Post on 04-Apr-2018
7/29/2019 pre-algebra chapter 6 notes.ppt
1/74
41
0011 0010 1010 1101 0001 0100 1011
PRE-ALGEBRACHAPTER 6
January 2013
7/29/2019 pre-algebra chapter 6 notes.ppt
2/74
41
0011 0010 1010 1101 0001 0100 1011
Ratios &
Unit Rates
7/29/2019 pre-algebra chapter 6 notes.ppt
3/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
Ratio: a comparison of two quantities by
division
Unit Rate: the rate for one unit of a given
quantity
7/29/2019 pre-algebra chapter 6 notes.ppt
4/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
1. 14 to 6
7/29/2019 pre-algebra chapter 6 notes.ppt
5/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
2. 7:21
7/29/2019 pre-algebra chapter 6 notes.ppt
6/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
4. 4:10
7/29/2019 pre-algebra chapter 6 notes.ppt
7/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
5. 15 cats : 50 dogs
7/29/2019 pre-algebra chapter 6 notes.ppt
8/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
6. 21 hired out of 105 applicants
7/29/2019 pre-algebra chapter 6 notes.ppt
9/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
7. 66 miles on 4 gallons
7/29/2019 pre-algebra chapter 6 notes.ppt
10/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
8. 48 wins : 18 losses
7/29/2019 pre-algebra chapter 6 notes.ppt
11/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Write each ratio as a fraction in simplest form.
10. 22 players : 2 teams
7/29/2019 pre-algebra chapter 6 notes.ppt
12/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
11. 96 students in 3 buses
7/29/2019 pre-algebra chapter 6 notes.ppt
13/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
13. $52.50 in 7 hours
7/29/2019 pre-algebra chapter 6 notes.ppt
14/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
14. 416 miles in 8 hours
7/29/2019 pre-algebra chapter 6 notes.ppt
15/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
15. $94.99 for 7 pizzas
7/29/2019 pre-algebra chapter 6 notes.ppt
16/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
16. 103.68 miles in 7.2 hours
7/29/2019 pre-algebra chapter 6 notes.ppt
17/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each ratio in simplest form.
17. Dena counted 14 robins
out of 150 birds.
7/29/2019 pre-algebra chapter 6 notes.ppt
18/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Express each rate as a unit rate.
18. Mr. and Mrs. Romero bought a 1,200square-foot house for $111,600. How much did
they pay per square foot?
7/29/2019 pre-algebra chapter 6 notes.ppt
19/74
41
0011 0010 1010 1101 0001 0100 1011
SolvingProportions
7/29/2019 pre-algebra chapter 6 notes.ppt
20/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
Proportion: a statement of equality of tworatios
Cross Product: the product of two numbers
on the diagonal when comparing two ratios
7/29/2019 pre-algebra chapter 6 notes.ppt
21/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Tell whether each pair of ratios isproportional.
7/29/2019 pre-algebra chapter 6 notes.ppt
22/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Tell whether each pair of ratios isproportional.
7/29/2019 pre-algebra chapter 6 notes.ppt
23/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Tell whether each pair of ratios isproportional.
7/29/2019 pre-algebra chapter 6 notes.ppt
24/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Tell whether each pair of ratios isproportional.
7/29/2019 pre-algebra chapter 6 notes.ppt
25/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
26/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
27/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
28/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
29/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
30/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
31/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
32/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
33/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.
7/29/2019 pre-algebra chapter 6 notes.ppt
34/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.One hundred nautical miles equals about 115 standard,
or statute, miles. How many statute miles equal 381
nautical miles? Round your answer to the nearest whole
number.
7/29/2019 pre-algebra chapter 6 notes.ppt
35/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.One hundred rods is about 275 fathoms. About how
many fathoms is 25 rods?
7/29/2019 pre-algebra chapter 6 notes.ppt
36/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.At the Copy Shoppe, 18 copies cost $1.08. at this rate,
how much will 40 copies cost?
