unit 3b review
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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 - PowerPoint PPT PresentationTRANSCRIPT
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