Lesson 59 P1

Transcription

Lesson 59 P1

Free Pre-Algebra
Lesson 59 ! page 1
Lesson 59: Review for Final Exam
Section VII. Proportions and Percents
Comprehensive Practice Lessons 37 - 42
Lesson 37: Scale and Proportion
Skill: Write ratios of sides for similar figures. Check
that ratios are equal using cross-products.
Worksheet 37 #1. Fill in the table with the information from
the rectangles.
Skill: Find a missing side of a triangle or rectangle
similar to a given triangle or rectangle.LARGE SMALL
LARGE
SMALL
HW37A #9. The
rectangles
are similar.
the width1.5
of the
L Find
3.75
smaller rectangle.
L
3.75
1.5
W 1.25
W
W 1.25
W
LARGE SMALL
LARGE SMALL
LENGTH
L
WIDTH
W
2. Use the cross-products to check whether or not the
rectangles are similar.
LARGE SMALL
L
3.75
1.5
W
1.25
W
Skill: Read a scale as a ratio and compare the original
to a scale model.LARGE
Find missing
values using the scale.
SMALL
HW37A #11.LPictured below is the Revell 1:180 USS
Lionfish Submarine model.
W
SCALE CONV.
MODEL
1
x feet
a. The actualREAL
length of the
submarine
is 311.5
180 311.5
feetfeet. What is
the length of the model, in feet?
SCALE CONV.
MODEL
REAL
1
180
SCALE
CONVERSION
b. What is the length of the model in inches?
MAP 5/4 inches
45/16 inches
REAL
500 miles
SCALE
MAP
5/4 inches
© 2010 Cheryl
Wilcox500 miles
REAL
x miles
CONVERSION
LARGE SMALL
L
W
SCALE CONV.
MODEL
MODEL
1
x feet
REAL
REAL
180 311.5 feet
SCALE CONV.
1
x feet
180
311.5 feet
SCALE CONV.
SCALE CONV.
MODEL
1
MODEL
1 and use in the context of a
Skill: Read
a map scale
REAL
180
map.
REAL
180
HW37A #12. A map legend shows that a length of 11/4
inches on the map corresponds to a distanceSCALE
of 500 miles. CONVERSION
SCALE
CONVERSION
MAP and
5/4Chicago,
inches
45/16 inches
The distance between Oakland, California
5/16 inches
MAP
5/4
inches
4
Illinois is about 45/16 inches on the map.
howmiles
many
REALAbout
500
x miles
miles apart
are the
cities?
REAL
500
miles
x miles
SCALE
MAP
5/4 inches
REAL
500 miles
SCALE
CONVERSION
CONVERSION
MAP 5/4 inches
REAL
500 miles
Free Pre-Algebra
Lesson 59 ! page 2
Lesson 38: Ratios and Rates with Weight
Skill: Find and compare unit prices.
Worksheet 37 #1. Unit prices: A bag of premium dog food
comes in a 6 lb size for $18.99 and a 15 lb size for $29.99.
Find the price per pound for each bag. (Round to the
nearest cent.)
Skill: Use the given formulas for computing blood
alcohol concentration.
Worksheet 37 #5. Blood alcohol: Use the formula
provided to approximate the blood alcohol concentration of
a 155 pound man who has had four drinks, each 0.6 oz
alcohol. Round to the nearest hundredth.
7A
W
Which bag has the lower price per pound?
Skill: Use the recommended dosage ratio to find a
medicine dosage given the patient’s weight.
Skill: Use the given formula for computing body mass
index (BMI).
HW37A #8. a. Convert 33 lbs to kilograms. (1 kg = 2.2 lb)
HW39A #8. A man 6 feet 1 inch tall is aiming for a BMI of
24. What is his desired weight?
BMI = 703
b. If a medicine has a recommended dose of 125 mg / kg,
and your child weighs 33 pounds, what amount of medicine
should you give?
W (lb)
H (inches)
2
c. If the medicine comes in 300 mg tablets, how many
whole tablets should you give?
Skill: Solve a density equation for any variable.
HW38A #9. a. You have a piece of cedar that is a
rectangular block measuring 4.1 cm by 6.7 cm by 1.2 cm.
What is the volume. to the nearest whole cm3?
b. The piece of wood weighs 12.5 g. What is the density
in g/cm3 rounded to the nearest hundredth?
© 2010 Cheryl Wilcox
c. Another piece of cedar is an unusual shape and it is
difficult to measure its volume. However you know that it
weighs 58 g. Use the density to find the volume to the
nearest whole cm3.