7/29/2019 pre-algebra chapter 6 notes.ppt
37/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.On a recent day, the exchange rate for U.S. dollars to
European euros was 1.32 dollars per euro. On that day,
about how many euros would you get for 25 dollars?
7/29/2019 pre-algebra chapter 6 notes.ppt
38/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Solve each proportion.Recently, the exchange rate for Mexican pesos to U.S.
dollars was 10.737 pesos = 1 dollar. If you were
vacationing in Mexico and had 250 pesos left, how many
dollars would you receive?
7/29/2019 pre-algebra chapter 6 notes.ppt
39/74
41
0011 0010 1010 1101 0001 0100 1011
7/29/2019 pre-algebra chapter 6 notes.ppt
40/74
41
0011 0010 1010 1101 0001 0100 1011
Similar Figures
Similar figures have same shape, not
necessarily same size.
Corresponding angles have equal measuresCorresponding sides are in proportion
Indirect measurement = using similar figures tocompute distances that are difficult to measure
directly.
7/29/2019 pre-algebra chapter 6 notes.ppt
41/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
Scale Drawing: a two-dimensional drawing thataccurately represents an object. (It is mathematically similar
to the object.)
Scale: gives the ratio of the dimensions in the drawing tothe dimensions of the object.
Scales can use the same units or different units.
All dimensions are reduced or enlarged using the same
scale.
7/29/2019 pre-algebra chapter 6 notes.ppt
42/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
Reduction: a scale drawing that is smaller than the actualobject
Enlargement: a scale drawing that is larger than the
actual object
7/29/2019 pre-algebra chapter 6 notes.ppt
43/74
41
0011 0010 1010 1101 0001 0100 1011
ExamplesThe scale of a drawing is in = 12 ft.
Find the actual measurement.
8 inches
7/29/2019 pre-algebra chapter 6 notes.ppt
44/74
41
0011 0010 1010 1101 0001 0100 1011
ExamplesThe scale of a drawing is in = 12 ft.
Find the actual measurement.
18 inches
7/29/2019 pre-algebra chapter 6 notes.ppt
45/74
41
0011 0010 1010 1101 0001 0100 1011
ExamplesThe scale of a drawing is 2 cm = 15 m.Find the length each measurement would be on a scale drawing.
225 m
7/29/2019 pre-algebra chapter 6 notes.ppt
46/74
41
0011 0010 1010 1101 0001 0100 1011
ExamplesThe scale of a drawing is 2 cm = 15 m.Find the length each measurement would be on a scale drawing.
622.5 m
7/29/2019 pre-algebra chapter 6 notes.ppt
47/74
41
0011 0010 1010 1101 0001 0100 1011
6-4 Fractions, Decimals, Percents
Percent = ratio that compares a number to 100
Write as a fraction or mixed number 5%
125%
58%
72%
144%
7/29/2019 pre-algebra chapter 6 notes.ppt
48/74
41
0011 0010 1010 1101 0001 0100 1011
Write as a decimal
1.5%
62.5%
125%
45%
7/29/2019 pre-algebra chapter 6 notes.ppt
49/74
41
0011 0010 1010 1101 0001 0100 1011
Write Each Decimal as a Percent
0.333
METHOD 1 = REWRITE AS AFRACTION
METHOD 2 = MOVE DECIMAL POINT
7/29/2019 pre-algebra chapter 6 notes.ppt
50/74
41
0011 0010 1010 1101 0001 0100 1011
Write each decimal as a percent
0.4
0.023
1.75
7/29/2019 pre-algebra chapter 6 notes.ppt
51/74
41
0011 0010 1010 1101 0001 0100 1011
Write a Fraction as a Percent
5/16
3/11
7/29/2019 pre-algebra chapter 6 notes.ppt
52/74
41
0011 0010 1010 1101 0001 0100 1011
Proportions and Percents
Find 65% of 245
7/29/2019 pre-algebra chapter 6 notes.ppt
53/74
41
0011 0010 1010 1101 0001 0100 1011
Proportions and Percents
Find 25% of 124
Find 43% of 230
Find 12.5% of 80
7/29/2019 pre-algebra chapter 6 notes.ppt
54/74
41
0011 0010 1010 1101 0001 0100 1011
Finding a Percent
What percent of 60 is 52?
