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Understanding Proportions: Equations of Equal Ratios

This lesson focuses on understanding proportions, which are equations stating that two ratios or rates are equal. To determine if two ratios form a proportion, you must demonstrate that the relationship between numerators matches that of the denominators. The lesson includes definitions, examples, and methods for checking proportionality through unit rates and equivalent fractions. Practice exercises reinforce learning by helping you evaluate and complete proportions effectively.

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Understanding Proportions: Equations of Equal Ratios

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  1. Proportions Lesson 6-3:

  2. Vocabulary • A proportion is an equation stating that two ratios or rates are equal. To prove that two ratios form a proportion, you must prove that they are equivalent. To do this, you must demonstrate that the relationship between numerators is the same as the relationship between denominators.

  3. Examples: Do the ratios form a proportion? x 3 Yes, these two ratios DO form a proportion, 7 21 , 10 30 x 3 ÷ 4 8 2 No, these ratios do NOT form a proportion, because the ratios are not equal. , 9 3 ÷ 3

  4. Completing a Proportion • Determine the relationship between two numerators or two denominators (depending on what you have). • Execute that same operation to find the part you are missing.

  5. Example ÷ 5 35 7 = 40 8 ÷ 5

  6. Proportion with Unit Rate Determine if the quantities in each pair of rates are proportional. Explain your reasoning and express each proportional relationship as a proportion Example: 5 laps swum in 8 minutes 11 laps swum in 16 minutes No; Since the rates are NOT proportional 5 laps 11 laps ≠ 16 min 8min

  7. Example #2 8 corrals with 56 horses 4 corrals with 28 horses ÷ 2 8 corrals 4 corrals = 56 horses 28 horses ÷ 2 Yes, this is an equal proportion since the fractions are equivalent.

  8. How to Determine If a pair of rates or ratios are proportional: 1. Use unit rates….to see if the same (from 6-1). 2. Use equal proportions

  9. Practice Time P331 # 1-5

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