Free Pre-Algebra
Lesson 59 ! page 3
Lesson 39: Units in Ratios and Rates
Skill: Recognize and use a rate. Solve problems with
rates using the units to set up an equation.
Skill: Recognize and use a ratio. Solve problems with
ratios using tables or words to set up a proportion.
HW39A #6. Find the population density (rate of people per
square mile) in San Francisco, California. Write the units
with the rate.
Population 776,733; Area 46.69 square miles
HW39A #5. The shadow of a bell tower is 80 feet long at
the same time a person 5.5 feet tall has a shadow of 4.8
feet. How tall is the bell tower?
Lesson 40: Percents
Skill: Underline the words that represent the base of a
percent in a sentence.
Convert any of fraction, decimal, or percent to any
other.
Worksheet 40 #2. Underline or supply the words that tell the HW41A #11. Fill in the blanks:
base of the percent.
FRACTION DECIMAL PERCENT
c. 28% of the test-takers studied more than
8 hours for the test.
1/8
0.5
75%
e. This jacket was 40% off.
3%
0.22
7/5
Free Pre-Algebra
Lesson 59 ! page 4
Lesson 41: Solving SImple Percent Problems
Skill: Identify the amount, base, and percent in a
percent sentence. Translate to a ratio or percent
equation.
Lesson 41 page 2: Identify the percent, base, and amount,
and write the percent sentence as a ratio.
Skill: Solve problems to find the percent
HW41A #12. Carlos earned 62 of the 70 points possible on
the assignment. What percent of the points did Carlos get?
Round to the nearest whole percent.
That piece is 75% of the pizza.
amount
=%
base
Skill: Solve problems to find the amount.
Skill: Solve problems to find the base.
HW41A #13. 80% of the crowd of 5000 wore the team
colors. How many people wore the team colors?
HW41A #14. Stuart had 480 car-themed songs on his ipod,
which was only 16% of all his songs. How many songs did
he have on his ipod?
Lesson 42: A Few Consumer Percents
Skill: Compute the sales tax given the rate and price.
Skill: Compute the tip for a restaurant bill.
Worksheet 42 #2. In Pleasant Hill, California, the total state
and local sales tax is 9.25%. Find the sales tax you pay on
a pair of shoes for $110 in Sun Valley mall in Pleasant Hill,
California.
Worksheet 42 #3. The dinner bill was $85.60. Figure a tip of
15% and one of 20% on the bill.
Skill: Compute simple interest on a loan or savings
account when t = 1.
Skill: Compute the sale price of an item on sale given
the discount rate.
Worksheet 42 #4. Juaquin borrowed $3000 at 8% interest.
At the end of the year he must pay back the $3000 plus the
interest. How much will he pay in all?
Worksheet 42 #6. The jeans originally cost $85, but the
sale was for 40% off. What was the sale price of the jeans?
!
Free Pre-Algebra
Lesson 59 ! page 1a
Section VII. Proportions and Percents
Comprehensive Practice Lessons 37 - 42 Answers
Lesson 37: Scale and Proportion
Skill: Write ratios of sides for similar figures. Check
that ratios are equal using cross-products.
SMALL LARGE
Worksheet 37 #1. Fill in the table with the information from
LENGTH
the rectangles.
Skill: Find a missing side of a triangle or rectangle
similar to a given triangle or rectangle.
HW37A #9. The rectangles are similar. Find the width of the
smaller rectangle.
WIDTH
LARGE SMALL
SMALL
LARGE
LENGTH
2.6
4.68
WIDTH
2.0
3.60
2. Use the cross-products to check whether or not the
rectangles are similar.
2.6 • 3.60 = 9.36
2.0 • 4.68 = 9.36
The cross-products are equal.
The rectangles are similar.
Skill: Read a scale as a ratio and compare the original
to a scale model. Find missing values using the scale.
LARGE SMALL
HW37A #11. Pictured below is the Revell 1:180 USS
L
3.75
Lionfish Submarine
model. 1.5
W
W
1.25
LARGE SMALL
L
3.75
1.5
W
1.25
W
MODEL
REAL
1
x feet
180
311.5 feet
180x = 311.5
180x / 180 = 311.5 / 180
SCALE CONV.
x ! 1.73 feet
MODEL
1
b. What is the length of the model in inches?