What percent of 250 is 138?
14 is what percent of 15?
7/29/2019 pre-algebra chapter 6 notes.ppt
55/74
41
0011 0010 1010 1101 0001 0100 1011
Finding a Whole Amount
207 is 46% of what number?
19 is 75% of what number?
310 is 99% of what number?
7/29/2019 pre-algebra chapter 6 notes.ppt
56/74
41
0011 0010 1010 1101 0001 0100 1011
Percents in Equations
What is 85% of 62?
What percent of 48 is 54?
What is 145.5% of 20?
7/29/2019 pre-algebra chapter 6 notes.ppt
57/74
41
0011 0010 1010 1101 0001 0100 1011
Commission Problem
A real estate agent makes a 4.5%
commission on property she sells. How
much commission does she make on thesale of a house that sells for $132,500.
7/29/2019 pre-algebra chapter 6 notes.ppt
58/74
41
0011 0010 1010 1101 0001 0100 1011
Solving a Percent Problem
In a survey, 952 people, or 68%, preferred
smooth peanut butter to crunchy. How
many people were surveyed?
7/29/2019 pre-algebra chapter 6 notes.ppt
59/74
41
0011 0010 1010 1101 0001 0100 1011
Percent ofChange
Seventh Grade
Mrs Dishman
7/29/2019 pre-algebra chapter 6 notes.ppt
60/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
Percent of Change: the amount, stated as a percent, that a
number increases or decreases
Percent of Increase: a percent change describing anincrease in quantity; when the amount goes up
Percent of Decrease: a percent change describing andecrease in quantity; when the amount goes down
fi i i
7/29/2019 pre-algebra chapter 6 notes.ppt
61/74
41
0011 0010 1010 1101 0001 0100 1011
Key Definitions
To Find % of Change
Amount of change
Original amount
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
62/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
1.) from 100 to 114
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
63/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
2.) from 2.0 to 3.2
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
64/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
3.) from 4,000 to 8,500
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
65/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
5.) 202 to 192
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
66/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
6.) 96 to 78
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
67/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
7.) 77 to 13
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
68/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
9.) 38 to 95
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
69/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
10.) 60.3 to 95
E l
7/29/2019 pre-algebra chapter 6 notes.ppt
70/74
41
0011 0010 1010 1101 0001 0100 1011
Examples
Find each percent of change. Round the answers to the
nearest tenth of a percent, if necessary.
11.) -7 to -10
7/29/2019 pre-algebra chapter 6 notes.ppt
71/74
41
0011 0010 1010 1101 0001 0100 1011
Markup and Discount
MARKUP = amount of increase a store puts
on an item.
A music stores percent of markup is 67%.A CD costs the store $10.15. Find the
markup.
7/29/2019 pre-algebra chapter 6 notes.ppt
72/74
41
0011 0010 1010 1101 0001 0100 1011
Markup and Discount
A computer store pays $6 for a computer
mouse. The percent of markup is 75%.
Find the mouses selling price.
7/29/2019 pre-algebra chapter 6 notes.ppt
73/74
41
0011 0010 1010 1101 0001 0100 1011
Markup and Discount
When an item goes on sale, the amount of
the price decrease is the discount.
Athletic shoes that are regularly $85.99 areon sale for 20% off. Find the discount.
7/29/2019 pre-algebra chapter 6 notes.ppt
74/74
41
0011 0010 1010 1101 0001 0100 1011
6-9 Applications of Rational
Numbers Examples provided in class..