1. Chapter 6 and 7-8 Notes

2. 6-1 Ratios and Unit Rates
Ratio = comparison of 2 quantities by division
Example: 10 to 15
10 : 15
10/15

3. Write each ratio as a fraction in simplest form
Examples: 9/27
3 out of 12 people live in a rural area
70 homes out of 125 have a personal computer

4. Finding rates and unit rates
Rate = a ratio that compares quantities in different units
Unit rate = a rate that has denominator of 1. For example: unit cost, gas mileage, and speed.

5. Find each unit rate Examples: 1. Two liters of spring water cost $1.98
2. A car goes 425 miles on 12.5 gallons of gas.

6. Find each unit rate - answers
Examples:
1. Two liters of spring water cost $1.98
$.99 per liter
2. A car goes 425 miles on 12.5 gallons of gas.
34 miles per gallon
A skydiver falls 144 ft in 3 seconds.

7. Converting a Rate 42 gallons in 7 mins. 676 miles in 13 hours
Which is a better buy?
12 fl oz for $1.08 or
20 fl oz for $2.20

8. Converting a Rate - answers
A skydiver falls 144 ft in 3 seconds. 48 ft/s
42 gallons in 7 mins. 6 gal/min
676 miles in 13 hours 52 mi/h
Which is a better buy?
12 fl oz for $1.08 or $.09/fl oz
20 fl oz for $ $.11/ fl oz

9. 6-2 Proportions Proportion = is an equality of 2 ratios
Cross products = multiply diagonally across the equal sign
In proportions, cross products are equal
Example: 6/9 = 8/12
6 x 12 = 9 x 8 = 72

10. Using Cross Products to Solve a Proportion
Example: x/9 = 4/6
H/9 = 2/3
4/5 = p/55
3. Y/36 = 21/27

11. Using Cross Products to Solve a Proportion- answers
Example: x/9 = 4/6 x=6
22/D = 6/21 D=77
4/5 = p/55 p=44
3. Y/36 = 21/27 Y=28

12. Testing for a Proportion
Do the ratios 4/6 and 10/14 form a proportion?
More examples: 6/9 and 4/6
15/20 and 5/7

13. 6-3 Similar Figures and Scale Drawings
Similar figures = have the same shape but not necessarily the same size
Similar figures have corresponding angles and corresponding sides
Corresponding angles are equal
Corresponding sides are proportional

14. Similar Figures
Open book to page 304.

15. Scale Drawing
Scale Drawing = an enlarged or reduced drawing that is similar to and actual object or place
Use a proportion or ratio to help find the actual measurements of a picture or object

16. Using Scale Drawings
Open book to page 305.

17. Examples:
The scale of a map is 1/5 inch for every 6 miles. Find the actual distance of these examples:
1 in
2.5 in
5 in

18. Examples:-answers
The scale of a map is 1/5 inch for every 6 miles. Find the actual distance of these examples:
1 in - 30 miles
2.5 in – 75 miles
5 in – 150 miles

19. 6-4 Probability Outcomes - the possible results of an action
Example: There are 6 outcomes when rolling a single number cube; 1,2,3,4,5,6
Event - any outcome or group of outcomes; the outcomes are called favorable outcomes

20. Probability Probability - when outcomes are equally likely
Probability of an event = P(event) = # of favorable outcomes
# of possible outcomes

21. Finding Probability Find P(rolling an even number):
# of favorable outcomes = 3 = 1
# of possible outcomes
Find: P(2)
P(5 or 6)

22. Finding Probability-answers
Find P(rolling an even number):
# of favorable outcomes = 3 = 1
# of possible outcomes
Find: P(2) = 1 6
P(5 or 6) = 2 = 1

23. Finding Odds
Think of probability as a part/whole = this is called odds - this describes the likelihood of an event
Odds in favor of an event =
# of favorable outcomes
# of unfavorable outcomes
Odds against an event =
# of favorable outcomes

24. Examples
Find the odds in favor of choosing a marble from 4 red, 5 blue, 6 yellow
Blue = 5/10
Red
Not red or yellow

25. Examples-answers
Find the odds in favor of choosing a marble from 4 red, 5 blue, 6 yellow
Blue = 5/10
Red = 4/11
Not red or yellow = 5/10

26. 6-5 Fractions, Decimals, and Percents
Percent - a ratio that compares a number to 100
Write a percent as a fraction:
5% = 5/100 = 1/20
125% = 125/100 = 5/4 = 1 1/4
Examples: 58% 72% 144%

27. 6-5 Fractions, Decimals, and Percents- answers
Percent - a ratio that compares a number to 100
Write a percent as a fraction:
5% = 5/100 = 1/20
125% = 125/100 = 5/4 = 1 1/4
Examples: 58% = 29/50 72% = 18/25 144% = 36/25

