Lesson 6-1
Ratios
Lesson 6-2
Rates
Lesson 6-3
Measurement: Changing Customary Units
Lesson 6-4
Measurement: Changing Metric Units
Lesson 6-5
Algebra: Solving Proportions
Lesson 6-6
Problem-Solving Investigation:
Draw a Diagram
Lesson 6-7
Scale Drawings
Lesson 6-8
Fractions, Decimals, and Percents
Lesson 6-9
Percents Greater Than 100% and
Percents Less Than 1%
Five-Minute Check (over Chapter 5)
Main Idea and Vocabulary
California Standards
Key Concept: Ratios
Example 1: Write Ratios in Simplest Form
Example 2: Identify Equivalent Ratios
Example 3: Real-World Example
• Write ratios as fractions in simplest form and
determine whether two ratios are equivalent.
• ratio
• equivalent ratios
Ratio – comparison of two numbers by division.
3 to 4
3:4
a to b
a:b
Equivalent Ratios: Two ratios that have the same
value.
=
=
=
Write the ratio 8 yards to 64 yards as a fraction in
simplest form.
=
Write the ratio 3 pounds to 10 pounds as a fraction
in simplest form.
Write the ratio 192 crayons to 8 crayons as a
fraction in simplest form.
=
Write Ratios in Simplest Form
APPLES Mr. Gale bought a basket of apples. Using
the table below, write a ratio comparing the Red
Delicious to the Granny Smith apples as a fraction
in simplest form.
Mr. Gale’s Apples
Red Delicious
Granny Smith
12 Fuji
9 Granny Smith
30 Red Delicious
Answer: The ratio of Red Delicious apples to Granny
Smith apples is
FLOWERS A garden has 18 roses and 24 tulips.
Write a ratio comparing roses to tulips as a fraction
in simplest form.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Identify Equivalent Ratios
Determine whether the ratios 12 onions to 15 potatoes
and 32 onions to 40 potatoes are equivalent.
Write each ratio as a fraction in simplest form.
The GCF of 12 and 15 is 3.
The GCF of 32 and 40 is 8.
Answer:
So, 12:15 and 32:40 are equivalent ratios.
Determine whether the ratios 3 cups vinegar to 8 cups
water and 5 cups vinegar to 12 cups of water are
equivalent.
A. yes
B. no
C. maybe
D. not enough
information
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
POOLS It is recommended that no more than one
person be allowed into the shallow end of an outdoor
public pool for every 15 square feet of surface area. If
a local pool’s shallow end has a surface area of 1,800
square feet can 120 people swim into that part of the
pool?
Recommended
ratio
Actual ratio
Answer: Since the ratios simplify to the same fraction,
the lifeguards are correct to allow 120 people
into the shallow end of the pool.
SCHOOL A district claims that they have 1 teacher for
every 15 students. If they actually have 2,700 students
and 135 teachers, is their claim correct?
A. yes
0%
B. no
C. maybe
D. not enough
information
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Five-Minute Check (over Lesson 6-1)
Main Idea and Vocabulary
California Standards
Example 1: Find Unit Rates
Example 2: Find Unit Rates
Example 3: Standards Example: Compare Using
Unit Rates
Example 4: Real-World Example: Use a Unit Rate
• Determine units rates.
• rate
• unit rate
Ratio: comparison of two numbers by
division.
Rate: A ratio that compares two numbers
with different kinds of units.
128 pounds of dog food for 16 dogs.
𝟏𝟐𝟖 𝒑𝒐𝒖𝒏𝒅𝒔 𝒐𝒇 𝒅𝒐𝒈 𝒇𝒐𝒐𝒅
𝟏𝟔 𝒅𝒐𝒈𝒔
1 gallon of milk for $2.59.
𝟏 𝒈𝒂𝒍𝒍𝒐𝒏 𝒐𝒇 𝒎𝒊𝒍𝒌
$𝟐.𝟓𝟗
Unit Rate: A rate that is simplified so that it
has a denominator of 1 unit.
140 meters running in 28 seconds.
=
96 pages of a book read in 3 hours.
𝟗𝟔 𝒑𝒂𝒈𝒆𝒔 𝒐𝒇 𝒃𝒐𝒐𝒌
𝟑 𝒉𝒐𝒖𝒓𝒔
=
𝟑𝟐 𝒑𝒂𝒈𝒆𝒔 𝒐𝒇 𝒃𝒐𝒐𝒌
𝟏 𝒉𝒐𝒖𝒓
$6 for 24 cookies.
$𝟔
𝟐𝟒 𝒄𝒐𝒐𝒌𝒊𝒆𝒔
=
$𝟎.𝟐𝟓
𝟏 𝒄𝒐𝒐𝒌𝒊𝒆𝒔
Find Unit Rates
READING Julia read 52 pages in 2 hours. What is
the average number of pages she read per hour?
