7-1 Ratio and Proportions

Ratio and Proportion The 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 OZ ID b

Ratio and Proportion The 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 OZ ID b

Ratio and Proportion The 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. OZ ID b

Ratio and Proportion The 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? OZ ID b

Ratio and Proportion The 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 OZ ID b 110

Ratio and Proportion The 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 OZ ID b 110

Ratio and Proportion The 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 OZ ID b 110

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 2 A poster is 1 m long and 52 cm wide. Find the ratio of width to length. Fill in correct measurements

Example 2 A 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?

Example 2 A 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.

Example 2 A 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

Example 2 A 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,

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

Example A 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