REAL
180
1.73 feet 12 inches
•
= 20.76 inches
1
1 foot
3.75
1.5
W
1.25
W
LARGE SMALL
3.75WL= (1.5)(1.25)
L
3.75WW= 1.875
3.75W / 3.75 = 1.875 / 3.75
W
W = 0.5
SCALE CONV.
The width is 0.5 feet.
MODEL
1
x feet
REAL
180and 311.5
feet
Skill: Read
a map scale
use in the
context of a map.
HW37A #12. A map legend shows that a length of 11/4
SCALE CONV.
inches on the map corresponds
to a distance of 500 miles.
MODEL
1
The distance between Oakland, California and Chicago,
Illinois is REAL
about 45/16 inches
180 on the map. About how many
miles apart are the cities?
SCALE
SCALE CONV.
L
LARGE SMALL
L
a. The actual length
W of the submarine is 311.5 feet. What is
the length of the model, in feet?
LARGE SMALL
CONVERSION
MAP
5/4 inches
45/16 inches
REAL
500 miles
x miles
! 69 $
5
8625
x = # SCALE
500 = CONVERSION
&
4
4
" 16 %
(
MAP
)
5/4 inches
5
8625
4 5
8625 4
x = 500 miles • x =
•
REAL
4
4
5 4
4
5
x = 1725
Oakland and Chicago are
about 1,725 miles apart.
Free Pre-Algebra
Lesson 59 ! page 2a
Lesson 38: Ratios and Rates with Weight
Skill: Find and compare unit prices.
Worksheet 37 #1. Unit prices: A bag of premium dog food
comes in a 6 lb size for $18.99 and a 15 lb size for $29.99.
Find the price per pound for each bag. (Round to the
nearest cent.)
Skill: Use the given formulas for computing blood
alcohol concentration.
Worksheet 37 #5. Blood alcohol: Use the formula
provided to approximate the blood alcohol concentration of
a 155 pound man who has had four drinks, each 0.6 oz
alcohol. Round to the nearest hundredth.
$18.99
! $3.17 per lb
6 lb
$29.99
! $2.00 per lb
15 lb
7A
W
=
7(4 • 0.6)
! 0.11
155
Which bag has the lower price per pound?
The larger bag costs less per pound.
Skill: Use the recommended dosage ratio to find a
medicine dosage given the patient’s weight.
Skill: Use the given formula for computing body mass
index (BMI).
HW37A #8. a. Convert 33 lbs to kilograms. (1 kg = 2.2 lb)
HW39A #8. A man 6 feet 1 inch tall is aiming for a BMI of
24. What is his desired weight?
33 lb
1 kg
•
= 15 kg
1
2.2 lb
b. If a medicine has a recommended dose of 125 mg / kg,
and your child weighs 33 pounds, what amount of medicine
should you give?
Since 33 lb = 15 kg,
multiply the dose by 15 kg.
125 mg 15 kg
•
= 1875 mg
1
1 kg
c. If the medicine comes in 300 mg tablets, how many
whole tablets should you give?
BMI = 703
W (lb)
H (inches)
2
6 feet 1 inch = 72 inches + 1 inch = 73 inches
24 = 703
W
732
703W
5329 703W
5329
= 24
•
= 24 •
5329
703 5329
703
W = 181.9288762
His desired weight is about 182 pounds.
1875 mg / 300 mg = 6.25
You should give 6 tablets.
Skill: Solve a density equation for any variable.
HW38A #9. a. You have a piece of cedar that is a
rectangular block measuring 4.1 cm by 6.7 cm by 1.2 cm.
What is the volume. to the nearest whole cm3?
c. Another piece of cedar is an unusual shape and it is
difficult to measure its volume. However you know that it
weighs 58 g. Use the density to find the volume to the
nearest whole cm3.
58 g
(4.1)(6.7)(1.2) = 33 cm3
b. The piece of wood weighs 12.5 g. What is the density
in g/cm3 rounded to the nearest hundredth?
12.5 g / 33 cm3 = 0.38 g/cm3
3
x cm
0.38x = 58
=
0.38 g
1 cm3
0.38x / 0.38 = 58 / 0.38
x ! 153 cm3
Free Pre-Algebra
Lesson 59 ! page 3a
Lesson 39: Units in Ratios and Rates
Skill: Recognize and use a rate. Solve problems with
rates using the units to set up an equation.
Skill: Recognize and use a ratio. Solve problems with
ratios using tables or words to set up a proportion.
HW39A #6. Find the population density (rate of people per
square mile) in San Francisco, California. Write the units
with the rate.