Write the rate as a fraction. Then find an equivalent rate
with a denominator of 1.
Write the rate as a
fraction.
Divide the
numerator and
denominator by 2.
Simplify.
Find the unit rate. 16 laps in 4 minutes
A. 4 laps per minute
B. 12 laps per minute
C. 20 laps per minute
D. 64 laps per minute
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Find Unit Rates
SODA Find the unit price per can if it costs $3 for 6
cans of soda. Round to the nearest hundredth if
necessary.
Write the rate as a
fraction.
Divide the numerator and
the denominator by 6.
Simplify.
Answer: The unit price is $0.50 per can.
Find the unit rate. $3 for one dozen cookies
A. $0.18 per cookie
B. $0.21 per cookie
0%
C. $0.25 per cookie
D. $3.60 per cookie
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Compare Using Unit Rates
The costs of 4 different sizes of orange juice are
shown in the table. Which container costs the least
per ounce?
A
B
C
D
96-oz container
64-oz container
32-oz container
16-oz container
Read the Item
Find the unit price, or the cost per ounce, of each size of
orange juice. Divide the price by the number of ounces.
Compare Using Unit Rates
Solve the Item
16-ounce container $1.28 ÷ 16 ounces = $0.08 per ounce
32-ounce container $1.92 ÷ 32 ounces = $0.06 per ounce
64-ounce container $2.56 ÷ 64 ounces = $0.04 per ounce
96-ounce container $3.36 ÷ 96 ounces = $0.035 per
ounce
The costs of different sizes of bottles of laundry
detergent are shown below. Which bottle costs the
least per ounce?
A. 96-oz container
B. 64-oz container
1.
2.
3.
4.
C. 32-oz container
0%
D. 16-oz container
A
B
C
D
A
B
C
D
Use a Unit Rate
POTATOES An assistant cook peeled 18 potatoes in 6
minutes. At this rate, how many potatoes can he peel
in 50 minutes?
Find the unit rate.
Then multiply this unit rate by 50 to find the number of
potatoes he can peel in 50 minutes.
Answer: The assistant cook can peel 150 potatoes in
50 minutes.
Sarah can paint 21 beads in 7 minutes. At this rate,
how many beads can she paint in one hour?
A. 21
B. 63
C. 120
D. 180
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-2)
Main Idea and Vocabulary
California Standards
Key Concept: Equality Relationships for Customary
Units
Example 1: Convert Larger Units to Smaller Units
Example 2: Convert Larger Units to Smaller Units
Example 3: Convert Smaller Units to Larger Units
Example 4: Convert Smaller Units to Larger Units
Example 5: Real-World Example
• Change units in the customary system.
• unit ratio
Standard 6AF2.1 Convert one unit of measurement
to another (e.g., from feet to miles, from centimeters
to inches).
Convert Larger Units to Smaller Units
Convert 2 miles into feet.
Multiply by
Divide out common
units.
= 2 ● 5,280 ft or 10,560 ft
Answer: 10,560 ft
Multiply.
Convert 8 yards into feet.
A.
B. 11 ft
C. 24 ft
D. 32 ft
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Convert Larger Units to Smaller Units
ELEVATOR The elevator in an office building has a
weight limit posted of one and a half tons. How many
pounds can the elevator safely hold?
Since 1 ton = 2,000
pounds, multiply by
. Then divide out
common units.
Multiply.
Answer: So, the elevator can safely hold 3,000 pounds.
Complete
.
A. 8,000
B. 8,500
0%
C. 9,000
D. 9,500
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Convert Smaller Units to Larger Units
Convert 11 cups into pints.
Multiply and divide out
common units.
Multiply.
Answer: 5.5 pints
Convert 21 quarts into gallons.
A. 4.75 gal
0%
B. 5.25 gal
C. 6.5 gal
D. 7 gal
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Convert Smaller Units to Larger Units
SOCCER Tracy kicked a soccer ball 1,000 inches.
How many feet did she kick the ball?
? lb.
Complete 78 oz = ___
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
LEMONADE Paul made 6 pints of lemonade and
poured it into 10 glasses equally. How many cups of
lemonade did each glass contain?
Begin by converting 6 pints to cups.
= 6 ● 2 cups or 12 cups
Find the unit rate which gives the number of cups per
glass.
Answer:
CANDY Tom has 3 pounds of candy he plans to
divide evenly among himself and his 3 best friends.
How many ounces of candy will each of them get?
