Unit 3B REVIEW

What is a ratio?A group of students had a choice of either hamburgers or pizza for lunch. There were 12 students. 5 chose pizza and 7 chose hamburgers for lunch.

What is a ratio (cont.)

• Ratios can be written to show: *part to whole *part to part *whole to part

• Ratios can be written in 3 ways: *with a colon ( : ) *with the word “to” *as a fractions

Write the Ratio in 3 Ways

• triangles to stars

• stars to circles

• stars to shapes

• circles to triangles

22 to 5; 2:5; 5

55 to 3; 5:3; 3

55 to 10; 5:10; 10

33 to 2; 3:2; 2

Ratio - Application

• 12 students tried out for the debate team. 7 students were selected. Write the ratio of students selected to those who tried out.

7:12

Unit Rate

• The value of 1 unit• Divide the total by the part

EX: 450 miles on 15 gallons of gas

450 = 30 miles per gallon15

Find the Unit Rate

A group paid $600 for 12 concert tickets. How much did each ticket cost? $50 per ticket

60012

Find the Unit Rate

400 ounces of ice cream was purchased for 80 students. How many cups of ice cream does each student get?

5 ounces

40080

Equivalent Ratios

• Using the ratio on the previous slide, how much paint would you need to paint two sheds?

• Amount needed to paint 2 sides of a shed.

• 16 red cans; 4 white cans 16: 4

Are the two ratios equivalent?

• 4:2 = 12:6• 5:10 = 1:2• 1:4 = 4:1• 1:2 = 2:3• 3:1 = 9:3• 1:6 = 2:12

Yes

Yes

Yes

Yes

No

No

Proportion

*Two ratios that are equal to each other.

*Can be used to find an unknown value

69 159 6 159 909 909 9

10

h

hhh

h

Solve the Proportion

7 14r

6

42 7w

5 414 a

r = 7 r = 28

7w = 42 67w = 252 7 7 w = 36

5a = 4 145a = 56 5 5 a = 11.2

Solve the Proportion8 409 m

3 12

17v 21 7

4k

8m = 9 408 3608 8

m = 45

m

7k = 4 217k 847 7

k = 12

12v = 3 1712 51 12 12 v = 4.25

v

Solve the Proportion

38 40

n 3

8 4t

38 16

s

8n = 3 408n 1208 8

n = 15

8s = 3 168 488 8

s = 6

s

4t = 3 84 244 4 t = 6

t

Set up a proportion to solve the problem

Ms. Smith’s homeroom has 12 car riders. The ratio of car riders to walkers is 6:3. How many students in Ms. Smith’s homeroom walk to school?

car riders 12 6 = = walkers 3

6x = 3 126 36 = 6 6

x = 6

x

x 6 walkers

Set up a proportion to solve the problem

A recipe calls for 2 eggs to make 10 pancakes. How many eggs will you need to make 35 pancakes?

2 = = 10 35

10x = 2 3510 70 10 10

x = 7

eggs xpancakes

x

7 eggs

Set up a proportion to solve the problem

Brooke drove 50 miles in 2 hours at a constant speed. Use a proportion to figure out how long it took her to drive 150 miles at the same speed.

miles 50 150 = = 2

50x = 150 250 300 = 50 50

x = 6

hour x

x

6 hours

Change a fraction to a decimal

• Divide the numerator by the denominator

numeratordenominator

Write the fraction as a decimal

450

25

38

920

.08 .375

.4 .45

Changing a percent to a fraction

• Write the percent in the numerator and 100 in the denominator. Simplify, if possible.

EX: 78%76 38 19 = =

100 50 25

Write the percent as a fraction

15% 75%

12% 7%

22% 46%

15 3 = 100 20

75 3 = 100 4

12 3 = 100 25

7100

22 11 = 100 50

46 23 = 100 50

Changing a percent to a decimal

• Move the decimal point 2 places to the left

EX: 76% .76

Write as a DECIMAL

27% 17%

6% 105%

8.3% 57.34%

5.64% 18.23%

8% 1.43%

.27 .17

.06 10.5

.083 .5734

.0564 .1832

.08 .0143

Changing a decimal to a percent

• Move the decimal two places to the right• Write a percent sign

EX: .389 38.9

Write as a PERCENT

.52 .02

.5 2

1.2 .25

52% 2%

50% 20%

120% 25%

Write a fraction as a percent

• Set up a percent proportion (equivalent fraction) OR divide the numerator by the denominator and move the decimal 2 places to the right.

