7-1 Ratio and Proportions

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

12

8

3

2

OZ

ID

120

60 70

146b

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

12

8

3

2

OZ

ID

120

60 70

146b

b6

14

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

b) Find the ratio of the measure of the smallest angle of the trapezoid to that of the

largest angles.

12

8

3

2

OZ

ID

120

60 70

146b

bb 3

7

6

14

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

b) Find the ratio of the measure of the smallest angle of the trapezoid to that of the

largest angles.

What is the measure of angle O?

12

8

3

2

OZ

ID

120

60 70

146b

bb 3

7

6

14

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

b) Find the ratio of the measure of the smallest angle of the trapezoid to that of the

largest angles.

What is the measure of angle O?

< D is the smallest and < Z is the largest

12

8

3

2

OZ

ID

120

60 70

146b

bb 3

7

6

14

110

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

b) Find the ratio of the measure of the smallest angle of the trapezoid to that of the

largest angles.

What is the measure of angle O?

< D is the smallest and < Z is the largest

12

8

3

2

OZ

ID

120

60 70

146b

bb 3

7

6

14

110

120

60

Ratio and ProportionThe ratio of one number to another is the quotient when the first number is divided by the

second. This quotient is usually expressed in simplest form.

The ratio of 8 to 12 is or

a) Find the ratio of OI to ZD

b) Find the ratio of the measure of the smallest angle of the trapezoid to that of the

largest angles.

What is the measure of angle O?

< D is the smallest and < Z is the largest

12

8

3

2

OZ

ID

120

60 70

146b

bb 3

7

6

14

110

120

60

2

1

Examples

The ratio of the measure of the smallest angle of the trapezoid to that of largest angle is 1 to 2.

Ratios can be used to compare two numbers. To find the ratio of the lengths of two segments, the segments must be measured in terms of the same unit.

Example 2A poster is 1 m long and 52 cm wide. Find the ratio of width to length.

Fill in correct measurements

length

width

Example 2A poster is 1 m long and 52 cm wide. Find the ratio of width to length.

Fill in correct measurements

because these units are not the same we cannot compare them until we make them the same unit of measure.

How many cm are in 1 m?

length

width

m

cm

1

52

Example 2A poster is 1 m long and 52 cm wide. Find the ratio of width to length.

Fill in correct measurements

because these units are not the same we cannot compare them until we make them the same unit of measure.

How many cm are in 1 m? 1m = 100cm re-write fraction.

length

width

m

cm

1

52

Example 2A poster is 1 m long and 52 cm wide. Find the ratio of width to length.

Fill in correct measurements

because these units are not the same we cannot compare them until we make them the same unit of measure.

How many cm are in 1 m? 1m = 100cm re-write fraction.

reduce

length

width

m

cm

1

52

cm

cm

100

52

Example 2A poster is 1 m long and 52 cm wide. Find the ratio of width to length.

Fill in correct measurements

because these units are not the same we cannot compare them until we make them the same unit of measure.

How many cm are in 1 m? 1m = 100cm re-write fraction.

reduce,

length

width

m

cm

1

52

cm

cm

100

52

25

13

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle?

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

x = 20

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

x = 20 so 2x =

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

x = 20 so 2x = 40 5x =

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

x = 20 so 2x = 40 5x = 100

Example 3

The measure of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

Let 2x, 2x, 5x represent the angle measures

How many degrees are in a triangle? 180

2x + 2x + 5x = 180

9x = 180

x = 20 so 2x = 40 5x = 100 so the angle measures are 40,40, 100

ExampleA Proportion is an equation stating that two ratios are equal. For example

and a:b = c:d are equivalent forms of the same proportion.

When 3 or more ratios are equal you can write an extended proportion

d

c

b

a

f

e

d

c

b

a