Bellwork 4/5 Do the Integrated Review Page 567 (31-45 odd)
Today’s Objective To be able to solve a proportion and use a proportion to solve a problem.
Ratio A ratio is a comparison of one value to another. Like a is to b or a/b or 1/2. In other words a ratio is a FRACTION like 3/4.
Proportion A proportion is a comparison of one ratio to another ratio, like a/b = c/d. 3/4 = 6/8
Black is to White as Red is to _________. Proportional Black is to White as Red is to _________. Round is to Basketball as Oblong is to ________. Green Football
Proportional
Proportional
Properties of Proportions 1.) If a/b = c/d, then b/a = d/c 3/4 = 6/8, then 4/3 = 8/6 2.) If a/b = c/d, then ad = bc 3/4 = 6/8, then 3•8 = 4•6 or 24 = 24
4/y = 24/30 24y = 120 (cross multiply) 24y/24 = 120/24 y = 5 Solving a Proportion 4/y = 24/30 24y = 120 (cross multiply) 24y/24 = 120/24 y = 5
3/y = 5/8 5y = 24 (cross multiply) 5y/5 = 24/5 y = 24/5 Solving a Proportion 3/y = 5/8 5y = 24 (cross multiply) 5y/5 = 24/5 y = 24/5
x/(x + 4) = 2/x x2 = 2(x + 4) (x multiply) x2 = 2x + 8 x2 - 2x - 8 = 0 Solving a Proportion x/(x + 4) = 2/x x2 = 2(x + 4) (x multiply) x2 = 2x + 8 x2 - 2x - 8 = 0
x2 - 2x - 8 = 0 (x - 4)(x + 2) = 0 x - 4 = 0 & x + 2 = 0 Solving a Proportion x2 - 2x - 8 = 0 (x - 4)(x + 2) = 0 x - 4 = 0 & x + 2 = 0 x = 4 & x = -2
3/y = 12/28 12y = 84 (cross multiply) 12y/12 = 84/12 y = 7 Solving a Proportion Your Turn 3/y = 12/28 12y = 84 (cross multiply) 12y/12 = 84/12 y = 7
x(x + 7) = 10(x + 1) x2 + 7x = 10x + 10 x2 - 3x - 10 = 0 Solving a Proportion Your Turn x/(x + 1) = 10/(x + 7) x(x + 7) = 10(x + 1) x2 + 7x = 10x + 10 x2 - 3x - 10 = 0
x2 - 3x - 10 = 0 (x - 5)(x + 2) = 0 x - 5 = 0 & x + 2 = 0 Solving a Proportion x2 - 3x - 10 = 0 (x - 5)(x + 2) = 0 x - 5 = 0 & x + 2 = 0 x = 5 & x = -2
Classwork Do Worksheet 11.1(1-18) Homework page 565 (7-21)