Population 776,733; Area 46.69 square miles
HW39A #5. The shadow of a bell tower is 80 feet long at
the same time a person 5.5 feet tall has a shadow of 4.8
feet. How tall is the bell tower?
776,733 people
46.69 mi2
x people
=
1 mi2
46.69x = 776,733
height (ft)
shadow (ft)
( )( )
4.8h = 5.5 80 = 440
46.69x / 46.69 = 776,733 / 46.69
4.8h = 440
x = 16,635.96059
h = 91.6
There are about 16,636 people per square
mile in San Francisco.
5.5 h
=
4.8 80
4.8h / 4.8 = 440 / 4.8
The tower is about 91.7 feet tall.
Lesson 40: Percents
Skill: Underline the words that represent the base of a
percent in a sentence.
Convert any of fraction, decimal, or percent to any
other.
Worksheet 40 #2. Underline or supply the words that tell the HW41A #11. Fill in the blanks:
base of the percent.
FRACTION DECIMAL PERCENT
c. 28% of the test-takers studied more than
8 hours for the test.
1/8
0.125
12.5%
28% of the test-takers
e. This jacket was 40% off.
40% of the original price
1/2
0.5
50%
3/4
0.75
75%
3/100
0.03
3%
11/50
0.22
22%
7/5
1.4
140%
Free Pre-Algebra
Lesson 59 ! page 4a
Lesson 41: Solving SImple Percent Problems
Skill: Identify the amount, base, and percent in a
percent sentence. Translate to a ratio or percent
equation.
Lesson 41 page 2: Identify the percent, base, and amount,
and write the percent sentence as a ratio.
That piece is 75%
amount
=
amount
=%
base
percent
Skill: Solve problems to find the percent
HW41A #12. Carlos earned 62 of the 70 points possible on
the assignment. What percent of the points did Carlos get?
Round to the nearest whole percent.
amount
Carlo's points
=
base
points possible
62
= .885714...
70
of the pizza.
•
base
size of piece
= 75%
size of pizza
Carlos got 89% of the possible points.
Skill: Solve problems to find the amount.
Skill: Solve problems to find the base.
HW41A #13. 80% of the crowd of 5000 wore the team
colors. How many people wore the team colors?
HW41A #14. Stuart had 480 car-themed songs on his ipod,
which was only 16% of all his songs. How many songs did
he have on his ipod?
percent • base = amount
0.80 • 5000 = 4000
percent • base = amount
0.16b = 480
0.16b / 0.16 = 480 / 0.16
b = 3000
4000 people wore the team colors.
He had 3000 songs on his ipod.
Lesson 42: A Few Consumer Percents
Skill: Compute the sales tax given the rate and price.
Skill: Compute the tip for a restaurant bill.
Worksheet 42 #2. In Pleasant Hill, California, the total state
and local sales tax is 9.25%. Find the sales tax you pay on
a pair of shoes for $110 in Sun Valley mall in Pleasant Hill,
California.
Worksheet 42 #3. The dinner bill was $85.60. Figure a tip of
15% and one of 20% on the bill.
0.0925 • $110 = $10.175
0.20 • $85.60 = $17.12
0.15 • $85.60 = $12.84
rounded to the nearest cent, $10.18.
Skill: Compute simple interest on a loan or savings
account when t = 1.
Skill: Compute the sale price of an item on sale given
the discount rate.
Worksheet 42 #4. Juaquin borrowed $3000 at 8% interest.
At the end of the year he must pay back the $3000 plus the
interest. How much will he pay in all?
Worksheet 42 #6. The jeans originally cost $85, but the
sale was for 40% off. What was the sale price of the jeans?
1.08 • $3000 = $3240
100% ! 40$ = 60%
0.6 • $85 = $51
He’ll pay $3240.
The jeans were on sale for $51.
!
Free Pre-Algebra
Lesson 59 ! page 5
Section VIII. Percents Continued
Comprehensive Practice Lessons 43 – 46*
*Optional Lessons 47 and 48 are not included.
Lesson 43: Interest
Skill: Compute simple interest using the memorized
formula.
Skill: Use the given formula to compute compound
interest. (See previous problem box for formula.)
Worksheet 43 #1. Find the simple interest earned if $3,500
is invested for six months at 1.6% per year.
Worksheet 43 #4. $50,000 was invested at 3.5%
compounded quarterly for 5 years. How much was in the
account at the end of that time?
