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Understanding Ratios and Proportions: A Guide to Simplification and Solving

This guide covers essential concepts in ratios and proportions, including the simplification of ratios and how to rewrite fractions with the same units. It provides examples, such as determining the ratio of losses to wins in a sports context and converting pounds to ounces. The guide also addresses solving proportions through cross multiplication, giving practical exercises to reinforce learning. Additional examples of ratios in triangle angles help illustrate concepts clearly. Ideal for students wanting to master these fundamental math skills.

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Understanding Ratios and Proportions: A Guide to Simplification and Solving

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  1. 8.1 – Ratios & Proportions

  2. Writing Ratios • The Blues have won 24 games and lost 20 games. What is the ratio of losses to wins? • 20/24 • Always simplify ratios • 5/6

  3. Rewriting Fractions so that numerator and denominator have same units • Example: 3 lb/ 6 ounces • 16 oz = 1 lb • Convert 3 lb to oz • 3 lb = 48 oz • 48 oz / 6 oz Simplify • 8 oz/ 1 oz • Conversion Rates are in your Agenda

  4. Solving proportions • Solve for x • Cross multiply! • 4x = 35 • X = 8.75

  5. Example • The angles of a triangle are in the ratio of 1:2:3. What are the angles • 1x + 2x + 3x = 180 • 6x = 180 • X = 30 • Angles are 30, 60, and 90

  6. Assignment • p. 461-463 18-44all, 51-53

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