14. Percent problems contain three important numbers:
Part follows the word “is”
Whole follows the word “of”
Percent
Indicated by a percent sign (%)
or the word percent.

15. When solving percent problems, Which part will be solved?
Example: 75% of 24 is 18.
Percent
Whole
Part

16. The following charts provide key words that will help identify what each number represents in a word problem.
Part
Follows the word “is”
Discounted Price
Interest
Down Payment
Amount Paid
Taxes
Tips
Whole
Follows the word “of”
Original
Principal
Beginning
Overall

17. One way to solve percent problems is to use the Percent Pyramid.
The pyramid will explain what operation is necessary to solve the problem.
In other words:
When given the PART, division is required.
When given the WHOLE and the PERCENT, multiplication is required.
Part ÷
Whole X
Percent

18. Finding the Part 30% of 60 = 60 x 0.30 ÷ 60 30% Part Whole Percent
If the problem is asking to find the part, the necessary operation is multiplication.
30% of 60 =
This is asking what part of 60 is 30%
Remember: When solving a percent problem, the percent must be changed to a decimal. (move 2 places to the left)
Part ÷
30% changes to .30
Whole X
Percent
60 x 0.30 60
30%

19. Solve 60
x0.30
There are two decimal places in the problem. It must be included in the answer.
1 8 1 8 .
18.00
Since the decimal point is behind the number, the zero can be dropped.
30% of 60 = 18

20. Finding the Whole 25% of what number is 33 = 33 ÷ 0.25 33 ÷ 25% Part
When given the part, it always goes first in the division problem.
This is asking what is the whole if 25% is 33.
If the problem is asking to find the whole, the necessary operation is division.
33 ÷ 0.25 33
Part
Remember: When solving a percent problem, the percent must be changed to a decimal.
(move 2 places to the left) ÷
Whole X
Percent
25% changes to .25
25%

21. Solve 25% of what number is 33 = 132 3 2 0.25) 33. 1 25) 3300 - 25 8
** The decimal in the divisor must be moved to the right to the back of the number. If the decimal has two places then the decimal is moved to places 3 2
0.25) 33. 1
Changes to
25) 3300
- 25
If the divisor’s decimal is moved 2 places, the dividend’s decimal must also be moved 2 places.
Start with the digit in the ones place and move two places to the right. 8
- 75 5
Steps for division:
Divide
Multiply
Subtract
Bring down
Repeat
- 50
25% of what number is 33 =
132

22. Finding the Percent What % of 40 is 8? 8 ÷ 40 8 ÷ 40 Part Whole
This is asking what is the percent if 40 is the whole and 8 is the part.
If the problem is asking to find the percent, the necessary operation is division. 8
When given the part, it always goes first in the division problem.
Part ÷
8 ÷ 40
Whole X
Percent 40

23. Solve
8 ÷ 40
40 cannot divide into 8, when this occurs, add a decimal and zeros as needed. .2
40) 8.0
40) 8
- 80
Changes to:
Steps for division:
Divide
Multiply
Subtract
Bring down
Repeat
The answer is in decimal form and must be changed to a percent.
Remember: To change a decimal to a percent, move the decimal two places to the right.
0.2 changes to
20%
What % of 40 is 8?
20%

24. Guided Practice ÷ 30% of 90 = ______ What % of 30 is 6?
Directions: Solve each problem using the Percent Pyramid. Draw out the pyramid for each problem.
30% of 90 = ______
What % of 30 is 6?
14 is 20% of what number?
Part ÷ X
Whole
Percent

25. Guided Practice ÷ 90 30% Whole 30% of 90 = ______ Part X
Remember to change the percent to a decimal before multiplying. 90
30% X
30% changes to .30
Whole
Percent

26. Guided Practice ÷ 90.0 x 0.30 90 30% 2 7 2 7 2 7. 0 0 0 Whole
30% of 90 = ______ 27
This number with the decimal at the end becomes a whole number and this zeros can be dropped in the answer.
Part ÷
Remember to change the percent to a decimal before multiplying.
90.0
x 0.30 90
30%
30% changes to .30 X
2 7
2 7
Whole
Percent
There are three decimal places in the problem, so include it in the answer.

27. Guided Practice
2. What % of 30 is 6?
Part 6 ÷ 30 X
Whole
Percent

28. Guided Practice 2. What % of 30 is 6? 20% 6 ÷ 30 .2 30) 6.0 - 60
Move the decimal straight up for the answer.
2. What % of 30 is 6?
20% .2
Remember to change the decimal to a percent. (move two places to the right)
6 ÷ 30
Changes to:
30) 6.0
- 60
*The part comes first in a division problem.
30 will not divide into 6.
A decimal point is added then add zeros as needed; in this case only one is needed.

29. Guided Practice ÷ 3. 14 is 20% of what number? 14 20% Whole Part X
Percent

30. 70 Guided Practice 3. 14 is 20% of what number? 14 ÷ 0.2 0.2) 14 7
**The decimal in the divisor must be moved to the right in order to get rid of the decimal.
**The part comes first in a division problem.
0.2) 14
14 ÷ 0.2
Changes to: . 7
2) 140
If the divisor’s decimal is moved 1 place, the dividend’s decimal must also be moved 1 place.
- 14
- 0

31. Steps for solving percent Word problems.
Read the problem.
Determine what the numbers represent.
Is the number the: Part, Whole, or Percent
This will also help determine what the problem wants to know.
Using the percent pyramid, determine what operation is necessary to solve the problem.
Solve.
Ask, “Does this answer make sense?”
There may be another step. BE CAREFUL!

32. 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?

33. What does down payment represent?
Step 2: Determine what the numbers represent.
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.

34. ÷ Step 3: Fill in the percent pyramid. part X whole percent
$146 was the part.
$146 ÷
The percent was also given. 25% X
25%
whole
percent
The pyramid indicates division is the operation needed to solve the problem.
HINT: Don’t forget to change the percent to a decimal!

35. Step 4 : Solving The Problem
Set up the division: Looks like: 00
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.
Another way to say this: what is done to one side must be done to the other side.

36. Step 4: Solving Problem Divide: 25 $14600. - 125 5 8 4 21 200 10 100 4-
200 10
100

37. Step 5: Read the problem again.
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?
What does the question want to know?
The price of the stove.
Is $584 a reasonable price for a stove?
YES

38. 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 1: Read the problem! Step 2: Determine what the numbers stand for. $39.50 was the total cost = whole 20 % = is the percent

39. 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.

40. Step 4: Solve the problem.
Multiply the problem.
After the problem is multiplied, look at the decimal places.
39.50
x .20 7 9 7 9
Changes to $7.90
* Count the number of decimal places in the problem and move the decimal that many places.

41. Step 5: Does the answer make sense?
Our meal was $39.50, but we got a 20% discount because our food was late. What did our meal cost after the discount?
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
$ 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.