Ratio
11/12
My bike’s fuel has
a ratio of
oil to gas
1 : 25
ratios
The comparison of two or
more numbers
notation
Can be written three ways
2/3
2:3
2 to 3
Writing
Ratios
Count the number of red and
green hearts
4 RED and 8 GREEN
Red : Green
4:8
Simplifying
ratios
You know how to simplify
fractions, simplifying with a colon
works the same way
Red : Green
4:8
Divide ÷
by 2
2:4
1:2
Divide ÷
by 2
The ratio of red to green is
Red : Green
1:2
This tells you that there
are 2 green hearts for
every red heart
You try
Copy and complete this
chart
Ratio
12 / 16
24 : 32
27 / 36
28 to 40
Simplest
terms
Copy and complete this chart
Ratio
Simplest terms
12 : 16
3:4
3/4
3 to 4
7 / 10
24 / 32
27 to 36
28 / 40
You try
Workbook
P 79
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Unit Rate and Proportional
Reasoning
11/13
rate
A ratio that compares two
numbers with different units
Miles per hour mph
Unit rate
The rate for one unit
mph is usually expressed as a
unit rate
Examples
Unit Rate
1. It takes 2 hours to get to a
friends house in Atlanta, 124
miles away. What would the
mph be?
2. You can solve 76 math
problems in 3 hours and 42
minutes. How many problems
do you solve per minute?
Examples
Unit price
1. 20 pieces of candy cost $2.40,
what does one piece of candy
cost?
2. Kaleigh’s dog food is $1.15
per pound. How much does a
40lb bag of food cost?
You try
Workbook
P 81
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• Turn in homework
• Get your workbook
• Sharpen pencil
• Sit down
• Get ready for notes
Turn in homework
Sharpen Pencils
Grab a workbook
Sit down and get
ready for notes
Proportions
11/16
Proportions - If two ratios are equal, they form a
proportion. Proportions can be used in
geometry when working with similar
figures.
1
2
=
4
8
1:3 = 3:9
Simplest
Form
Examples
If the ratios form a proportion, then
the simplified forms of the ratios
will equal.
Determine if the ratios form a
proportion by writing each ratio in
simplest form.
• 4/8, 10/20
• 15/20, 10/12
• 24/30, 9/15
Common If the ratios form a proportion, then
Multiplier the numerator and denominator
will share a multiplier.
Examples
Determine if the ratios form a
proportion by finding a common
multiplier
• 8/15, 32/40
• 60/140, 3/7
• 10/24, 30/70
Cross
If a/b = c/d then ad = bc
Multiplying
a
c
=
b
d
ad = bc
If the ratios form a proportion, then the
cross products are equal
Examples
Determine if the ratios form a
proportion by cross multiplying
• 2/3, 4/5
• 10/5, 6/3
• 5/6, 50/72
You Try
Workbook
Page 85
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Proportions
Solving Proportions
11/18
- If two ratios are equal, they form a
proportion. Proportions can be used in
geometry when working with similar
figures.
1
2
Similar
=
4
8
1:3 = 3:9
- Similar describes things which have the
same shape but are not the same size.
Cross
Multiplying
If a/b = c/d then ad = bc
a
c
b = d
ad = bc
Examples
1. 2/3 = 4/6
2. 10/x = 6/3
3. 5/6 = x/72
Ratio
The ratio of the smaller figure to the larger figure is
1:2 (said “one to two”). This can also be written as a
fraction of ½.
Proportion A proportion
can be made
relating the
height and the
4 ft
width of the
smaller figure to
the larger
figure: 4 ft 8 ft
=
2 ft
4 ft
8 ft
2 ft
4 ft
Solving
Proportion
Problems
First, designate the unknown
side as x. Then, set up an
equation using proportions.
What does the numerator
represent? What does the
height
denominator represent?
width
6 ft
2 ft
18 ft
=
18 feet
x ft
Then solve for
x by cross
multiplying:
6x = 2 ∙ 18
6x = 36
x=6
6 feet
2 feet
? feet
You try
Workbook
P 87
start at # 6
Binder Check
1. What was the topic for the notes given
on 11/18?
2. What was the answer to number 1 from
the homework assigned 11/16, p 258259, 1-23 odd.
3. Write the calculator policy from the
Classroom Guidelines and Procedures
handout.
Similar Shapes
11/20
Similar shapes are very important
because if we know the dimensions of
one shape and one of the dimensions of
another shape similar to it, we can figure
out the unknown dimensions.
Similar
figures
Figures are similar if the ratio
between each side make a
proportion
Write each example off the white
board
You Try These two stick figures are similar.
1.
2.
8 feet
12 feet
3 feet
x feet
Write a proportion
relating the similar
shapes.
Find the missing
width.
You Try These two trapezoids are similar.
1.
10
2.
Write a proportion
relating the similar
shapes.
Find the missing sides.
a
15
x
24
40
Leonardo
da Vinci
1452 - 1519
Write a
ratio that
represents
each
statement.
The average adult human figure is about 7
to 7.5 heads tall.
7 head heights
1 body height
The arms' wingspan (measured from the tips
of the middle fingers) is about equal to the
body height.
1 wingspan
1 body height
The length of the foot is about equal to the
length of the forearm.
1 foot length
1 forearm length
da Vinci
Proportions
Activity
Measure in
inches
Head Height
Estimated total height
Wingspan
Estimated total height
Actual height
Foot length
Estimated
forearm length
Actual forearm length
•The eyes are at the mid-height of the head.
•The head also can be divided into thirds
•top of the head to the bottom of the forehead
•bottom of the forehead to bottom of the nose
Use these
•bottom of nose to the bottom of the chin.
proportions
to draw a •Width of head is between four and five eyes wide.
head.
•Height of the face is about equal to length of
hand.
•Eyes are apart by a distance of one eye width.
•Bottom of the nose to the corner of the eye is
equal to the height of the ear.
•Width of base of nose is equal to width of the eye.
•The width of the mouth is equal to the distance
between pupils, or the width of two eyes.
Draw like
da Vinci
Maps and Scale Drawings 11/30
Scale
Drawing
An enlarged or reduced drawing of an
object that is similar to the actual object
A small
picture of
Kaleigh is
similar to
Kaleigh
Scale
The ratio that compares a length in a
drawing to the corresponding
length of the actual object.
The scale of
this picture is
2 in : 1 foot.
What is
Kaleigh’s real
height?
Scale
Drawing
Real
=
6 in
Values
Drawing
Real
You Try 1. The scale of a drawing is 1in : 6 ft.
Find the actual length for a drawing
length of 4.5 inches.
The scale of a map is 1 inch : 10
miles. Find the actual distance
given the distance on the map.
2. 4 inches
3. 1 foot
4. 6.75 inches
Scale
Kaleigh’s actual
length is 3.5
feet. Her length
in the drawing
is 7 inches.
Find the scale.
Values
Drawing
Real
=
7 in
Scale
Drawing
Real
Plug in the values and simplify to find the
scale
You Try
5. The actual length between the
wheels of a mountain bike is
260cm. The length between the
wheels in the scale drawing is
4cm. Find the scale of the
drawing.
You Try Workbook
p 91
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p 92
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