4. WHAT IS A PERCENT?
A percent 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
Percent literally means “per 100”
5. Decimal and percents both express portions of a whole
number and are both used used everyday.
For Example: grocery stores and department stores
Mayo – $2.99
Pickles – $2.49 ea or 2/ $4.00
Olive Oil - $6.49
Shoes – 25% off
6. PERCENTS AND MONEY
$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
Practice: dimes in her pants pocket, what
percent of a dollar does she have?
25 + 25 + 10 +10 + 10 = 80 80%
7. WHAT IS 100%?
100% stands for one whole object.
Practice:
What percent of the box is 13 squares out
shaded? of 100 are
shaded. 13%
What percent of the box is
not shaded? 87 squares out of
100 are not shaded. 13 + 87 = 100
87%
8. CHANGING A PERCENT TO A DECIMAL
When solving a percent problem, the percent
must be changed to a decimal.
Change to a decimal: 52%
9. STEPS FOR CHANGING A PERCENT TO A DECIMAL
1) Take away the percent sign.
52 %
2) Change the % sign to a decimal point.
52 .
10. 3) Move the decimal two places to the left.
52.
52% changed to a decimal becomes:
0 . 52
4) After the decimal is moved and no digit is at the front of
the decimal, use a zero (0) as a placeholder. The zero will
be to the left of the decimal point.
11. STEPS TO CHANGE A DECIMAL TO A PERCENT
Change 0.34 to a percent
1) Move the decimal two places to the
right.
0.34
2) After the decimal is moved two places
to the right, the point is changed back to
a percent sign.
34.
3) Place the % sign after the number 34%
12. GUIDED PRACTICE- BOARDS OR PAPER
Change to a percent
1. 0.23 = ________
2. 0.84 = ________
3. 0.02 = ________
Change to a decimal
1. 78% = ________
2. 45% = ________
3. 5% = ________
13. GUIDED PRACTICE
Change to a percent
1. 0.23 = __23%___
2. 0.84 = __84%___
3. 0.02 = __2%____
Change to a decimal
1. 78% = ___.78___
2. 45% = ___.45___
3. 5% = ___.05____
14. Write each decimal as Write each percent as a
a percent decimal
0.14 25%
0.4 100%
6 72%
0.013 7%
0.26 33%
0.7
15. PERCENT PROBLEMS CONTAIN THREE IMPORTANT NUMBERS:
Part follows the word is
Whole follows the word of
PercentIndicated by a percent sign (%) or the
word percent
16. WHEN SOLVING PERCENT PROBLEMS: IDENTIFYING
THE NUMBERS
Example: 75% of 24 is 18.
Percent Whole Part
17. The following charts provide key words that will
help identify what each number represents in a
word problem.
Whole Part
Follows the word “of” Follows the word “is”
Discounted Price
Original
Interest
Principal
Down Payment
Beginning
Amount Paid
Overall
Taxes
Tips
18. 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
19. Finding the Part
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 30%
60 x 0.30=18 18 is the part
20. Finding the Whole
When given the part, it
25% of what number is 33 = always goes first in the
This is asking what is the whole if 25% of the whole is 33. division problem. (Top to
Bottom on the pyramid)
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% 0.25) 33.
25% of what number is 33 =132
21. Finding the Percent
What % of 40 is 8? 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
Part in the division problem.
÷
8 ÷ 40= 0.2
Whole X Percent
0.2 changes to 20%
40
What % of 40 is 8? 20%
22. GUIDED PRACTICE
Directions: Solve each problem using the Percent Pyramid.
Draw out the pyramid for each problem.
1. 30% of 90 = ______
2. What % of 30 is 6? Part
3. 14 is 20% of what number?
÷
X
Whole Percent
23. ANSWERS
30% of 90 = ______
Remember to change
Part the percent to a decimal
before multiplying.
