1. 2.7 Solving Proportions: Proportion: An equation that states that two ratios are equal:

2. Beaded Necklace:

3. We can find the number of red/blue beads using the following concept: 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

4. 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.

5. We use cross-product to solve problems involving proportions with unknowns (variables) Using cross-product we have the following: 5(y) = 3(3) Cross product 5y = 9 Multiplication ___ __ 5 5 Inverse of Multiplication Don’t forget to check!

6. YOU TRY IT:

7. Solution: 4(x) = 3(8) Cross Product 4x = 24 Multiplication 4x = 24 Inverse of Multiplication ___ ____ 4 4 X = 6 Don’t forget to check!!

8. 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?

9. Solution: Set up proportion Cross Product Multiplication x(8oz) = 97mg(12oz) 8oz(x) =1164mgoz ________ _________ 8oz 8oz X = 145.5 mg Don’t forget to check! 8oz(x) =1164mgoz Inverse of multiplication

10. YOU TRY IT: What is the solution to the following proportion:

11. YOU TRY IT (Solution): Given proportion Cross Product Distributive prop. Move smallest variable n(6) = 5(2n+4) 6n= 5(2n) +5(4) 6n= 10n +20 -6n 0 = 4n +20 -20 = -20 Isolate variable -20 = 4n ___ ____ 4 4 Inverse of multiplication n = - 5 Don’t forget to check!

12. VIDEOS: Proportions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-an- unknown-in-a-proportion https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/writing- proportions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-an- unknown-in-a-proportion-2

13. CLASS WORK: Pages: 127– 129 Problems: As many as it takes to master the concept.