A. 1 oz
B. 12 oz
C. 15 oz
D. 24 oz
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-3)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Convert Units in the Metric System
Example 2: Convert Units in the Metric System
Example 3: Real-World Example
Key Concept: Customary and Metric Relationships
Example 4: Convert Between Measurement Systems
Example 5: Convert Between Measurement Systems
Example 6: Real-World Example
• Change metric units of length, capacity, and mass.
• metric system
•
•
•
•
meter
liter
gram
kilogram
Standard 6AF2.1 Convert one unit of measurement
to another (e.g., from feet to miles, from centimeters
to inches).
Convert Units in the Metric System
Complete 7.2 m = ? mm.
To convert from meters to millimeters, use the
relationship 1 m = 1,000 mm.
1 m = 1,000 mm
7.2 ×1 m = 7.2 × 1,000 mm
7.2 m = 7,200 mm
Answer: 7,200 mm
Write the relationship.
Multiply each side by 7.2.
To multiply 7.2 × 1000,
move the decimal point 3
places to the right.
Complete 7.5 m = ? cm.
A. A.
A 0.75
B. 75
B. B
C. 750
D. D
0%
0%
D
0%
C
A
D. 7,500
0%
B
C. C
Convert Units in the Metric System
Complete 40 cm = ? m.
To convert from centimeters to meters, use the
relationship 1 cm = 0.01 m.
1 cm = 0.01 m
40 × 1 cm = 40 × 0.01 m
40 cm = 0.40 m
Answer: 0.40 m
Write the relationship.
Multiply each side by 40.
To multiply 40 × 0.01,
move the decimal point
2 places to the left.
Complete 3,400 mm = ? m.
A. A.
A 0.034
B. 0.34
B. B
C. 3.4
D. D
0%
0%
D
0%
C
A
D. 340
0%
B
C. C
FARMS A bucket holds 12.8 liters of water. Find the
capacity of the bucket in milliliters.
To convert from centimeters to meters, use the
relationship 1 L = 1,000 mL.
1 L = 1,000 mL
12.8 × 1 L = 12.8 × 1,000 mL
12.8 L = 12,800 mL
Answer: 12,800 mL
Write the relationship.
Multiply each side
by 12.8.
To multiply 12.8 × 1000,
move the decimal point
3 places to the right.
TRAVEL The drive from Jennifer’s home to a popular
state park is 62.4 kilometers. Find the distance in
A. meters.
A
A. 0.624 meter
B. B.
B 62.4 meters
C. 6,240 meters
D. D
0%
0%
D
0%
C
A
D. 62,400 meters
0%
B
C. C
Convert Between Measurement Systems
Convert 7.13 miles to kilometers. Round to the
nearest hundredth if necessary.
Use the relationship 1 mile  1.61 kilometers.
1 mile  1.61 km
Write the relationship.
7.13 × 1 mile  7.13 × 1.61 km
Multiply each side by
7.13 since you have
7.13 miles.
7.13 miles  11.4793 km
Simplify.
Answer: So, 7.13 miles is approximately
11.48 kilometers.
Convert 3.25 cups to milliliters. Round to the nearest
hundredth if necessary. (1 c  236.59 mL)
A. A
A. 2.95 mL
B. B.
B 768.92 mL
C. 72.8 mL
D. D
0%
0%
D
0%
C
A
0%
B
C. D.
C 76.89 mL
Convert Between Measurement Systems
Convert 925.48 grams to pounds. Round to the
nearest hundredth if necessary.
Since 1 pound  453.6 grams, multiply by
.
Multiply by
Simplify.
Answer: So, 925.48 grams is approximately 2.04 lb.
.
Convert 2500 kilograms to tons. Round to the nearest
hundredth if necessary. (1 T = 907.2 kg)
A. A
A. 2.76 T
B. 2,268,000 T
B. B
C. 0.36 T
D. D
0%
0%
D
0%
C
A
0%
B
C. D.
C 3.63 T
FARMS Pike’s Peak near Colorado Springs, Colorado
rises to a height that is 14,110 feet above sea level.
About how many meters high is Pike’s Peak?
Since the height above sea level is 14,110 feet, use the
relationship 1 ft  0.30 m.
1 ft  030 m
Write the relationship.
14,110 × 1 ft  14,110 × 0.30 m Multiply each side by
14,110 since you have
14,110 ft.
14,110 ft  4,233 m
Simplify.
Answer: So, Pike’s Peak is about 4,233 m high.
ANIMALS A grazing hippopotamus may eat up to
150 pounds of grass per night. About how many
do they eat? (1 lb  0.4536 kg)
A. kilograms
A
A. 330.69 kg
B. B.
B 33.07 kg
C. 680.4 kg
C. C
0%
D
0%
C
A
D. D
0%
B
0%
D. 68.04 kg
Five-Minute Check (over Lesson 6-4)
Main Idea and Vocabulary
California Standards
Key Concept: Proportion
Example 1: Identify Proportional Relationships
Example 2: Solve a Proportion
Example 3: Solve a Proportion
Example 4: Real-World Example
• Solve proportions.
