2.7 Solving Proportions: Fraction: A term with numerator and denominator ( where b ≠ 0) . Proportion: An equation that states that two ratios are equal: Beaded Necklace: We can find the number of red/blue beads using the following concept: Cross Product: the products of a proportion: If = ≠ 0 and d ≠ 0, then a∙d = b∙c Since we have 2 read beads every 1.25 in, we can find out how many we need for a 20 in by using the following: . = 1.25in(x) 2red(20in) ________ = _______ 1.25in 1.25in x = 32 red We can repeat this process to find the number of blue beads: Since we have 3 read beads every 1.25 in, we can find out how many we need for a 20 in by using the following: . = 1.25in(x) 3blue(20in) ________= ______ 1.25in 1.25in x = 48 blue Thus if we are following the same pattern, we will need 32 red and 48 blue beads to make a 20 in necklace. We use cross-product to solve problems involving proportions with unknowns (variables Ex: What is the solution to the proportion: = ? Using cross-product we have the following: 5(y) = 3(3) Cross product 5y = __ 9 ___ 5 5 Y= Multiplication Inverse of Multiplication Don’t forget to check! YOU TRY IT: What is the solution to the proportion: = ? Solution: What is the solution to the proportion: = ? 4(x) = 3(8) Cross Product 4x = 24 Multiplication 4x =____ 24 ___ 4 4 Inverse of Multiplication X=6 Don’t forget to check!! REAL-WORLD: An 8-oz can of orange juice contains about 97 mg of vitamin C. About how many milligrams of vitamin C are there in a 12-oz can of orange juice? Solution: = Set up proportion x(8oz) = 97mg(12oz) Cross Product 8oz(x) =1164mgoz Multiplication 8oz(x) ________ =1164mgoz _________ 8oz 8oz X = 145.5 mg Inverse of multiplication Don’t forget to check! YOU TRY IT: What is the solution to the following proportion: = + ? YOU TRY IT (Solution): = + ? n(6) = 5(2n+4) 6n= 5(2n) +5(4) Given proportion Cross Product Distributive prop. 6n= 10n +20 -6n -6n Move smallest variable 0 = 4n +20 -20 = -20 ___ =____ -20 4n n=-5 4 4 Isolate variable Inverse of multiplication Don’t forget to check! VIDEOS: Proportions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/writingproportions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-anunknown-in-a-proportion https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-anunknown-in-a-proportion-2 CLASS WORK: Pages: 127– 129 Problems: As many as it takes to master the concept.