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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