Compound Interest
!
r$
A = P # 1+ &
n%
"
nt
Same as simple interest, except
A = amount in account after t years
n = number of compounding periods per year
Skill: Find the combined simple interest for one year from an investment split into two accounts.
Worksheet 43 #3. Liling has $60,000 to invest in two accounts. She puts $25,000 in one account earning 2.1% simple
interest and the rest in another account earning 4.7% simple interest. How much interest will she receive from the two
accounts at the end of the year?
Lesson 44: Percents in Mixtures
Skill: Find the amount of a substance in a measured
mixture given the percent.
Skill: Estimate the percent of a substance in a mixture
of two different concentrations.
Worksheet 44 #3. A 900 ml solution of alcohol and water is
78% alcohol. How many ml of alcohol are present?
Worksheet 44 #5. Mixture C is formed by combining
Mixtures A and B.
How many ml of water?
Mixture A: 2 cubic meters of soil mixture, 35% sand
Mixture B: 6 cubic meters of soil mixture, 15% sand
a. The percent of sand in Mixture C is between ______%
and _______%.
Free Pre-Algebra
Lesson 59 ! page 6
Lesson 44: Percents in Mixtures Continued
Skill: Find the percent concentration of a mixture.
b. Solution C is ______ liters in total.
Worksheet 44 #7.
c. How many liters of alcohol are in Solution A?
Solution A: 80 liters of 20% alcohol
Solution B: 40 liters of 50% alcohol
Solution C is formed by combining Solutions A and B.
d. How many liters of alcohol are in Solution B?
e. How many liters of alcohol are in Solution C?
f. What percent of Solution C is alcohol?
Lesson 45: Percent Decrease
Skill: Solve a sales discount problem for any variable.
Worksheet 45 #1. An item that originally cost $218.90 is on
sale for 25% off. What is the sale price?
Skill: Solve a percent decrease problem for any
variable.
HW46A #9. If a man’s weight changes from 218 lb to 186
lb, what is the percent decrease in weight?
The sale price is $164.18.2. The sale price of $38.36 is
30% off the original price. What was the original price of the
item?
PQ #20. The number of students fell to 20,056, a 4% drop
in enrollment. What was the previous enrollment?
3. The original price was $44.80, and the sale price is
$35.84. What is the percent discount?
Free Pre-Algebra
Lesson 59 ! page 7
Lesson 46: Percent Increase
Skill: Solve a percent increase problem for any
variable.
Skill: Fill in the blank in a news story with a percent
increase.
Worksheet 46 #1. If your hourly pay increased from $14.50
to $15.66, what is the percent increase of your raise?
HW47A #13. Fill in the blank: “Of the 2.9 million youth age
16 to 24 who graduated from high school in January
through October 2009, 2.1 million (____ percent) were
enrolled in college in October 2009.” U.S. Bureau of Labor
Statistics
2. If your hourly pay of $16.80 increases by 5%, how much
will you make?
3. If your hourly pay increases 6% to $19.61, what was your
original pay?
!
Free Pre-Algebra
Lesson 59 ! page 5a
Section VIII. Percents Continued
Comprehensive Practice Lessons 43 – 46* Answers
*Optional Lessons 47 and 48 are not included.
Lesson 43: Interest
Skill: Compute simple interest using the memorized
formula.
Skill: Use the given formula to compute compound
interest. (See previous problem box for formula.)
Worksheet 43 #1. Find the simple interest earned if $3,500
is invested for six months at 1.6% per year.
Worksheet 43 #4. $50,000 was invested at 3.5%
compounded quarterly for 5 years. How much was in the
account at the end of that time?
I = Prt
= ($3,500)(0.016)(6 / 12)
= $28
P = $50,000
r = 0.035
t=5
n=4
Compound Interest
!
r$
A = P # 1+ &
n%
"
4•5
(
)
A = 50,000 (1.190339799)
A = 50,000 1.00875
nt
Same as simple interest, except
A = amount in account after t years
n = number of compounding periods per year
!
0.035 $
A = 50,000 # 1+
4 &%
"
20
= 59516.98997
After 5 years, there was
$59,516.99 in the account.
Skill: Find the combined simple interest for one year from an investment split into two accounts.
Worksheet 43 #3. Liling has $60,000 to invest in two accounts. She puts $25,000 in one account earning 2.1% simple
interest and the rest in another account earning 4.7% simple interest. How much interest will she receive from the two
accounts at the end of the year?
$60,000 – $25,000 = $35,000
2.1% of $25,000 + 4.7% of $35,000 =
0.021 • $25,000 + 0.047 • $35,000 =
$525 + $1645 = $2170
The total interest was $2,170.