EX: 1520

15 ?20 100

? = 75%

Write as a PERCENT

35

2350

910

34

60%

90%

46%

75%

Application

• If Suzanne answers 16 out of 20 questions correctly, what will her final percent grade be?

80%

Application

• 80% of Ms. Chokshi’s students ride the bus. What FRACTION of the class does NOT ride the bus?

20 1 = 100 5

1 of the students don't ride the bus5

Percent of*Change the percent to a decimal*Change of to multiply*Multiply

EX: 25% of 15 (.25)(15) 3.75

42% of 50 9% of 25

12% of 33 7% of 75

(.42)(50) 21

(.09)(25) 2.25

(.12)(33) 3.96

(.07)(75) 5.25

7% of 23 43% of 65 (.07)(23) 1.61

5% of 43 25% of 56

(.43)(65) 27.95

(.05)(43) 2.15

(.25)(56) 14

Discount

• Find the “percent of the original price”. • To find the sale price, subtract the discount

from the original price.

EX: 15% off of a $35 shirt (.15)(35) 5.25 (discount)

35 – 5.25 = $29.75

$29.75

Discount 30% off of a $75 pair of shoesWhat is the discount?(.3)(75)22.5 discount

What is the sales price?75 – 22.5 = 52.50 $52.50

Discount

10% off of a $29.99 Wii gameWhat is the discount?(.10)(29.99)2.99 discount

What is the sale price?29.99 – 2.99 = $27 $27

Tax

• Find the “percent of the original cost”• To find the total cost: add the tax to the

original cost of the item.

EX: 6% sales tax on a Target bill of $75.23 (.06)(75.23) $4.5138 = 4.15 sales tax

75.23 + 4.15 = $79.38$79.38

Tax A snowboard costs $475.

What would be 6% tax? (.06)(475) $28.5

What is the total cost of the snowboard, after tax? 475 + 28.5 $503.50

Tax A book costs $21.49

How much is 6% sales tax? (.06)(21.49) 1.2894 = 1.29 sales tax

What is the total of the book, after tax? 21.49 + 1.29 $22.78

Tip• Find the “percent of the bill”• To find the total bill: add the tip to the original bill.

EX: Jamie’s family ordered pizza. The bill was $25.47. They want to tip the delivery person 15%. What is the total amount they will pay? (.15)(25.47) 3.8205 = $3.82 tip

25.47 + 3.82 = $29.29$29.29

Tip• Ron spent $13.50 on lunch.

He wants to leave a 17% tip. What is the tip? 17% of 13.50 (.17)(13.50) 2.295 $2.30 tip

What is the total amount that Ron spent on lunch? 13.50 + 2.30 = 15.80 $15.80

Tip• Mrs. Skelton and her husband went out to dinner. The bill

was $27.50

• The Skelton’s left a 20% tip. How much did they tip the server?

20% of $27.50 (.2)(27.50) $5.50 tip

What was the total amount they spent on dinner? 5.50 + 27.50 = 33 $33

Circle Graph – How many?• To find the percent – set up a “percent of”

problem.

EX: The answers of 25 students are shown on a circle graph. Eight percent of the students said their favorite color is blue. How many students like the color blue? 8% of 25

(.08)(25) 22 students

Green38%

Red16%

Pink25%

yellow13%

purple9%

Favorite Color

• How many people like green the best?

(.37)(32) = 11.8412 people• How many people like pink

the best?(.25)(32) = 88 people• How many people like

yellow the best?(.09)(32) = 2.883 people32 people

Circle Graph - degrees

• To find the degrees – set up as percent of 360°

EX: The answers of 25 students are shown on a circle graph. Eight percent of the students said their favorite color is blue. What would be the measurement of the blue section on the circle graph? 8% of 360

(.08)(360) 28.8 29

Green38%

Red16%

Pink25%

yellow13%

purple9%

Favorite Color

• How many degrees is the green section?

(.37)(360) = 133.2133°• How many degrees is the

red section?(.16)(360) = 57.658°• How many degrees is the

purple section?(.09)(360) = 32.432°32 people