• proportional
• cross product
• Ratio: a comparison of two numbers by division.
They can be written as follows:
x to y
x:y
x
y
Proportion: an equation stating that two ratios
are equal. Such as:
=
3 9

6 18
=
Proportions will usually have one missing part.
Identify Proportional Relationships
MATH Before dinner, Mohammed solved 8 math
problems in 12 minutes. After dinner, he solved 2
problems in 3 minutes. Is the number of problems he
solved proportional to the time?
Method 1 Compare unit rates.
Since the unit rates are equal, the number of math
equations is proportional to the time in minutes.
Identify Proportional Relationships
Method 2 Compare ratios by comparing cross products.
?
?
8 × 3 = 12 × 2 Find the cross products.
24 = 24 
Multiply.
Answer: Since the cross products are equal, the number
of math equations is proportional to the time in
minutes.
Determine if the quantities $30 for 12 gallons of
gasoline and $10 for 4 gallons of gasoline are
proportional.
A. yes
B. no
C. maybe
D. not enough
information
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Solve a Proportion
Write the proportion.
5x = 8 ● 18
Find the cross products.
5x = 144
Multiply.
Divide each side by 5.
Answer: x = 28.8
BrainPOP:
Using Proportions
A. 9.4
B. 12
C. 10.8
D. 18.6
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Solve a Proportion
Write the proportion.
3.5 ● n = 14 ● 6
3.5n = 84
Find the cross products.
Multiply.
Divide each side by 3.5.
n = 24
Simplify.
Answer: The solution is 24.
A. 5.25
0%
B. 5.5
C. 5.75
D. 6.25
1.
2.
3.
4.
A
A
B
C
D
B
C
D
FLAGS According to specifications, the ratio of the
length of the U.S. flag to its width must be 1.9 to 1.
How long must a U.S. flag be if it is designed to have
a width of 2.5 feet?
length
width
Write a proportion.
Find the cross products.
Multiply.
Answer: The length of a U.S. flag having a width of 2.5
feet must be 4.75 feet.
SCHOOL The ratio of boys to girls at Blue Hills
Middle School is 4 to 5. How many girls attend the
school if there are 96 boys?
A. 72 girls
B. 108 girls
C. 120 girls
D. 148 girls
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1: Draw a Diagram
• Solve problems by drawing a diagram.
Standard 6MR2.5 Use a variety of methods, such
as words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Standard 6NS2.1 Solve problems involving
addition, subtraction, multiplication, and division of
positive fractions and explain why a particular
operation was used for a given situation.
Draw a Diagram
ROCK CLIMBING A rock climber stops to rest at a
ledge 90 feet above the ground. If this represents 75%
of the total climb, how high above the ground is the
top of the rock?
Explore You know that 90 feet represents 75% of the
total climb.
Plan
Draw a diagram showing the fractional part of
the distance.
Solve
If 75% of the distance is 90 feet, then 25% of
the distance would be 30 feet. So the missing
25% must be another 30 feet.
The total distance from the ground to the top of
the rock is 90 + 30 or 120 feet.
Draw a Diagram
Check
Since 75% of the total distance is 90 feet,
and 0.75(120) = 90, the solution checks.
Answer: 120 ft
Interactive Lab:
Scale Drawings
INVENTORY A retail store has taken inventory of 400
items. If this represents 80% of the total items in the
store, what is the total number of items in the store?
A. 420
B. 435
C. 475
D. 500
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-6)
Main Idea and Vocabulary
California Standards
Example 1: Use a Map Scale
Example 2: Use a Blueprint Scale
Example 3: Use a Scale Model
Example 4: Find a Scale Factor
• Solve problems involving scale drawings.
• scale drawing
• scale model
• scale
• scale factor
Standard 6NS1.3 Use proportions to solve
problems (e.g. determine the value of n if
find the length of a side of a polygon similar to a
known polygon). Use cross-multiplication as a
method for solving such problems, understanding
it as the multiplication of both sides of an equation
by a multiplicative inverse.
Use a Map Scale
MAPS On the map below, the distance between
Portland and Olympia is about 1.69 inches. What is
the actual distance between Portland and Olympia?
Let d = the actual distance
between the cities. Write
and solve a proportion.
Use a Map Scale
Scale
map
actual
Portland to Olympia
map
actual
0.375d = 38.87
Divide each side by 0.375.
Answer: The distance between Portland and Olympia is
about 103.7 miles.