Lesson 44: Percents in Mixtures
Skill: Find the amount of a substance in a measured
mixture given the percent.
Skill: Estimate the percent of a substance in a mixture
of two different concentrations.
Worksheet 44 #3. A 900 ml solution of alcohol and water is
78% alcohol. How many ml of alcohol are present?
Worksheet 44 #5. Mixture C is formed by combining
Mixtures A and B.
0.78 • 900 ml = 702 ml
How many ml of water?
900 ml – 702 ml = 198 ml
Mixture A: 2 cubic meters of soil mixture, 35% sand
Mixture B: 6 cubic meters of soil mixture, 15% sand
a. The percent of sand in Mixture C is between
___15___% and ____35___%.
Free Pre-Algebra
Lesson 59 ! page 6a
Lesson 44: Percents in Mixtures Continued
Skill: Find the percent concentration of a mixture.
b. Solution C is ___120___ liters in total.
Worksheet 44 #7.
c. How many liters of alcohol are in Solution A?
Solution A: 80 liters of 20% alcohol
Solution B: 40 liters of 50% alcohol
Solution C is formed by combining Solutions A and B.
20% of 80 liters is
0.2 • 80 = 16 liters
d. How many liters of alcohol are in Solution B?
50% of 40 liters is
0.5 • 40 = 20 liters
e. How many liters of alcohol are in Solution C?
16 liters + 20 liters = 36 liters
f. What percent of Solution C is alcohol?
36/120 = 0.3 = 30%
Lesson 45: Percent Decrease
Skill: Solve a sales discount problem for any variable.
Worksheet 45 #1. An item that originally cost $218.90 is on
sale for 25% off. What is the sale price?
25% off means 75% is paid
0.75 • $218.90 = $164.175
The sale price is $164.18.2. The sale price of $38.36 is
30% off the original price. What was the original price of the
item?
$38.36 is 70% of the original price.
$38.36 = 0.7x
x = $38.36 / 0.7 = $54.8
The original price was $54.80.
3. The original price was $44.80, and the sale price is
$35.84. What is the percent discount?
Original Price – Sale Price
$44.80 – $35.84 = $8.96
You save $8.96, which is
some percent of the original price.
$8.96 / $44.80 = 0.2 = 20%
20% discount
Skill: Solve a percent decrease problem for any
variable.
HW46A #9. If a man’s weight changes from 218 lb to 186
lb, what is the percent decrease in weight?
decrease is 218 – 186 = 32
decrease / original = 32 / 218 = 0.14678…
about a 14.7% decrease
PQ #20. The number of students fell to 20,056, a 4% drop
in enrollment. What was the previous enrollment?
20,056 is 96% of previous enrollment
0.96x = 20,056
x = 20,056 / 0.96 = 20,891.666…
About 20,892 students.
Free Pre-Algebra
Lesson 59 ! page 7a
Lesson 46: Percent Increase
Skill: Solve a percent increase problem for any
variable.
Skill: Fill in the blank in a news story with a percent
increase.
Worksheet 46 #1. If your hourly pay increased from $14.50
to $15.66, what is the percent increase of your raise?
HW47A #13. Fill in the blank: “Of the 2.9 million youth age
16 to 24 who graduated from high school in January
through October 2009, 2.1 million (____ percent) were
enrolled in college in October 2009.” U.S. Bureau of Labor
Statistics
The increase is 15.66 – 14.5 = 1.16
The percent increase is
1.16 / 14.50 = 0.08 = 8%
2.1 million / 2.9 million = 0.7241…
2. If your hourly pay of $16.80 increases by 5%, how much
will you make?
(_72_ percent)
The new wage is 105% of the old wage.
1.05 • 16.80 = 17.64
New wage is $17.64 per hour.
3. If your hourly pay increases 6% to $19.61, what was your
original pay?
New pay is 106% of original pay.
19.61 – 1.06x
x = 19.61 / 1.06 = 18.5
Original wage was $18.50
!
Free Pre-Algebra
Lesson 59 ! page 8
Section IX. The Number Line
Comprehensive Practice Lessons 49 – 52*
*Optional Lessons 53 and 54 not included.
Lesson 49: Squares and Square Roots
Skill: Write the related square and square root
equations for a given number.
Worksheet 49 #2. Write the related square and square root
problems for 62.
Skill: Evaluate square roots with a calculator.
HW 49A #14. Find the square roots using your calculator.