28. Writing a number as a percent
0.333 = 333/1000 = 33.3/100 = 33.3%
7/80
46/200
1.75

29. Writing a number as a percent-answers
0.333 = 333/1000 = 33.3/100 = 33.3%
7/80 = 8.75%
46/200 = 23%
1.75 =175%

30. Ordering Rational Numbers
To compare and order fractions, decimals, or percents, write each fraction or percent as a decimal.
Order from least to greatest 0.35, 2/5, 30%, 53%
Order from least to greatest 88%, 91%, 5/6, 0.71

31. Ordering Rational Numbers-answers
To compare and order fractions, decimals, or percents, write each fraction or percent as a decimal.
Order from least to greatest 0.35, 2/5, 30%, 53%
30%, .35, 2/5, 53%
Order from least to greatest 88%, 91%, 5/6, = .71, 5/6, 88%, 91%

32. 6-6 Proportions and Percents
You can solve a percent problem by writing and solving a proportion.
IS = %
OF 100

33. Write and solve a proportion
8 is 25% of ?
31 is 49% of ?
Find 60% of 15

34. Write and solve a proportion-answers
8 is 25% of ?
25/100 = 8/x; x=32
31 is 49% of ?
49/100 = 31/x; x=63.3
Find 60% of 15
60/100 = x/15; x=9

35. Word Problems
A bicycle cost $250 last year. The same bike costs $200 this year. What percent of last year’s cost is this year’s costs?
You invested some money and made $55. Your profit was 11% of your investment. How much did you invest?

36. Word Problems-answers
A bicycle cost $250 last year. The same bike costs $200 this year. What percent of last year’s cost is this year’s costs?
200/250 = x/100; x=80%
You invested some money and made $55. Your profit was 11% of your investment. How much did you invest?
11/100 = 55/x; x=500

37. 6-7 Percents and Equations
Percent equations are still using the following formula:
IS = %
OF 100

38. Examples
An agent makes 16% commission on an athlete’s signing bonus. If the bonus is $26,000, what is the agent’s commission?
Todd bought a stock at $20 per share and sold it at $27 per share. What percent profit did he make?

39. Examples-answers
An agent makes 16% commission on an athlete’s signing bonus. If the bonus is $26,000, what is the agent’s commission?
(.16)(26000)= x; x=4160
Todd bought a stock at $20 per share and sold it at $27 per share. What percent profit did he make?
20x = 27; x=1.35 change to percent 135%

40. 6-8 Percent of Change
Percent of change = the percent a quantity increases or decreases from its original amount
Percent of change = amount of change
original amount

41. Examples Find the percent of increase or decrease: From 4 to 7.5

42. Examples-answers Find the percent of increase or decrease:
From 4 to % increase
From 1500 to % decrease
From 4.5 to % decrease

43. Word Problems
In 10 years, the average number of hours of TV watched per week by teenagers dropped from 25.6 to Find the percent of change.
Bob was earning $8.50 per hour when he got a 5% increase in pay. What was his rate of pay after the increase?

44. Word Problems-answers
In 10 years, the average number of hours of TV watched per week by teenagers dropped from 25.6 to Find the percent of change.
=28.9%
Bob was earning $8.50 per hour when he got a 5% increase in pay. What was his rate of pay after the increase?
$8.93

45. 6-9 Markup and Discount
To make a profit, stores charge more for merchandise than they pay for it.
The amount of increase is called markup.

46. How to find the % of markup
Use a proportion to find the % of markup.
Example: A music store’s percent of markup is 67%. A CD costs the store $ Find the markup and selling price.
A $5 cap has a 70% markup. Find the markup and selling price.

47. How to find the % of markup-answers
Use a proportion to find the % of markup.
Example: A music store’s percent of markup is 67%. A CD costs the store $ Find the markup and selling price.
markup-$6.80 selling price-$16.95
A $5 cap has a 70% markup. Find the markup and selling price.
markup-$3.50 selling price - $8.50

48. Discount
When an item goes on sale, the amount of the price decreases is called the discount.
Sale price = regular price - discount

49. How to find the % of discount
Example: Athletic shoes that regularly sell for $85.99 are on sale for 20%. Find the discount and selling price.
Pants priced at $21.99 are marked 15% off. Find the discount and selling price.

50. How to find the % of discount-answers
Example: Athletic shoes that regularly sell for $85.99 are on sale for 20%. Find the discount and selling price.
discount-$17.20 selling price-68.79
Pants priced at $21.99 are marked 15% off. Find the discount and selling price.
Discount selling price-18.69

51. 7-8 Simple and Compound Interest
When you first deposit money in a savings account, your deposit is called principal.
The bank takes the money and invests it. In return, the bank pays you interest based on interest rates.
Simple interest is interest paid only on the principal.

52. Simple interest formula
I = prt
I = interest
P = principal
R = interest rate per year
T = time in years