6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
November 17, 2016
Ratios
A ratio is a comparison of two or more quantities.
Ratios should always in simplest form (similar to fractions),
but do not write as a mixed number because mixed numbers
do not show a comparison of amounts!
ORDER MATTERS!
Jul 2­10:53 AM
Ratios can be written in three ways.
As a fraction
a
b
With a symbol
a:b
In words
a to b
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
November 17, 2016
Ratios can show three different kinds of comparisons.
Part to part: The ratio of white circles to gray circles is:
6 6:4 6 to 4
4
Part to whole: The ratio of white circles to the total number of circles is:
6
10
6:10
6 to 10
Whole to whole: The ratio of the number of triangles to the number of circles is:
0
10
0:10
0 to 10
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Examples
1. What is the ratio of cats to dogs in a
neighborhood that has 9 dogs and 3 cats?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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2. What is the ratio of girls to boys in a
class of 20 students that has 12 boys?
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3. In a language class, there are 5 girls for
every 8 boys. If there are a total of 65
students, how many girls are there?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
1. The table shows the eye colors of the students in
Mr. Matthew's class.
Color
Number of Students
Brown
15
Blue
6
Green
3
Hazel
2
For every student with green eyes, how many
students have brown eyes?
Jul 2­11:03 AM
2. Matt's DVD collection contains 8 comedies, 6 dramas, 3
adventures, and 7 science fictions. What is the ratio of
comedies and dramas to the total number of DVDs in Matt's
collection?
Jul 2­11:06 AM
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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3.
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4.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Equivalent Ratios
Equivalent ratios form a proportion.
A proportion is an equation that shows that
two ratios are equal.
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When we write proportions (or set them up),
we follow:
W
K
word ratio
known ratio
U
unknown ratio
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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You can find equivalent ratios by
multiplying or dividing both sides by
the same number, similar to finding
equivalent fractions.
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Example
Emma is driving at a constant speed. She drives 4 miles in
5 minutes. If she continues to drive at the same speed, how
many miles will she drive in 15 minutes?
W
K
U
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
A builder mixes 10 shovels of cement with 25 shovels of
sand. Write two equivalent ratios of cement to sand.
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Equivalent Ratios with Ratio Tables
You can look for patterns or relationships in a table
to find equivalent ratios.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Example
Using the table given, at this rate how many books can
you buy with $5?
How much would it cost to buy 9 books?
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Practice
1. To make iced tea, Sahara adds 5 scoops of
sugar to 1 gallon of tea. Use the ratio table to find how
many scoops of sugar she would use for 4 gallons of iced
tea.
Gallons of
Tea
1
4
Scoops of
Sugar
5
■
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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2. Laurie exchanged $10 for 45 tokens to play arcade games.
Use a ratio table to find how many tokens she would receive
for $16.
Tokens
45
■
Dollars
10
16
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3.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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4.
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Equivalent Ratios with Cross Products
In a proportion, if the ratios are equivalent, then the
cross products are equal. Think of equal fractions.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Are these proportional?
2 = 6
7 21
8 = 6
24 20
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To find a missing term in a proportion, use cross
products. Multiply first, and then divide by the
remaining number. Use a variable, a letter that stands for
a number, to represent the missing term.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Example
The Rangers scored 4 runs in the first 3 innings. If they
continue at this rate, how many runs will be scored in the
entire game (without any extra innings)?
W
K
U
Jul 2­12:00 PM
Practice
1. In a horror movie featuring a giant beetle, the beetle
appeared to be 50 feet long. However, a model that was used
for the beetle, was really only 20 inches long. A 30 inch tall
model building was also used in the movie. How tall did the
building seem in the movie?
W
K
U
Jul 2­12:02 PM
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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2. A bush casts a shadow 8 feet long. If a person 5 feet tall
casts a shadow 6 feet long, how tall is the bush?
W
K
U
Jul 2­12:04 PM
3. Sebastian swam laps every day in the community swimming
pool. He swam 45 minutes each day, 5 days a week, for 12 weeks.
In that time, he swam 1800 laps.
A. How much time was spent swimming?
B. Knowing the amount of time, what was his average rate in laps
per hour?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Equivalent Ratios with Tape
Diagrams
Tape diagrams are best used to model ratios when
the two quantities have the same units.
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Example
Grandma knits 3 striped sweaters for every 4 total
sweaters that she knits. How many total sweaters
did she knit if she made 24 striped sweaters?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
1. David and Jason have marbles in a ratio of 2:3.
Together, they have a total of 35 marbles. How
many marbles does each boy have?
