Transcript MJ Math 1 : 02 Ratios and Rate Reasoning : 02.09 Module

MJ MATH 1 : 02 RATIOS AND
RATE REASONING :
02.09 Module Two Test Review
MJ Math 1 :
02 Ratios and Rate Reasoning
Objectives:
•
•
•
•
•
•
•
You will use ratio language to describe the relationship between two quantities.
You will write a ratio to describe the relationship between two quantities.
You will describe a rate and unit rate in words and understand its meaning in a
situation.
You will calculate and write rates from contexts.
You will make tables of equivalent ratios.
You will use tables to find missing values and compare ratios.
You will solve unit rate problems by reasoning about ratios and rates.
• You will define a percentage as a ratio of a number to 100, calculate a
percent of a number as a rate per 100, and solve a variety of problems
involving percentages.
• You will define the standard units of measure for given quantities.
• You will use different methods of ratio reasoning to convert units and solve
problems that involve the conversion of units.
• You will determine the appropriate conversion factor when converting units.
• You will convert units between metric and customary systems.
Lesson 02.01
Understanding a Ratio
Ratio: a comparison between two
amounts, sometimes using division
Compare 6 boys and 4
girls
1. Read it 6 to 4
2. Write it 6/4
or
3. 6:4
Ratio Terms: the numbers that show the
comparison (ex: 6 and 4)
Scaling ratios:
 Let‘s scale 6:4
 1st you could write it like a
fraction. 6
4
 2nd divide the fraction by the
same number on top and
bottom to make it smaller
(simplifying)
 6
÷2
3 or 3:2
 4
÷2
2
Lesson 02.01
Understanding a Ratio
Types of Ratios
Examples:
 Part to part
 Part to part
 8 to 6
 Comparing two parts of
different things
 Part to whole
 6 to 14
 Comparing part of one
thing to the total amount
of things
 You are comparing how many
soccer balls you have vs. how
many tennis balls. 8 soccer
balls to 6 tennis balls or 8:6
 Part to whole
 You are comparing how many
tennis balls you have
compared to the TOTAL
amount of balls or 6:14. You
could also compare soccer
balls to total for 8:14.
Lesson 02.01-Let’s Practice
Understanding a Ratio
Types of Ratios
Scaling Ratios:
 Your Turn!

Part to part
 Q.Rewrite 12 to 8 two different
ways.
 1.
 2.

Part to whole
 Your Turn!

Part to part
 Q.Scale 12 to 8
 1.

Part to whole
 Q.Rewrite 3 to 9 two different
 Q.Scale 3 to 9
ways.
 1.
 2.
 1.
Lesson 02.01-Let’s Practice
Understanding a Ratio
Types of Ratios
Scaling Ratios:
 Check your work!

Part to part
 Rewrite 12 to 8 two different
ways.
 1. 12/8 fraction
 2. 12:8 use colon

 Check your work!

Part to part
 Scale 12 to 8
 1. 12
÷4
3

÷4
2
8
Part to whole
 Rewrite 3 to 9 two different

ways.
 1. 3/9 fraction
 2. 3:9 use colon
 Scale 3 to 9
Part to whole
 1. 3
÷3
1

÷3
3
9
Lesson 02.02
The Unit Rate
RATE:a ratio where two measurements are related to
each other
Writing rates
1) Kiki can buy 18 ounces of
cereal for $3.29.
 Steps:
 Step 1: Write your ratio as a
fraction- $3.29

$$$ on top
18 oz.
 Step 2: Compare units-ounces
vs. dollars. This means that Kiki
pays $3.29 for 18 ounces of
cereal.
2) Mae throws a football 70 feet in 4
seconds.
 Steps:
 Step 1: Write your ratio as a
fraction- 70 feet

4 seconds
 Step 2: Compare units-feet vs.
seconds. This means that Mae
throws 70 feet in 4 seconds.
Lesson 02.02
The Unit Rate
Unit rate and 2nd unit rate
How to find the unit rates:
 First Unit rates are easily
 Examples:
calculated. Once a rate has
been created, divide both
of the terms of the rate by
the second term.
 Second unit
rate(reciprocal)-
 Kiki can buy 18 ounces of
 Flip the numbers and compare :
 18oz
5.5 oz.
 $3.29
$1
cereal for $3.29.
 Step 1: Write your ratio as a
fraction- $3.29

18 oz.
 $3.29
18
Divide the
numerator by the
denominator.