÷ 30% changes to .30
90 30% 90 x .30 = 27
X
Whole Percent 30% of 90 = 27
24. ANSWERS
2. What % of 30 is 6?
Part ÷ Whole = Percent
6 ÷ 30 = .2
Part
The question asks for the
6 Percent, so we move the
÷ decimal two places to the right
to get
30
20%
X
Whole Percent
25. ANSWERS
3. 14 is 20% of what number?
Part ÷ Percent = Whole
Part Remember to use the decimal form!
14
14 ÷ 0.2 = 70
÷
X 20%
Whole Percent
27. STEPS FOR SOLVING PERCENT WORD PROBLEMS.
1. Read the problem.
2. Determine what the numbers represent.
a. Is the number the: Part, Whole, or Percent
b. 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!
28. 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?
29. 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?
What does the $146 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.
30. Step 3: Fill in the percent pyramid.
$146 was the part. 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!
STEP 4 : SOLVING THE PROBLEM
31. 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
32. 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
33. Step 3: Draw and fill in the triangle.
Notice that you have both numbers part
on the bottom of the triangle. When ?
this happens, you simply multiply.
÷
$39.50 X 20%
whole percent
34. STEP 4: SOLVE THE PROBLEM.
Multiply the problem.
39.50
x .20
7.90
35. 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.
Our question was what did our meal cost after the discount.
Check to make sure that your answer is reasonable.
Is $7.90 reasonable?
NO- because we got only a 20% discount. If we paid $7.90 for
our meal, then the discount would have had to be bigger.
So we need to subtract:
39.50-7.90=31.60
This is how much we paid.
36. MORE WORD PROBLEMS
Mr. Gomez pays his supplier $80 for a jacket. He
puts a 30% markup on each jacket for his
customers. Find the amount of the markup.
What do we have?
$80 is the whole
30% is the percent
So we are looking for the part.
To find the part we calculate 30% of $80
Change 30% to a decimal 30%=.30
Multiply
0.3 x $80 = $24 The markup is $24.
37. Lois got a 6% commission for selling a house. Her
commission was $7,200. Find the selling price of
the house.
What do we have?
6% is the percent
$7,200 is the part
So we are looking for the whole.
Remember to change 6% to a decimal 6% = 0.6
To find the whole we divide
7200/.06 = 120,000
So the cost of the house was $120,000
38. IXL Resources
Calculate tax, tip and markup Level H.G.7
Percent Word Problems Level K.D.3
Find the Percent: Level K.D.7
Homework
Keys Page 18, 20, 21– Percents
43. Ratios are comparisons made between two sets
of numbers.
For example:
There are 8 girls and 7 boys in a class.
The ratio of girls to boys is 8 to 7.
44. Ratios are used everyday. They are used for:
Miles per hour
The cost of items per pound, gallon, etc.
Hourly rate of pay
80 miles to 1 hour = 80mph
45. 1. Write the ratio using the word “to” between the two
numbers being compared.
For example: There are 8 girls and 5 boys in a math
class. What is the ratio of girls to boys?
The ratio is: 8 girls to 5 boys
8 to 5
46. 2. Write a ratio using a colon between the two
numbers being compared.
For example: There are 3 apples and 4 oranges in the
basket. What is the ratio of apples to oranges?
The ratio is: 3 apples to 4 oranges.
3:4
47. 3. Write a ratio as a fraction.
For example:
Hunter and Brandon were playing basketball. Brandon
scored 5 baskets and Hunter scored 6 baskets. What
was the ratio of baskets Hunter scored to the baskets
Brandon scored?
The ratio of baskets scored was:
6 baskets to 5 baskets
6
5
48. Directions: Write the ratio in three different ways.
There are 13 boys and 17 girls in sixth grade.
Find the ratio of boys to the girls in sixth grade.
13
13 to 17 13 : 17
17
49. 1. When writing ratios, the numbers should be
written in the order in which the problem asks for
them.
For example: There were 4 girls and 7 boys at the birthday
party. What is the ratio of girls to boys?