Round to three decimal places if rounding is necessary.
a.
c.
95
Skill: Estimate a square root using perfect squares.
Worksheet 49 #3 Which two perfect squares is the number
between?
30
Skill: Evaluate squares and square roots with negatives
appropriately.
HW50A #1. Evaluate. Round to three decimal places if
rounding is necessary.
b.
361
!121
c. ! 121
d.
(!11)2
Skill: Use the square root symbol correctly in the order
of operations when simplifying.
Worksheet 49 #6. Evaluate.
a.
100
25
c.
36 • 9
d.
36 • 9
b.
100
25
a.
100 ! 36
b.
100 ! 36
c.
25 + 144
d.
25 + 144
Free Pre-Algebra
Lesson 59 ! page 9
Lesson 50: The Pythagorean Theorem
Skill: Identify the right angle, hypotenuse, and legs of a
right triangle.
Skill: Use the memorized Pythagorean Theorem to find
any missing side of a right triangle.
Worksheet 50 #2. Label the sides of the triangle a, b, and
c. Label the legs and hypotenuse.
Worksheet 50 #3. Find the length of the hypotenuse.
any missing side of a right triangle. Round
appropriately.
Worksheet 50 #6. Find the missing length.
Free Pre-Algebra
Lesson 59 ! page 10
Lesson 51: Practical Uses of the Pythagorean Theorem
Skill: Apply the converse of the Pythagorean Theorem
to determine whether or not a given angle is right (90º).
Skill: Apply the Pythagorean Theorem in a variety of
physical situations.
HW51A #13. If the diagonal measures 34 inches, is the
frame square?
Worksheet 51 #2. Gutters are to be installed along the
roofline and extend another 6 inches past the end of the
roof. How many feet of gutter are needed?
Lesson 52: The Real Numbers
Skill: Use the vocabulary for sets of real numbers,
including natural numbers; whole numbers; integers;
rational numbers; irrational numbers; real numbers.
Skill: Determine whether statements about the real
number system are true or false. Explain.
Identify to which set a particular number belongs.
Worksheet 53 #3. Answer true or false, and give a reason
for your answer.
Worksheet 52 #3 a. Circle the irrational numbers.
a. True or False? A rational number must be positive.
c. Circle the integers.
b. True or False? An integer is always negative.
c. True or False? The real numbers do not include !.
Free Pre-Algebra
Lesson 59 ! page 11
Section X. Get Ready for Algebra I
Comprehensive Review Lesson 55 Answers
Lesson 55: Perimeter Problems with Related Variables
Skill: Use a given relationship between length and
width in a rectangle to write an expression for width in
terms of length, and substitute in the perimeter
formula.
Skill: Solve the perimeter equation to find the length
and width of the rectangle.
Worksheet 55 #1. The perimeter of each rectangle is 120
inches. Fill in the missing part of the equation. Do not solve.
Worksheet 55 #7. The perimeter is 82 inches, and the width
is 3 inches less than the length. Find the width and length.
The width of the rectangle is 10 more than the length.
P = 2L + 2W
120 = 2L + 2(
)
The width of the rectangle is 10 less than the length.
P = 2L + 2W
120 = 2L + 2(
)
The width of the rectangles is 5 times the length.
P = 2L + 2W
120 = 2L + 2(
)
The width of the rectangle is 1/5 of the length.
P = 2L + 2W
120 = 2L + 2(
)
!
Free Pre-Algebra
Lesson 59 ! page 8a
Section IX. The Number Line
Comprehensive Practice Lessons 49 – 52* Answers
*Optional Lessons 53 and 54 not included.
Lesson 49: Squares and Square Roots
Skill: Write the related square and square root
equations for a given number.
Worksheet 49 #2. Write the related square and square root
problems for 62.
(6)
2
Skill: Estimate a square root using perfect squares.
Worksheet 49 #3 Which two perfect squares is the number
between?
25 < 30 < 36
= 36
Skill: Evaluate square roots with a calculator.
HW 49A #14. Find the square roots using your calculator.
Round to three decimal places if rounding is necessary.
a.
95 ! 9.747
c.
361 = 19
5 < 30 < 6
30
36 = 6
30 is between 5 and 6.
Skill: Evaluate squares and square roots with negatives
appropriately.
b.
!121 not a real number
c. ! 121 = !11
d.
(!11)2 = 121 = 11
Worksheet 49 #6. Evaluate.
a.
100
25
=
10
=2
5
b.
c.