MAPS On a map of California, the distance between
San Diego and Bakersfield is about
centimeters.
What is the actual distance if the scale is
1 centimeter = 30 kilometers?
A. about 317 km
D. about 342 km
0%
D
A
0%
A
B
0%
C
D
C
C. about 330 km
A.
B.
0%
C.
D.
B
B. about 325 km
Use a Blueprint Scale
ARCHITECTURE On the blueprint of a new house,
each square has a side length of
inch. If the
length of a bedroom on the blueprint is
what is the actual length of the room?
inches,
Use a Blueprint Scale
Write and solve a proportion.
Scale
blueprint
actual
Length of Room
blueprint
actual
Cross products
Multiply.
Use a Blueprint Scale
Simplify. Multiply
each side by 4.
Answer: The length of the room is 15 feet.
ARCHITECTURE On a blueprint of a new house,
each square has a side length of
inch. If the width
of the kitchen on the blueprint is 2 inches, what is the
actual width of the room?
A. 6 feet
B. 18 feet
C. 24 feet
0%
1.
2.
3.
4.
A
B
C
D
A
D. 36 feet
B
C
D
Use a Scale Model
PHOTOGRAPHY A model is being created from a
picture frame which has a length of
inches. If the
scale to be used is 8 inches = 1 inch, what is the
length of the model?
Write a proportion using the scale.
Scale
Length
model
model
actual
actual
Use a Scale Model
Find the cross
products.
38 = m
Multiply.
Answer: The scale model is 38 inches long.
FURNITURE A model is being created from a childsized rocking chair which has a height of 8 inches. If
the scale to be used is 12 inches = 1 inch, what is the
height of the model?
A.
B.
C. 12 in.
0%
1.
2.
3.
4.
A
D. 96 in.
A
B
C
D
B
C
D
Find a Scale Factor
Find the scale factor of a blueprint if the scale is
Convert 3 feet to inches.
Multiply by
to eliminate the
fraction in the numerator.
Divide out the common units.
Find a Scale Factor
Answer: The scale factor is
on the blueprint is
That is, each measure
the actual measure.
Find the scale factor of a blueprint if the scale is
1 inch = 4 feet.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-7)
Main Idea
California Standards
Example 1: Percents as Fractions
Example 2: Percents as Fractions
Example 3: Fractions as Percents
Example 4: Fractions as Percents
Example 5: Fractions as Percents
Example 6: Fractions as Percents
Key Concept: Common Equivalents
• Write percents as fractions and decimals and vice
versa.
Reinforcement of Standard 5NS1.2 Interpret
percents as a part of a hundred; find decimal and
percent equivalents for common fractions and
explain why they represent the same value;
compute a given percent of a whole number.
Percents as Fractions
NUTRITION In a recent consumer poll, 41.8% of the
people surveyed said they gained nutrition
knowledge from family and friends. What fraction is
this? Write in simplest form.
Write a fraction with a
denominator of 100.
Simplify.
Percents as Fractions
Answer:
ELECTION In a recent election, 64.8% of registered
voters actually voted. What fraction is this? Write in
simplest form.
A.
B.
C.
0%
0%
A
B
D.
A. A
B. 0% B
C. C
C
D. D
0%
D
Percents as Fractions
Write
as a fraction in simplest form.
Write a fraction.
Divide.
Percents as Fractions
Simplify.
Answer:
A.
B.
0%
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Fractions as Percents
PRODUCE In one shipment of fruit to a grocery
store, 5 out of 8 bananas were still green. Find this
amount as a percent.
To find the percent of green bananas, write
percent.
as a
Write a proportion.
500 = 8n
Find the cross products.
Fractions as Percents
Divide each side by 8.
Simplify.
Answer:
A. 26%
0%
B. 38%
C. 52%
1.
2.
3.
4.
A
D. 60%
A
B
C
D
B
C
D
Fractions as Percents
500 = 12n
Find the cross products.
500 ÷ 12 ENTER 41.66666667
Answer:
Use a calculator to
simplify.
A. 11%
B. 68.75%
C. 73.33%
D. 140%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Fractions as Percents
Multiply by 100 and add the %.
Answer: 42.86%
A. 9.11%
B. 64.32%
C. 81.82%
D. 122.22%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Fractions as Percents
FARMS A farmer calculated that
of her goats
were brown. What percent of the goats were brown?
= 45%
Answer: 45%
Multiply by 100 and add the %.
MARBLES Benson calculated that
of his marble
collection were multi-colored marbles. What percent
of his collection were multi-colored?
