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SECTION 6.1
Ratio----- Is a multiplicative comparison of two quantities.
For example.
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5 ounces to 10 ounces as a ratio would be:
5 ounces
5 1

 ,
10 ounces 10 2
Write as a ratio:
1. 3 to 5
which is a
2. 14 :21
5. 3 inches to 15 inches
8. Monthly income=$2,500
1 to 2 ratio
or
3. 0.9 to 0.6
4. 8 ounces to 1 pound
6. 3 inches to 4 feet
Monthly cost of gas= $300
1 : 2 ratio
7. 4 hours to 2 days.
Monthly cost of food= $456
a) Write the ratio of the monthly cost of gas to the monthly income.
b) Write the ratio of the monthly cost of food to the monthly cost of gas.
9. Five of every six students interviewed favored a change in library hours. Draw a picture
of this situation to help answer the questions.
A) Among those interviewed, what is the ratio of those who favor a change to those who
do not favor a change?
B) Among those interviewed, what is the ratio of those who do not favor a change to the
those who favor a change?
C) The number of students who do not favor a change is _______ times the number of
students who do favor a change.
D) The number of students who do favor a change is _______ times the number of
students who do not favor a change.
RATIOS - APPLICATIONS
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1. Below is a diagram of a candy bar that is being shared between two people:
The bar will be shared with a 3 to 4 ratio of part A to part B.
A) What fraction of the bar will part A receive?
B) Part B is how much of the bar?
C) Part A is ____ times as large as part B.
D) Part B is ____ times as large as part A.
2. Two landscapers mowed the lawn of a wealthy family. When they finished, landscaper
A had mowed only
3
7
as much as the more experienced landscaper B mowed.
A
B
A) What is the ratio of A's part to B's part?
B) What is the ratio of A's part to B's part?
C) A's part is what part of the lawn?
D) A's part is ____ times as much as B's part.
E) If they are paid $150 for mowing the lawn, what would be a fair split of the $150?
3. Pat and Ron split a cake. Pat's share is 2/3 as large as Ron's share.
A) What is the ratio of Pat's part to Ron's part?
B) What fraction of the cake did Pat receive?
C) Ron's share is ____ times as large as Pat's share.
D) What is the ratio of Ron's share to Pat's share? ______
4. Tim worked 30 hours last week, which was
How many hours did Robert work?
5
3
times as many hours as Robert worked.
Rate---Is the multiplicative comparison of
For example.
to two quantities with different units.
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5 people to 10 horses as a rate would be:
5 people
1 person

10 horses
2 horses
Write as a rate:
1. 15 applications for 18 openings.
2. 75 days on 20 gallons of water.
Unit Rate—Is the rate per one unit.
For example.
3. Three squished ants for every step .
Denominator =1
5 people to 10 horses as a rate would be:
5 people
 0.5 people per horse 0r 0.5 people
horse
10 horses
Write as a unit rate:
1. 40 miles in 2 hours
2. 60 revolutions in 5 minutes
3. 108 occurrences in 12-month
Unit cost—Cost per unit-- cos t
unit
For example. You buy 4.5 lbs of flank steak for $10.23. What is the unit cost.
cos t $10.23

 $2.27 per lb
unit
4.5lbs
Find the unit cost:
1. 150 barrels cost $4,950.
2. 17cents for 3 minutes
3. $4 billion over 5 months.
Applications of Rates
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1. Which is a better buy for cold medication 20 tablets for $4.29 or 50 tablets for $9.59?
2. A car travels 345 miles in 6 hours, and a truck travels 376 miles in 6.2 hours. Which vehicle is going
faster?
3. Richy Rich worked 27 hours and earned $4,206.23. What is his hourly rate of pay (pay per hour)?
4. In one community the electric bill was 575 kilowatt-hours of electricity for $38.81. In a second
community, a bill for 831kwh was $58.10. In which community is electricity cheaper?
5. A) 3 bags of tea are used with 4 cups of water in one teapot, and 10 bags of tea with 12 cups of water in
another teapot. Which pot will have the stronger tea, or will the two have the same strength? Explain your
answer.
B) 5 scoops of coffee are used with 8 cups of water in one coffee pot, while 7 scoops of coffee are used with
10 cups of water in another coffee pot. Which pot will have the stronger coffee? Explain your answer.
6. There are four water slides at the Six Flags Atlantis water park. The following are the measurements of
the four water slides. Circle the letter of the steepest slide.
A)
Length: 100 ft.; height: 81 ft.
B)
Length: 60 ft.; height: 45 ft.
C)
Length: 80 ft.; height: 70 ft.
D)
Length: 10 ft.; height: 7 ft.
SECTION 6.2
Proportions/ratio warm up.
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1) What is the ratio of circles to triangles?_________
What is the ratio of triangles to circles?_________
2) What is the ratio of circles to triangles?_________
What is the ratio of triangles to circles?_________
Are the ratios of circles to triangles the same in 1 and 2? Why?
A proportion is two equal ratios
1) Using Cross Multiplication
3 6