36 • 9 = 324 = 18
d.
36 • 9 = 6 • 3 = 18
100
= 4 =2
25
a.
100 ! 36 = 10 ! 6 = 4
b.
100 ! 36 = 64 = 8
c.
25 + 144 = 5 + 12 = 17
d.
25 + 144 = 169 = 13
Free Pre-Algebra
Lesson 59 ! page 9a
Lesson 50: The Pythagorean Theorem
Skill: Identify the right angle, hypotenuse, and legs of a
right triangle.
any missing side of a right triangle.
Worksheet 50 #2. Label the sides of the triangle a, b, and
c. Label the legs and hypotenuse.
Worksheet 50 #3. Find the length of the hypotenuse.
482 + 552 = 2304 + 3025 = 5329
c 2 = 5329
5329 = c
c = 73 cm
any missing side of a right triangle. Round
appropriately.
Worksheet 50 #6. Find the missing length.
452 + a 2 = 472
2025 + a 2 = 2209
a 2 = 2209 ! 2025 = 104
104 = a
a " 13.565 cm
Free Pre-Algebra
Lesson 59 ! page 10a
Lesson 51: Practical Uses of the Pythagorean Theorem
Skill: Apply the converse of the Pythagorean Theorem
to determine whether or not a given angle is right (90º).
Skill: Apply the Pythagorean Theorem in a variety of
physical situations.
HW51A #13. If the diagonal measures 34 inches, is the
frame square?
Worksheet 51 #2. Gutters are to be installed along the
roofline and extend another 6 inches past the end of the
roof. How many feet of gutter are needed?
a2 + b2 = c2
302 + 162 = c 2
900 + 256 = c 2
c 2 = 1156
c = 1156 ! 34
Yes, since 302 + 162 = 342, the corner
must be square (a right angle).
Each side of the roof is calculated using the
Pythagorean theorem.
a2 + b2 = c2
182 + 62 = c 2
c 2 = 360
c = 360 ! 18.974
The six inches we need to add is 0.5 feet, so
the total length of one side is 19.474 feet.
For the two sides, that is 38.947 feet.
About 39 feet of gutter.
Lesson 52: The Real Numbers
Skill: Use the vocabulary for sets of real numbers,
including natural numbers; whole numbers; integers;
rational numbers; irrational numbers; real numbers.
Skill: Determine whether statements about the real
number system are true or false. Explain.
Identify to which set a particular number belongs.
Worksheet 53 #3. Answer true or false, and give a reason
for your answer.
Worksheet 52 #3 a. Circle the irrational numbers.
a. True or False? A rational number must be positive.
False. The rational numbers are the results
of integer division and so include negative
fractions. For example, –1/2 is a rational
number.
c. Circle the integers.
b. True or False? An integer is always negative.
False. The integers include the natural
numbers, which are positive. For example, 3
is an integer.
c. True or False? The real numbers do not include !.
False. ! is an irrational number, and the real
numbers include all the irrational and all the
rational numbers.
Free Pre-Algebra
Lesson 59 ! page 11a
Section X. Get Ready for Algebra I
Comprehensive Review Lesson 55 Answers
Lesson 55: Perimeter Problems with Related Variables
Skill: Use a given relationship between length and
width in a rectangle to write an expression for width in
terms of length, and substitute in the perimeter
formula.
Skill: Solve the resulting equation to find the length and
width of the rectangle.
Worksheet 55 #1. The perimeter of each rectangle is 120
inches. Fill in the missing part of the equation. Do not solve.
Worksheet 55 #7. The perimeter is 82 inches, and the width
is 3 inches less than the length. Find the width and length.
P = 2L + 2W
82 = 2L + 2( L – 3 )
The width of the rectangle is 10 more than the length.
82 = 2L + 2L – 6
P = 2L + 2W
82 = 4L – 6
120 = 2L + 2(L + 10)
4L – 6 = 82
The width of the rectangle is 10 less than the length.
4L = 88
P = 2L + 2W
120 = 2L + 2(L – 10)
The width of the rectangles is 5 times the length.
P = 2L + 2W
4L / 4 = 88 / 4
L = 22
The length is 22 inches.
The width is 3 inches less than the length.
22 – 3 = 19, so the width is 19 inches.
120 = 2L + 2( 5L )
The width of the rectangle is 1/5 of the length.
P = 2L + 2W
120 = 2L + 2(L / 5)
!
4L – 6 + 6 = 82 + 6

Lesson 59 P1

Transcription

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