A. 13%
B. 25%
C. 47%
D. 52%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 6-8)
Main Idea
California Standards
Example 1: Percents as Decimals or Fractions
Example 2: Percents as Decimals or Fractions
Example 3: Decimals as Percents
Example 4: Decimals as Percents
Example 5: Decimals as Percents
• Write percents greater than 100% and percents
less than 1% as fractions and as decimals, and vice
versa.
Reinforcement of Standard 5NS1.2 Interpret
percents as a part of a hundred; find decimal and
percent equivalents for common fractions and explain
why they represent the same value; compute a given
percent of a whole number.
Percents as Decimals or Fractions
Write 0.6% as a decimal and as a fraction in
simplest form.
0.6% = .006
= 0.006
Divide by 100 and remove %
symbol.
Decimal form
Fraction form
Answer:
Write 0.4% as a decimal and as a fraction in simplest
form.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Percents as Decimals or Fractions
STOCKS During a stock market rally, a company's
stock increased in value by 430%. Write 430% as a
mixed number and as a decimal. Then interpret its
meaning.
Definition of percent
Mixed number form
= 4.3
Answer:
Decimal form
; the stock’s new price was 4.3
times as great as before the rally.
Write 375% as a decimal and as a mixed number in
simplest form.
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Decimals as Percents
Write 5.12 as a percent.
5.12 = 5.12
= 512%
Answer: 512%
Multiply by 100.
Add % symbol.
Write 9.35 as a percent.
A. 0.0935%
0%
B. 0.935%
C. 93.5%
D. 935%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Decimals as Percents
Write 0.0015 as a percent.
0.0015 = 0.0015
Multiply by 100.
= 0.15%
Add % symbol.
Answer: 0.15%
Write 0.0096 as a percent.
A. 0.96%
B. 9.6%
C. 96%
D. 960%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Decimals as Percents
RUNNING On Sunday, Marjorie ran 0.875 of her
goal, in miles. What percent of her goal did Marjorie
run on Sunday?
0.875 = 0.875
= 87.5%
Multiply by 100.
Add % symbol.
Answer: Marjorie ran 87.5% of her goal.
FUND RAISING The band boosters have raised 0.745
of their goal so far. What percent of their goal have
the band boosters raised?
A. 0.745%
B. 7.45%
C. 74.5%
D. 745%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Checks
Image Bank
Math Tools
Scale Drawings
Using Proportions
Lesson 6-1 (over Chapter 5)
Lesson 6-2 (over Lesson 6-1)
Lesson 6-3 (over Lesson 6-2)
Lesson 6-4 (over Lesson 6-3)
Lesson 6-5 (over Lesson 6-4)
Lesson 6-6 (over Lesson 6-5)
Lesson 6-7 (over Lesson 6-6)
Lesson 6-8 (over Lesson 6-7)
Lesson 6-9 (over Lesson 6-8)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
(over Chapter 5)
A. 3
B. 5
C. 6
D. 7
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Chapter 5)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Chapter 5)
A. 24
B. 10
0%
1.
2.
3.
4.
C.
D.
A
B
C
D
A
B
C
D
(over Chapter 5)
A.
B.
C. 8
D.
0%
0%
A
B
0%
C
0%
D
A.
B.
C.
D.
A
B
C
D
(over Chapter 5)
A. 9
0%
B. 16
C.
1.
2.
3.
4.
A
B
C
D
A
D. 12
B
C
D
(over Chapter 5)
Guy purchased a one-gallon container of ether for a science
experiment. When he was finished,
of the container was
full. How many fluid ounces of ether did Guy use?
A.
8
1.
2.
3.
4.
0%
B.
12
C.
64
D.
120
A
B
C
D
A
B
C
D
(over Lesson 6-1)
Write the ratio 36 to 21 as a fraction in simplest form.
A.
B.
C.
D.
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 6-1)
Write the ratio 16 to 64 as a fraction in simplest
form.
A. 4
B. 2
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-1)
Write the ratio 22 meters to 180 meters as a fraction
in simplest form.
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 6-1)
Determine and explain whether the ratios 4:6 and
52:78 are equivalent.
and 52:78 =
D. No; 4:6 =
and 52:78 =
0%
and 52:78 =
A
C. No; 4:6 =
A. A
B. B
0%
0%
C. C
D. D
0%
D
B. Yes; 4:6 =
C
and 52:78 =
B
A. Yes; 4:6 =
(over Lesson 6-1)
Determine and explain whether the ratios 8:17 and
32:64 are equivalent.
A. Yes; 8:32 =
and 17:64 =
B. Yes; 8:32 =
and 17:64 =
C. No; 8:17 =
D. No; 8:17 =
and 32:64 =
and 32:64 =
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
(over Lesson 6-1)
Among the staff at Roosevelt Elementary, 68
teachers prefer coffee and 20 prefer tea. Which ratio
shows the relationship of coffee drinkers to tea
drinkers in simplest form?