Hint: The question asks for girls to boys; therefore, girls will be listed
first in the ratio.
4 girls
4 girls to 7 boys 4 girls : 7 boys
7 boys
50. Example: There were 4 girls and 7 boys at the
birthday party. What is the ratio of boys to girls?
Hint: The question asks for boys to girls, so boys must be listed first
in the ratio.
7 boys
7 boys to 4 girls 7 boys : 4 girls
4 girls
51. Directions: Solve and write ratios in all three forms.
1. The Panthers played 15 games this season. They won 13
games. What is the ratio of games won to games played?
The questions asks for Games won to Games played.
13
13 to 15 13:15
15
52. 2. Amanda’s basketball team won 7 games and lost 5.
What is the ratio of games lost to games won?
Games lost = 5 to Games won = 7
5 to 7 5:7 5
7
53. Ratios can be reduced without changing their
relationship.
2 boys to 4 girls =
1 boy to 2 girls =
54. Steps:
1. Read the word problem.
2. Set up the ratio.
For example:
You scored 40 answers correct out of 45 problems on a
test. Write the ratio of correct answers to total questions in
lowest form.
Step 1: Read the problem. What does it want to know?
40 to 45 40 : 45 40
45
55. Step 3. Reduce the ratio if necessary.
Reduce means to break down a fraction or ratio into the
lowest form possible.
Reduce = smaller number; operation will always be division.
HINT: When having to reduce ratios, it is better to set up the ratio in the
vertical form. (Fraction Form)
Determine the largest
40
40 to 45 = number possible that will go
45
into both the numerator and
denominator. Then divide.
Look at the numbers in the ratio. What ONE
number can you divide BOTH numbers by?
40 ÷ 5 = 8
45 ÷ 5 = 9
56. Guided Practice:
Directions: Solve each problem. Remember to reduce.
1. There are 26 black cards in a deck of playing cards. If there are 52
cards in a deck, what is the ratio of black cards to the deck of cards?
Step 1: Read the problem. (What does it want to know?)
Step 2: Set up the ratio.
26 black cards to 52 cards
Step 3: Can the ratio be reduced? If so, set it up like a fraction.
26 ÷ 26 = 1
52 ÷ 26 = 2
57. Example: Kelsey has been reading Hunger Games for
class. She read 15 chapters in 3 days. What is the
ratio of chapters read to the number of days she read?
15 chapters to 3 days
15 ÷ 3 = 5
÷ =
3 3 1
Hint: When a one is on the
bottom, it must remain there. If
the one is dropped, there is no
longer a ratio.
58. To determine a proportion true, cross multiply.
For example:
4 = 20
If the cross products
5 25 are equal, then it is a
true proportion.
20 x 5 = 4 x 25
100 = 100
The cross products were equal, therefore
4 and 20 makes a true proportion.
5 25
60. For Example: Eric rode his bicycle a total of 52 miles in 4
hours. Riding at this same rate, how far can he travel in 7
hours?
Look for the two sets of You have 52 miles in 4 Then, you have 7 hours.
ratios to make up a hours. This is the first The problem is missing
proportion. ratio. the miles. Thus, the miles
becomes the variable.
52 miles
4 hours n miles
7 hours
The proportions should be
set equal to each other. 52 = n
4 7
61. When solving proportions, follow these rules:
1. Cross multiply.
2. Divide BOTH sides by the number connected to the variable.
3. Check the answer to see if it makes a true proportion.
Since the 4 is connected
From our example:
52 n to the variable, DIVIDE
= both sides by the 4.
4 7
4 x n = 52 x 7
Check your answer!
Which number is
connected to the 4n = 364
52 = 91
variable? 4 4
4 7
n = 91 miles
52 x 7 = 91 x 4
4 ÷ 4 = 1; therefore you are left 364 = 364
with “n” on one side. If it comes out equal, then
the answer is correct.
