Aim: How do we solve proportion problems?

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Presentation transcript:

Aim: How do we solve proportion problems? PROPORTIONS

Aim: How do we solve proportion problems? RATIO REVIEW Ratio - comparison between 2 numbers by division. *Note: To find the ratio of 2 quantities, both quantities must be expressed in the same unit of measure before finding their quotient. For example, to compare the value of a nickel to a penny, we first convert the nickel to 5 pennies and then find the ratio, which is 5:1 (i.e. a nickel is worth 5 times as much as a penny).

Aim: How do we solve proportion problems? Proportion - an equation that states that two ratios are equal (AKA: equivalent ratios) a and d are called extremes (1st and 4th terms, 'outers'); b and c are called means (2nd and 3rd, 'inners') Note: In a proportion, the product of the means is equal to the product of the extremes

Aim: How do we solve proportion problems? Using your knowledge of ratios, what is another way you can write this proportion? a : b = c : d

Aim: How do we solve proportion problems? A 6-foot man casts a 10-foot shadow. How many feet tall is a nearby tree that casts a 50-foot shadow at the same time? 6 = x 10 50 300 = 10 x 10 10 x= 30 ft

Aim: How do we solve proportion problems? Is 5 4 16 20 = a "TRUE" proportion? To check, you can: a) Multiply the means and the extremes to see if they are equivalent b) Reduce each ratio to simplest form to see if they become the same c) Use a calculator to find the decimal form of each ratio NO, not a proportion because -4(20) = 5(16) -80 = 80

Aim: How do we solve proportion problems? GUIDED PRACTICE 3. 1. 4. 2. 25:x = 5:2

Aim: How do we solve proportion problems? GUIDED PRACTICE 3. 2x(n) = 4r(m) 2xn = 4rm 2n 2n x= 2rm n 1. 4(42) = 6(x) 168 = 6x 28 = x 2. 4. 25 = 5 x 2 50 = 5x 5 5 250 = 25x 10 = x 3(x-3) = x+7 3x-9 = x+7 2x = 16 x = 8

Aim: How do we solve proportion problems? INDEPENDENT PRACTICE CHALLENGE: 7x-1 5 = 3x+3 3

Aim: How do we solve proportion problems? INDEPENDENT PRACTICE yes yes no We will go over these in class CHALLENGE: 7x-1 5 = 3x+3 3

HW textbook pg. 146: 18, 22, 44, 48