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2. A fruit punch recipe requires 2 cups of grape juice
for every 3 cups of apple juice. How many cups of
apple juice will you need if you use 9 cups of grape
juice?
Oct 6­11:40 AM
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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3. The ratio of Abby's money to Daniel's money is
2:9. Daniel has $45. If Daniel gives Abby $15, what
will the new ratio of Abby's money to Daniel's?
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Equivalent Ratios with the Coordinate
Plane
When equivalent ratios are graphed, they always form a
straight line that goes through the origin.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Example
Soda is on sale: 2 bottles for $4. How much would it cost to
buy 5 bottles of soda? Use a graph to solve this problem.
Bottles
Cost ($)
2
$4
5
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Practice
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Hours Worked
Total Pay (in dollars)
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Unit Conversions
You can convert measurements using equivalent ratios.
1 inch = 2.54 centimeters
1 kilometer = 0.62 mile
1 cup = 8 fluid ounces
1 meter = 39.37 inches
1 pound = 16 ounces
1 pint = 2 cups
1 mile = 5,280 feet
1 pound = 0.454 kilogram
1 quart = 2 pints
1 mile = 1,760 yards
1 kilogram = 2.2 pounds
1 gallon = 4 quarts
1 mile = 1.609 kilometers
1 ton = 2,000 pounds
1 gallon = 3.785 liters
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
1. Nancy ran 8 miles. How many yards did she run?
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2. A fishbowl has a capacity of 192 fluid ounces. How
many quarts is that?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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3. A package weighs 4.25 kilograms. How many pounds
does the package weigh?
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4. Dante bought a wooden board that was 32.5 inches long.
How many centimeters of wood did Dante purchase?
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5.
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6.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Unit Rate
A rate is a special ratio in which the two terms are in different
units. When rates are expressed as a quantity of 1 (the
denominator is 1), they are called unit rates.
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Some examples of unit rates are shown below:
30 miles
1 gallon
Miles per gallon:
Cost:
Pay rate:
$0.90
1 pound
$9.50
1 hour
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Any ratio can be converted into a
unit rate by dividing the
numerator and denominator by
the denominator, or by setting up
a proportion.
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Example
A motorcycle can travel 230 miles on 4 gallons of gasoline.
Find the average mileage per gallon.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
1. Ling is driving at a constant speed of 55 miles per
hour. At that rate, how long will it take him to drive
275 miles?
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2. Nate biked 54 miles in 4 ½ hours.
What was Nate’s average speed?
Oct 6­1:56 PM
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3.
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4.
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Unit Price
When prices are expressed as a quantity of 1, they are called
unit prices. The unit price will tell you the cost of one of what
you want to buy.
Unit price is often used in a grocery store to compare the price
of two or more brands of the same item.
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Example
Mr. Wilson spent $252 to stay 3 nights at Pavia Pavilions.
What is the cost for 1 night?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Practice
1.
Oct 6­2:06 PM
2. The table below shows how much money a grocery store
receives for selling different amounts of asparagus. If they unit
rate is constant, what are the total sales for the 12 pounds of
asparagus?
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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3. At a grocery store, you see a sign that says “5 avocados for
$2.00” and a sign that says “6 oranges for $3.00.” What would
the total cost be if you bought 2 avocados and 2 oranges?
Oct 6­2:11 PM
Percents
A percent is a ratio that means “per hundred.” A percent can be
written as a fraction with a denominator of 100.
To find a percent of a number, you need to setup a proportion
and use cross products to solve.
=
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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Example
There are 180 students going on a class field trip. Of those
students, 40% are boys. How many students on the field
trip are boys?
Oct 6­2:15 PM
Practice
1. A baseball player won 80% of the games he pitched. If
he won 28 games, how many games did he pitch?
Oct 6­2:19 PM
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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2. A group of students is trying out for the soccer team. Of those
students, 22 are 7th graders. If 55% of the students trying out are
7th graders, how many students in all are trying out?
Oct 6­2:20 PM
3. In Ms. Perron's class, 75% of the students are boys.
There are 18 boys in the class. What is the total number of
students in Ms. Perron's class?
Oct 6­2:22 PM
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6th Grade Math Ratios and Proportional Relationships Notes Answer Key.notebook
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4. At a sale, a shirt sold for $15 each. This price was 80%
of their original price. What was the original price? What
percent was the discount?
Oct 6­2:22 PM
5. Dana has 120 songs on her iPod. Of those 120 songs, 25%
of them are country songs. Of the songs that are country
songs, 2/5 are sung by Lady Antebellum. How many songs
on her iPod are sung by Lady Antebellum?
Oct 6­2:23 PM
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6.
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7.
8.
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