62. Example: Justin’s car uses 40 gallons of gas to drive
250 miles. At this rate, approximately, how many
gallons of gas will he need for a trip of 600 miles.
40 gal x gal 40 x
250 mi = 600mi 250 = 600
Cross Multiply: 250x = 24000
Divide: 250x = 24000
250 250
x = 96
Check:
40 96
250 = 600
24000 = 24000
63. 2. If a 3 gallon jug of milk cost $9, how many 3
gallon jugs can be purchased for $45?
1 jug = n jugs
9 dollars 45 dollars
9n = 45
9n = 45
9 9 1 n
=
n=5 9 45
Check: n=5
5 jugs of milk can be 1 5
purchased for $45 =
9 45
45 = 45
64. 3. On Thursday, Karen drove 400 miles in 8 hours. At this
same speed, how far can she drive in 12 hours?
400 miles = x miles
8 hours 12 hours
400 x_
=
8 12
400 x_
=
8 12
8x = 4800
x = 600 miles
65. 4. Susie has two flower beds in which to plant tulips and
daffodils. She wants the proportion of tulips to daffodils to be
the same in each bed. Susie plants 10 tulips and 6 daffodils in
the first bed. How many tulips will she need for the second bed
if she plants 15 daffodils?
10 tulips = x tulips
6 daffodils 15 daffodils
10 x
= Check: x = 25 tulips
6 15
10 x_
6x = 150 = 15
6
10 25
6x 150 = 15
= 6
6 6
x = 25 150 = 150
66. IXL.com
◦ Ratios
Level H. AA.1
Level H. AA.3
Level H. AA.4
◦ Proportions
Level K.C.5
Level K.C.6
Worksheet:
◦ Keys pg 24-25
◦ Tabe 96-98
68. VOCABULARY
Numerator: The top number of a fraction
Denominator: The bottom number of a fraction
Reduce/simplify: these words both mean to break a
fraction down to its simplest form.
Proper fraction: A fraction where the top number is
smaller than the bottom number.
69. REDUCING PROPER FRACTIONS
In order to reduce proper fractions you need to find a
number that will divide evenly into both the numerator
and the denominator (The number cannot be one).
2 ÷2 = 1
4 ÷2 = 2
In the above example, two will divide evenly into both the
numerator and the denominator. Two divided by two
equals one and four divided by two equals two. The final
reduced fraction is
1
2
70. TIPS FOR REDUCING FRACTIONS
If both the numerator and denominator are even
numbers, reduce them both by 2.
If both the numerator and denominator end in zero,
divide them both by 10.
If one number ends in 5 and the other ends in 0,
divide them both by 5.
Also check to see if the numerator divides evenly
into the denominator.
71. GUIDED PRACTICE
Reduce the following fractions
6 ÷ 6= 3 ÷ 3=
1) 12 ÷ 6 = 2) 9 ÷ 3=
8 ÷ 2= 12 ÷ 4 =
3) 4) 16 ÷ 4 =
10 ÷ 2 =
We chose a number for you that divides
evenly into the numerator and denominator.
72. TRY IT ON YOUR OWN!
Reduce the following fractions
5 3 4
1) 2) 3)
15 12 10
Keep going, but remember to show your division.
4) 14 5) 10 6) 15 7) 25
21 20 35 30
8) 12 9) 27 10) 14 11) 28
28 36 22 42
73. ADDING AND SUBTRACTING FRACTIONS
WITH THE SAME DENOMINATORS
When you add and subtract fractions with common
denominators (the bottom numbers are the same),
just add or subtract the top numbers. Remember to
keep the bottom numbers the same.
1 2 3
Ex. 4 + 4 = 4
After you have solved the problem, make
sure your answer does not need to be reduced.
75. MULTIPLYING FRACTIONS
When you multiply fractions just multiply across the
top and across the bottom. Don’t forget to reduce
your answer.
1 2 2
2 x 3 = 6 reduce your answer
Two will fit into both two and six therefore your
answer is: 1
3
