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Understanding Fractions and Solving Proportions with Cross Products

This detailed guide explains fractions and proportions, focusing on solving proportion problems using cross products. We illustrate how to determine quantities in real-world scenarios, such as calculating the number of red and blue beads needed for a necklace based on given ratios. Examples are provided, moving from setup to solution, ensuring you grasp how variables interact within proportions. You'll also find practice problems and checks to reinforce your understanding. Perfect for students learning about ratios and proportions!

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Understanding Fractions and Solving Proportions with Cross Products

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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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