Ratios, Proportions, & Geometric Mean

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Presentation transcript:

Ratios, Proportions, & Geometric Mean

Definition – Ratio a:b a b An ___________ that can be written: Always reduce!! expression a b a:b or

Ratios Simplify the ratio

Definition – Proportion An ____________ that states 2 ratios are _______. expression equal a c b d =

Proportions Solve the following proportions: Find the measures of the angles of a triangle that are in the ratio of 3 : 5 : 10

Proportions Example: The area of a rectangular garden is 108 square feet, and the ratio of the length to the width is 4 : 3. Find the length and width of fence needed to enclose the garden.

Proportions Example 3: You have been hired to paint a rectangular wall on the south side of the school. You know that the perimeter of the wall is 484 feet and that the ratio of its length to its width is 9 : 2. Find the area of the wall.

6 x a x x 9 x b = Geometric Mean You find the geometric mean of two numbers like this: 6 x x 9 a x x b = Where a and b are numbers

Geometric Mean Find the geometric mean of the following numbers: 12 and 27 18 and 54 16 and 18

Proportions 3x 6 8 4 8 4 = 3x 6 = Solve the following proportions: 8 4 8 4 3x 6 = = What’s the difference between these two?

Proportions 6x 20 6x 9 9 6 = 20 6 = Solve the following proportions: 9 6 6x 9 20 6 = = What’s the difference between these two?

Proportions Solve the following proportions: 4x 8 12 6 4x + 12 14 12 6 = = What’s the difference between these two?

Homework p. 360 #3-35 odds, 49-53 odds, 61-65 odds