Ratio11/12

My bike’s fuel has a ratio of

oil to gas

1 : 25

The comparison of two or more numbers

Can be written three ways

2/3

2:3

2 to 3

ratios

notation

Count the number of red and green hearts

Red : Green

4 : 8

4 RED and 8 GREEN

Writing Ratios

Red : Green

4 : 8

You know how to simplify fractions, simplifying with a colon works the same way

Divide ÷ by 2

Divide ÷ by 2

Divide ÷ by 2

Divide ÷ by 2

2 : 4

1 : 2

Simplifying

ratios

The ratio of red to green is

Red : Green

1 : 2

This tells you that there are 2 green hearts for

every red heart

Copy and complete this chart

Ratio Simplest terms

12 / 16

24 : 32

27 / 36

28 to 40

You try

Copy and complete this chart

Ratio Simplest terms

12 : 16 3 : 424 / 32 3 / 4

27 to 36 3 to 428 / 40 7 / 10

Workbook

P 79

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You try

Unit Rate and Proportional Reasoning 11/13

rate A ratio that compares two numbers with different units

Miles per hour mph

The rate for one unitUnit ratemph is usually expressed as a unit rate

1. It takes 2 hours to get to a friends house in Atlanta, 124 miles away. What would the mph be?

Examples

Unit Rate

2. You can solve 76 math problems in 3 hours and 42 minutes. How many problems do you solve per minute?

1. 20 pieces of candy cost $2.40, what does one piece of candy cost?

Examples

Unit price

2. Kaleigh’s dog food is $1.15 per pound. How much does a 40lb bag of food cost?

Workbook

P 81

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You try

•Turn in homework

•Get your workbook

•Sharpen pencil

•Sit down

•Get ready for notes

Turn in homeworkSharpen PencilsGrab a workbookSit down and get ready for notes

Proportions 11/16Proportions

12

48

=1:3 = 3:9

- If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.

If the ratios form a proportion, then the simplified forms of the ratios will equal.

Simplest Form

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

Examples

If the ratios form a proportion, then the numerator and denominator will share a multiplier.

Common Multiplier

Determine if the ratios form a proportion by finding a common multiplier

• 8/15, 32/40• 60/140, 3/7• 10/24, 30/70

Examples

a c b d

Cross

MultiplyingIf a/b = c/d then ad = bc

ad =

=

Determine if the ratios form a proportion by cross multiplying

• 2/3, 4/5• 10/5, 6/3• 5/6, 50/72

Examples

bc

If the ratios form a proportion, then the cross products are equal

Workbook

Page 85

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You Try

Solving Proportions11/18

Proportions

1

248

= 1:3 = 3:9

- If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.

Similar - Similar describes things which have the same shape but are not the same size.

a c b d

Cross

Multiplying If a/b = c/d then ad = bc

ad =

=

1. 2/3 = 4/6

2. 10/x = 6/3

3. 5/6 = x/72

Examples

bc

A proportion can be made relating the height and the width of the smaller figure to the larger figure:

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.

Ratio

2 ft

4 ft

8 ft

4 ft4 ft

2 ft=

8 ft

4 ft

Proportion

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 denominator represent?

2 feet

6 feet

18 feet

? feet

6 ft

2 ft=

18 ft

x ft

6x = 2 ∙ 18

6x = 36

x = 6

Then solve for x by cross multiplying:

height

width

Workbook

P 87

start at # 6

You try

Binder Check1. 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 258-259, 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.

Figures are similar if the ratio between each side make a proportion

Write each example off the white board

Similar figures

You Try

1. Write a proportion relating the similar shapes.

2. Find the missing width.

3 feet

8 feet 12 feet

x feet

These two stick figures are similar.

You Try These two trapezoids are similar.1. Write a proportion

relating the similar shapes.

2. Find the missing sides.

15x

a

24

40

10

Leonardo da Vinci1452 - 1519

The average adult human figure is about 7 to 7.5 heads tall.

The arms' wingspan (measured from the tips of the middle fingers) is about equal to the

body height.

The length of the foot is about equal to the length of the forearm.

Write a ratio that represents each statement.

7 head heights1 body height

1 wingspan1 body height

1 foot length1 forearm length

Head Height

Estimated total height

Wingspan

Estimated total height

Actual height

Foot length

Estimatedforearm length

Actual forearm length

da VinciProportionsActivity

Measure in inches

•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•bottom of nose to the bottom of the chin.

•Width of head is between four and five eyes wide. •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

Use these proportions to draw a head.

Maps and Scale Drawings 11/30Scale 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

ScaleThe 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?

6 in

Drawing DrawingReal Real

Scale Values

=

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.

7 in

Drawing DrawingReal Real

Values

=Scale

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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