~ Chapter 4 ~
Solving & Applying Proportions
Lesson 4-1 Ratios & Proportions
Lesson 4-2 Proportions & Similar Figures
Lesson 4-3 Proportions & Percent Equations
Lesson 4-4 Percent of Change
Lesson 4-5 Applying Ratios to Probability
Lesson 4-6 Probability of Compound Events
Chapter Review
Ratios & Proportions
Cumulative Review
Ratios & Proportions
Notes
A ratio is a comparison of 2 numbers by division. It
is represented as a:b or a/b where b ≠ 0.
A unit rate is a ratio in which the denominator is 1.
If a 25 oz. box of cereal costs $3.59 and a 17 oz
box of cereal costs $2.99, determine the unit rate
for each. Which is the better buy?
Proportion – shows two ratios that are equal.
a/b = c/d, where b ≠ 0 & d ≠ 0
You can solve proportions by multiplying by the LCD
or using cross products!
Ratios & Proportions
Practice 4-1
Proportions & Similar Figures
Notes
Similar Figures – same shape but not necessarily the same size. “~” means
“similar to”. In similar figures… corresponding angles are congruent and
corresponding sides are proportional.
In the following figures where
ABC ~
DEF, find x.
AB = AC
DF
DE
15 = 21
10 x
Proportions & Similar Figures
Notes
Applying Similarity
A tree casts a 26 ft shadow. A boy standing nearby casts a 12 ft shadow.
His height is 4.5 ft. How tall is the tree?
26 = x
12 4.5
A house casts a 56 ft shadow. A girl standing nearby casts a 7.2 ft shadow.
Her height is 5.4 ft. What is the height of the house?
Scale drawing – an enlarged or reduced drawing that is similar to an actual
object or place. (maps, floor plans, blueprints, etc)
The scale for the map is 1 in = 10 miles.
How far is it from Valkaria to Wabasso?
Valkaria to Wabasso is 1.75 in.
What is the distance from Grant to Gifford?
Proportions & Similar Figures
Homework
Practice 4-2 all
Proportions & Percent
Equations
Practice 4-2
Proportions & Percent
Equations
Notes
Finding the Percent…
What percent of 80 is 18?
Part  18 = x
Whole  80 100
80x = 1800
x = 22.5%
What percent of 40 is 30?
Finding the part…
Find 75% of 320
Part  75 = x
Whole  100 320
100x = 24,000
x = 240
Find 30% of 40…
Proportions & Percent
Equations
Notes
Finding the whole…
Carlos worked 31.5 hours at a hospital as a volunteer. This represents 87.5%
of his school’s requirement for community service. How many hours does his
school require for community service?
Part  31.5 = 87.5
Whole x
100
87.5x = 3150
x = 36 hours
Using a percent equation…
(1) What is 85% of 320?
(% as decimal) x whole = part
(2) 393 is 60% of what number? (3) What percent of 170 is 68?
Percents greater than 100% and less than 1%...
What percent of 90 is 135?
Proportions & Percent
Equations
Notes
x · 90 = 135
x = 1.5 (convert to percent ~ multiply by 100)
150%
105 is 125% of what number?
What percent of 320 is 1.6?
A store advertises sneakers on sale for 33% off. The original price of the
sneakers is $56. Estimate the amount the sneakers would be marked down.
Estimate the sale price.
Homework ~ Practice 4-3 odd
Percent of Change
Practice 4-3
Percent of Change
Notes
Percent of Change = amount of change
original amount
Percent of change can be an increase or decrease…
(1) Find the percent of change if the price of a CD increases from $12.99 to
$13.99. Round to the nearest percent.
13.99-12.99 = 1
12.99
12.99
0.07698
= 0.08 = 8% increase
(2) In 1990, there were 1330 registered alpacas in the U.S. By the summer of
2000, there were 29,856. What was the percent of increase in registered
alpacas? Round to the nearest percent.
29,856 – 1330 =
1330
28,526
1330
= 21.448 = 2145% increase
Percent of Change
Notes
Percent of Error
The greatest possible error in a measurement is one half of that measuring
unit.
To find the greatest possible error… Look at the smallest measurement unit.
For example: (1) You measure the mass of a rock and read the scale to
measure 3.3 g. What is the greatest possible error?
The mass was measured to the nearest ________,
0.1 g
So half of 0.1 g is _________.
0.05 g
(2) You measure a desk top to be 25 cm wide. What is the greatest possible
error in your measurement?
Finding maximum & minimum areas
You measure a room to be 15 ft by 10 ft. What is the maximum & minimum
possible areas for the room.
Greatest possible error = ______
So… 14.5 ft x 9.5 ft = 137.75 ft2 (min) & 15.5 ft x 10.5 ft = 162.75 ft2 (max)
Percent of Change
Notes
Percent of Error = greatest possible error
measurement
So back to the 3.3 g rock… what is the percent of error?
0.05 = 0.0151515 = 1.5%
3.3
Desk top percent of error?
0.5 = 0.02 = 2%
25
Homework Practice 4-4 odd
Applying Ratios to
Probability
Practice 4-4
Applying Ratios to Probability
Notes
Probability – P(event) – how likely it is that something will occur.
Outcome – result of a single trial. (omg – what happened?) (favorable or
unfavorable)
Event – any outcome or group of outcomes.
Sample space – all of the possible outcomes.
Theoretical probability – P(event) = number of favorable outcomes
number of possible outcomes
Probablity can be written as a fraction, a decimal or a percent. Probability
ranges from 0 to 1. 0 would be an impossible event, 1 would be certain…
Suppose you write the names of the days of the week on identical pieces of
paper. Find the theoretical probability of picking a piece of paper at random
that has the name of a day that starts with the letter T.
What is the probability of rolling an even number on a number cube?
A jar contains all the letters of the alphabet on wooden squares. What is
the probability of drawing a vowel?
Applying Ratios to Probability
Notes
Complement of an event is all the outcomes not in the event.
The sum on an event and its complement is always equal to 1..
So… P(event) + P(not event) = 1 or P(not event) = 1 – P(event)
Find the probability of not picking a piece of paper at random that has the
name of a day that starts with the letter T.
What is the complement of rolling an even number on a number cube?
A jar contains all the letters of the alphabet on wooden squares. What is
the probability of not drawing a vowel?
Experimental probability = P(event) = number of times an event occurs
number of times the experiment is done
The manufacturer decides to inspect 2500 skateboards. There are 2450
skateboards that have no defects. Find the probability that a skateboard at
random has no defects.
The same manufacturer has 8976 skateboards in its warehouse. If the
probability that a skateboard has no defect is 99.2%, how many are likely to
have no defect.
Probability of Compound Events
Practice 4-5
Probability of Compound Events
Notes
Independent events – events that do not influence one another.
Probability of two independent events
P(A and B) = P(A) · P(B)
Suppose you roll a red number cube and a blue number cube. What is the
probability that you will roll a 5 on the red cube and a 1 or 2 on the blue cube?
Suppose you roll 2 number cubes. What is the probability that both will be a
number less than 6?
Less than 5?
(If you choose an item from a container and replace the item and choose
again, the rules for independent events apply)
Dependent Events – events that influence each other.
Probability of two dependent events
P(A then B) = P(A) · P (B after A)
A bag contains 6 white counters, 5 red counters, and 19 counters of other
colors. Find the probability of choosing a white and then a red counter if you
do not replace the first counter before choosing the second counter.
Probability of Compound Events
Homework
Homework - Practice 4-6 & Review Chap 4
Probability of Compound Events
Practice 4-6
~ Chapter 4 ~
Chapter Review
~ Chapter 4 ~
Chapter Review