0%
A. 10:34
B. 17:5
C. 5:17
1.
2.
3.
4.
A
D. 34:10
A
B
C
D
B
C
D
(over Lesson 6-2)
Find the unit rate. Round to the nearest hundredth if
necessary. $3.99 for 16 ounces
A. $0.25 per ounce
B. $4.01 per ounce
C. $12.01 per ounce
D. $19.99 per ounce
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-2)
Find the unit rate. Round to the nearest hundredth if
necessary. 730 miles in 14 hours
A. 52.14 hours per mile
0%
B. 52.14 miles per hour
C. 3,128.4 seconds per mile
D. 3,128.4 miles per second
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-2)
Find the unit rate. Round to the nearest hundredth if
necessary. $28 for 15 cassettes
A. $0.46 per cassette
0%
B. $0.54 per cassette
1.
2.
3.
4.
C. $1.78 per cassette
D. $1.87 per cassette
A
B
A
B
C
D
C
D
(over Lesson 6-2)
Which is the better unit price: $1.99 for a 3-ounce
bottle or $2.49 for a 4-ounce bottle?
A. $1.99 for a 3-ounce bottle
B. $2.49 for a 4-ounce bottle
A
B
C
A
0%
0%
0%
C
C. Both are equal.
B
1.
2.
3.
(over Lesson 6-2)
Determine whether the following statement is sometimes, always,
or never true. Explain by giving an example or a counterexample.
The denominator of a unit rate can be a decimal.
A.
Sometimes; a unit rate is a comparison of two
numbers with different units by division. For
example,
is read 65 miles in 3 hours.
B.
Always; a unit rate is a ratio of two measurements
1.
A
having different units. For example, $16 for 22.
B
3.
C
pounds.
C.
Never; a unit rate is a rate that is simplified so that it
has a denominator of 1 unit. For example, the unit
rate
is read 50 words per minute.
0%
A
B
C
(over Lesson 6-2)
Cassandra leaves college to go home for the
summer. She lives 424 miles away and arrives in
8 hours. Which ratio shows her rate of travel in
simplest form?
0%
A. 53:1
1.
2.
3.
4.
B. 53
C. 1:53
D. 212:4
A
B
C
D
A
B
C
D
(over Lesson 6-3)
Complete 21 ft = __ yd.
A. 3
B. 7
C. 15
D. 63
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-3)
Complete 160 oz = __ lb.
A. 10
B. 20
C. 40
D. 80
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-3)
Complete
= __ ft.
A. 3,960
0%
B. 5,280
1.
2.
3.
4.
C. 6,600
D. 9,240
A
B
A
B
C
D
C
D
(over Lesson 6-3)
Complete 2 c = __ fluid oz.
A. 32
B. 16
C. 8
D. 4
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-3)
Stella lives 2 miles from school. How many feet from
the school does Stella live?
A. 10,560 feet
0%
B. 5,280 feet
C. 3,520 feet
D. 1,760 feet
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-3)
If 1,760 yards = 1 mile, then 4 miles =
yards.
A.
0%
B. 4
1.
2.
3.
4.
C. 440
D. 7,040
A
B
A
B
C
D
C
D
(over Lesson 6-4)
Complete 640 cm = ■ m.
A. 6,400
A. A
B. 64
B. B
C. 6.4
D. D
0%
D
0%
C
0%
B
A
C. D.C 0.64
0%
(over Lesson 6-4)
Complete 0.05 m = ■ mm.
A. 0.0005
A. A
B. 0.05
B. B
C. 5
D. D
0%
D
0%
C
0%
B
A
C. D.C 50
0%
(over Lesson 6-4)
Complete 894 mg = ■ g.
A. 0.894
A. A
B. 8.94
B. B
C. 89.4
D. D
0%
D
0%
C
0%
B
A
C. D.C 8,940
0%
(over Lesson 6-4)
Complete 124.5 kL = ■ L.
A. 1.245
A. A
B. 12.45
B. B
C. 12,450
D. D
0%
D
0%
C
0%
B
A
C. D.C 124,500
0%
(over Lesson 6-4)
Complete 65,000 mL = ■ L.
A. 6,500
A. A
B. 650
B. B
C. 65
D. D
0%
D
0%
C
0%
B
A
C. D.C 6.5
0%
(over Lesson 6-4)
The longest suspension bridge in the United States
is the Verrazano–Narrows in the Lower New York
Bay. It spans 1,298 meters. How many kilometers
A. long
A is this bridge?