7 14
2) Using Equivalent fractions:
3 6

7 14
3) Using a unit rate:
14
21
=
6
9
Picture form:
Solve for x:
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1) Cross multiplying:
3 x

6 8
2) Using Equivalent fractions:
4 2

x 8
3) Using a unit rate:
125 x

250 7
4) Using a table:
15 10

3.3 x
Numerator Denominator
15
Solve for x:
3 x
1.

6 8
3.3
Notes
Given
2.
4 2

x 8
3.
x 1 2

7
21
WORD PROBLEMS INVOLVING PROPORTIONS
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My shadow is 4 feet long and I’m 6 feet tall. How tall is a tree with a shadow of 8 feet?
We set 𝒙 = 𝑻𝒉𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒕𝒓𝒆𝒆.
Set up two ratios. One involving one comparison, and the other involving the variable. Like Ian’s shadow
to Ian’s Height and The Trees shadow to the Trees Height. In this case the first sentence can be made
into the first ratio and the unknown will be in the second ratio.
tree
Ian' s Shadow Trees Shadow

Ian' s Height Trees Height
then solve
4 8

6 X
to find the answer.
Set up a proportion and solve.
me
4 feet 8 feet

6 feet
x
1. As part of a spring clearance, a men’s store put dress shirts on sale , 2 for $25.98. How much will a
business man pay if he buys five shirts?
2. A recipe for spaghetti sauce requires 4 bottles of ketchup to make 2 gallons of sauce. How many bottles
of ketchup are needed to make 10 gallons of sauce?
3. Jim can run 4 miles in 1.5 hours. How many miles can he run in 4 hours?
4. If three apples cost 45 cents, how much would five apples cost?
5. (special) $60 is to be divided between Brian and Kate in the ratio 2:3. How much does Kate get?
SECTION 6.3
American Units of Measurement
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Perform the conversions
1) 4 feet to inches
4 feet

1
2) 2
 ________________inches
2
feet to inches
3
8 feet

3
 ________________inches
3) 21 feet to yards
4) 8 pounds to ounces
2
5) 4 yards to feet
3
6) 2.5 tons to ounces
7) 2 quarts to fluid ounces
8) 3 gal to fluid ounces
9) 3 days to seconds
10) 240 minutes to days
11)
2
day to minutes
3
13) 2 miles to yards
SECTION 6.4
Metric Units of Measurement
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g - grams, unit measure of weight
m - meters, unit measure of length
l - liters, unit measure of volume
1 m, or 1 meter, is approximately 3 feet.
1L, or 1 liter, of soda. The amount of liquid the bottle holds has a volume of 1 liter.
1g, or 1 gram, is about the weight of a paperclip.
Questions:
1) What is the approximate weight of five paperclips?
2) What is the volume of a barrel that can hold the contents of seven of the above soda bottles?
3) A person who is 6 feet tall is about how many meters tall?
4) What unit of measure would you use to determine the weight of an object?
5) What unit of measure would you use to determine the length of an object?
6) What unit of measure would you use to determine the amount of volume an object displaces?
A mnemonic device to remember the metric prefixes is:
Kilo
Hecto
Deka
Base Deci
Centi
Mili
“King Henry Died By Drinking Chocolate Milk.”
1 kg is said “1 kilogram.”
1 kilogram = 1000 grams
1000
2 hm is said “2 hectometers.”
2 hectometers =2(100)meters= 200 meters
100
1 dl is said “1 deciliter.” 1
deciliters = 1/10 liters
1/10
Metric Units of Measurement
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Change 300 dm to km
300
Convert the following to centi. Ex:
Change 0.4 hl to cl
Change 7g to cg
0.4
7
4.5 dm = 45 cm
1) 0.3 m
2) 1.3 kl
3) 65.78 dag
4) 3 mm
Convert the following to the base unit grams, meters or liters
1) 4.5 cm
2) 6.45 mm
3) 7hm
4) 4000kg
Convert the following to kilo.
1) 456 m
2) 73 hg
3) 54.444 ml
4) 500mg
SECTION 6.5
US to Metric and visa-versa YouTube Video
1. Convert 100 yds to meters.
2. Convert 40 grams to ounces.
3. Convert 5 qts to liters.
4. Convert 7 miles to Km.
5. Convert 60 mph to kph.
6. Convert 100 Kph to mph.