Kiki pays $0.18 per ounce or $0.18

1 oz.
Lesson 02.02
The Unit Rate
Comparing Unit Pricing and
Unit Sizes
How to find the unit rate:
 Fertilizer is 6.75lbs for
 Step 1
$9.00 vs. 14.8lbs for $18.50

Bag 1- 6.75lbs for $9.00

Step 1: Write your ratio as a fraction-
$9.00
 Which is the better deal?

 Bag 1 vs. Bag 2

 Bag 1= $1.33 per pound

 Bag 2= $1.25 per pound
6.75lbs
$9.00
6.75
$1.33
1 lb.

Bag 2- 14.8lbs for $18.50

$18.50

14.8lbs
$1.25
1 lb.
Lesson 02.02-LET’S PRACTICE
The Unit Rate
Find the unit rate:
Comparing Unit Pricing
 Your Turn!
 Q.Bag 1-Chicken wings are is
20.75lbs for $40.25
 Your Turn!
 Which is the better deal?
 Bag 1 vs. Bag 2
 What is the unit rate?
 A.
 Q.Bag 2-Chicken wings are is
20.75 lbs for $50.25
 What is the unit rate?
 A.
 A. Compare the unit
rate for bag 1 cost vs.
bag 2 cost.

(hint:Which is cheaper?)
Lesson 02.02-LET’S PRACTICE
The Unit Rate
Find the unit rate:
Comparing Unit Pricing
 Check your work
 Q.Bag 1-Chicken wings are is
20.75lbs for $40.25
 What is the unit rate?
 A.$40.25

20.75lbs.
 Which is the better deal?
 Bag 1 vs. Bag 2
$1.94
1lb
 Q.Bag 2-Chicken wings are is
25.30 lbs for $50.25
 What is the unit rate?
 A. $50.25

25.30lbs
 Check your work
$1.99
1lb.
 A. Bag 1= $1.94/1lb

Bag 2=$1.99/1lb
The better deal is
Bag 1= $1.94/1lb
because it is 4cents cheaper
per pound.
Lesson 02.03
Equivalent Ratios
ratios that have the same simplest
form and express the same
relationship between two quantities
Horizontal Chart
 Adding or multiplying
 The instructions recommend
that for every 2 fluid ounces of
syrup, she must mix in 8 fluid
ounces of water to taste the best
Syrup
2 (+2)
4 (+2) 6(+2)
8(+2)
Water
8(+8)
16(+8) 24(+8) 32(+8)
10 fl oz
of syrup
40 fl oz
of water
Lesson 02.03
Equivalent Ratios
ratios that have the same simplest
form and express the same
relationship between two quantities

Vertical Chart
 Adding or multiplying
The instructions recommend that for
every 2 fluid ounces of syrup, she must
mix in 8 fluid ounces of water to taste
the best
Syrup
Water
Syrup
Water
2 (add 2)
8 (add 8)
2 (* 2)
8 (*2)
4
16
4
16
6
24
6
24
8
32
8
32
10
40
10
40
Lesson 02.03
Equivalent Ratios
Finding unit rates
ratios that have the same simplest
form and express the same
relationship between two quantities

and using tables
The instructions recommend that
for every 2 fluid ounces of syrup, she
must mix in 8 fluid ounces of water
to taste the best
Syrup
2fl oz. of syrup
2 = 1 oz. syrup
8oz of water
2
Water
Syrup
Water
4(+4)
1 (*4)=
4
8
2
8
3
12
3
12
4
16
4
16
5
20
5
20
1 (+1)
2
A
d
d
4oz water
Lesson 02.03-LET’S PRACTICE
Equivalent Ratios
Unit rates
and using addition vertically
Your turn!

The instructions recommend that for every 2
tablespoons of chocolate, Zoe must mix in 12
fluid ounces of milk to make hot chocolate.

Q. How many tablespoons would you
need for 5floz. of milk?
Unit rates
and using multiplication horizontally
Your turn!
Q. How many ounces of milk would you
need for 7 tablespoons chocolate?
Chocolate
Chocolate
Milk
Milk
Lesson 02.03-LET’S PRACTICE
Equivalent Ratios
Unit rates
and using addition vertically
Unit rates
and using multiplication horizontally
Check your work!

The instructions recommend that for every 2
tablespoon of chocolate, Zoe must mix in 12
fluid ounces of milk to make hot chocolate.