A. 1,298,000 km
B. B
B. 129.8 km
D. 1.298 km
D. D
0%
0%
D
0%
C
A
0%
B
C. C.C 12.98 km
(over Lesson 6-5)
A. yes
B. no
0%
A
B
1. A
2. B
(over Lesson 6-5)
A. yes
B. no
0%
0%
1.
2.
A
B
A
B
(over Lesson 6-5)
A. yes
0%
B. no
1. A
2. B
A
B
(over Lesson 6-5)
Solve the proportion
.
A.
B.
C. 9
D. 49
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-5)
Solve the proportion
.
A. 5
B. 7
C. 30
D. 45
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-5)
The ratio of native Spanish speakers to native
English speakers in a local high school is 3 to 8. If
there are 256 students at the school that are native
English speakers, how many students are native
Spanish speakers?
0%
1.
2.
3.
4.
A. 32
B. 36
C. 96
D. 682
A
B
C
D
A
B
C
D
(over Lesson 6-6)
The Rockwells have driven 180 miles, which is about
of the way to their family reunion. What is the
total distance to their family reunion?
A. 90 miles
B. 120 miles
C. 270 miles
0%
D
0%
C
A
D. 300 miles
0%
B
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 6-6)
Tomi is eating a candy bar that is 12 inches long.
She has already eaten
of the candy bar. How many
inches of the candy bar does she have left?
A.
in.
B.
in.
1.
2.
3.
4.
0%
C. 6 in.
D.
in.
A
B
C
D
A
B
C
D
(over Lesson 6-6)
Toki has filled
or 12 ounces of his glass. Find the
total capacity of his glass.
A. 16 ounces
0%
1.
2.
3.
4.
B. 9 ounces
C. 12 ounces
D. 14 ounces
A
B
A
B
C
D
C
D
(over Lesson 6-6)
If an 8-ounce serving of yogurt provides 10% of the
daily requirement for calcium, what percent of the
calcium requirement would a 20-ounce serving
provide?
A. 16%
B. 25%
C. 20%
0%
D
0%
C
0%
B
D. 8%
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 6-6)
Mrs. Jackson has $620 in her checking account after
writing checks for $39.70, $211.80 and $65. What was
her balance before she wrote the three checks?
A. $303.50
0%
B. $936.50
C. $935.50
1.
2.
3.
4.
A
B
C
D
A
D. $896.80
B
C
D
(over Lesson 6-7)
Suppose you are making a scale drawing. Find the length
of the object on the scale drawing with the given scale.
Then find the scale factor.
a subway car 34 feet long; 1 inch = 5 feet
A.
B.
D.
0%
D
A
B
0%
C
D
C
A
0%
B
C.
A.
B.
0%
C.
D.
(over Lesson 6-7)
Suppose you are making a scale drawing. Find the
length of the object on the scale drawing with the given
scale. Then find the scale factor.
a table 1.5 meters long; 3 centimeters = 0.25 meters
A.
0%
1.
2.
3.
4.
B.
C.
D.
A
B
C
D
A
B
C
D
(over Lesson 6-7)
Suppose you are making a scale drawing. Find the length
of the object on the scale drawing with the given scale.
Then find the scale factor.
a football field that is 120 yards; 1 foot = 30 yards
A.
1.
2.
3.
4.
0%
B.
C.
D.
A
B
C
D
A
B
C
D
(over Lesson 6-7)
The distance between New York City and Washington,
D.C., is 3.75 inches on a map of the United States. If
the scale on the map is 1 inch to 90 miles, how far is
Washington, D.C., from New York City?
A. 375.5 mi
B. 337.5 mi
C. 28.1 mi
0%
D
0%
C
A
0%
B
0%
D. 24.0 mi
A.
B.
C.
D.
A
B
C
D
(over Lesson 6-7)
Which ratio accurately shows the relationship between
the actual distance from Atlanta to New Hope and the
scale distance if the actual distance is 425 miles and the
scale distance is
0%
A.
1.
2.
3.
4.
B.
C.
A
B
C
D
A
D.
70.8 :1
B
C
D
(over Lesson 6-8)
Write 8% as a fraction in simplest form.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-8)
Write 56% as a fraction in simplest form.
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 6-8)
Write 32% as a fraction in simplest form.
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 6-8)
A. 0.47%
B. 4.71%
C. 47.06%
D. 470.59%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 6-8)
A. 214.29%
0%
B. 21.43%
C. 2.14%
1.
2.
3.
4.
A
B
C
D
A
D. 0.21%
B
C
D
(over Lesson 6-8)
Three out of every 7 car owners keep a flashlight in
their glove compartment. What percent of car
owners is this? Round to the nearest integer if
necessary.
A. 3%
1.
2.
3.
4.
0%
B. 33%
C. 43%
D. 57%
A
B
C
D
A
B
C
D
This slide is intentionally blank.