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2.7 Solving Proportions:

Fraction: A term with numerator and denominator ( where b ≠ 0) . 2.7 Solving Proportions:. 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:.

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2.7 Solving Proportions:

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  1. Fraction: A term with numerator and denominator ( where b ≠ 0) . 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: 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

  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 beadsto make a 20 in necklace.

  5. 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 Multiplication 5y = 9 ___ __ 5 5 Inverse of Multiplication Y = Don’t forget to check!

  6. YOU TRY IT: What is the solution to the proportion:?

  7. YOU TRY IT: (Solution) What is the solution to the proportion:? 4(x) = 3(8) Cross Product 4x = 24 Multiplication 4x = 24 Inverse of Multiplication ___ ____ 4 4 X = 6 Don’t forget to check!!

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

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

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

  12. Class Work: Pages: 127-128 Problems: 11, 17, 19, 25, 34, 35, 36, 40, 48, 49, 50, 51

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