Q. How many tablespoons would you
need for 30 floz. of milk?
Check your work!
Q. How many ounces of milk would you
need for 7 tablespoons chocolate?
Chocolate
Milk
Chocolate
Milk
1 (*6) =
6
1(+1)
6(+6)
2
12
2
12
3
18
3
18
4
24
5
30
4
24
6
36
5
30
7
42
Lesson 02.05
Percentages
A percentage is a part-to-whole ratio
that compares a number to 100;
percentages are written with the
percent symbol (%).
 Words:
 26 out of 100
 26 for every 100
 Ratio




26:100
26 to 100 or
26
100
 Percentage
 26%
Using Percentages:
Multiplying by 100, turn a decimal into a percent:
• When you multiply a number by 100, you move the
decimal point of the factor two places to the right.
For example: 0.43 × 100 = 43 or 27.6 × 100 = 2,760
If you have a decimal, it can be written as a
percent by multiplying the number by 100.
For example: 0.16 × 100 = 16% or 0.035 100 = 3.5%
When you divide a number by a 100,
you move the decimal point of the
number being divided two places to
the left. For example:
54
100 = 0.54 or 8.23 ÷ 100 = 0.0823
Lesson 02.05
Percentages
How to find a part using an equivalent
ratio:
 For example: What percent
is 6 out of 25?
 Create a table and use
equivalent ratios until the
second term is 100.
Start
6
2
12
2
24
25
2
50
2
100
Lesson 02.05
Percentages
Examples:
 What is 35% of 75?
First
Part
Whole
35 = 0.35
35 100……..
Lesson 02.05-LET’S PRACTICE
Percentages
Percentages by using
equivalent ratios
Percentages by using
multiplication
Your turn!

Q. What percent is 4 out of
20?
4
20
Your turn!

Q. What is 35% of 75?
 A. ?
Lesson 02.05-LET’S PRACTICE
Percentages
Percentages by using
equivalent ratios
Check your work!

Percentages by using division
Check your work!
Q. What percent is 4 out of
20?
4
5=
20
5=
20
100

Q. What is 35% of 75?
 A.
20% 
Step 1:
convert 35% to 0.35
Step 2: 0.35* 75
 =26.25
Lesson 02.06
Measurements
US Customary Units
Lesson 02.06
Measurements
Conversions
Scenarios:
 Step 1: Identify the
conversion from the table.
 1 pint=2 cups
 Step 2: Make a chart

Q- A recipe calls for 3 pints of cream and
caramel sauce to make ice cream. How
many cups of cream do you need?
Determine number to multiply by
top number for your recipe.
Pints
1
3
3
cups
2
3
6 cups for recipe
Conversion Factor
Lesson 02.06
Measurements
Double line Conversion
Lesson 02.06-Let’s Practice
Measurements
Conversions
Your turn!
 Q. A recipe for oatmeal
calls for 6 quarts of milk.
How many pints would
you have?
Quarts
Pints
Your turn!
Q. If you ran 7 ½ yards, how
many feet did you run?
Lesson 02.06-Let’s Practice
Measurements
Conversions
Check your work!
 Q. A recipe for oatmeal
calls for 6 quarts of milk.
How many pints would
you have?
Quarts
1(*6) =
6
Pints
2(*6)=
12 pints
Check your work!
Q. If you ran 7 ½ yards, how
many feet did you run?

 A. 12 pints
16
Feet
A. 16 feet
Lesson 02.07
Unit Conversions
Converting from one unit of measurement to
another unit of measurement
 Step 1: Identify the
conversion in your table.
Conversion factor: a factor used to multiply or
divide a quantity when converting from one unit
to another so that units can cancel, which has an
overall value of 1
 How many pounds are in
10 Kilograms?

Set the units from the numerator to match the
denominator of the second conversion factor to cancel
out the units.
1.

The units cancel out.
2.

Now multiply
across to find the converted unit.
.
3.
Lesson 02.07-Let’s Practice
Unit Conversions
Converting from one unit of measurement to
another unit of measurement
Your turn!
 Q. How many centimeters
are in 55 inches?
55 inches=? centimeters
 Q. How many liters are in 5
gallons?
 5 gallons=? liters
.
Lesson 02.07-Let’s Practice
Unit Conversions
Converting from one unit of measurement to
another unit of measurement
Check your work!!
 Q. How many centimeters
 Q. How many liters are in 5
gallons?
are in 55 inches?
 A. 5 gallons=? liters
A.
1.
1.
.