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Proportions: Solving Ratios Equations

johnathanhairston avatar
johnathanhairston
8 diapositives · 122 Views · Jan 04, 2020

Learn how to solve proportions by comparing ratios, finding cross products, and simplifying fractions. Practice with examples and solve for unknowns using verbal models.

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Proportions: Solving Ratios Equations
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  1. Review of solving Proportions

  2. Vocabulary • A proportion is an equation stating that two ratios are equal. • Examples: or • The cross products of a proportion are equal. or

  3. Example #1 Determine if the following ratios form a proportion. ? If two ratios are proportional, then their cross products will be equal. Since 85 ≠ 84, then this is not a proportion.

  4. Example #2 Determine if the following ratios form a proportion. If two ratios are proportional, then their cross products will be equal. ? Since 420 = 420, then this is a proportion. Don’t forget comparing ratios! You could also simplify the fractions to see if they are equal…..

  5. Example #3 Solve for x in the proportion below. Since this is a proportion, the cross products must be equal.

  6. Example #4 Solve for y in the proportion below. Since this is a proportion, the cross products must be equal.

  7. Example #5 If recycling 2000 pounds of paper saves 17 trees, how many trees would be saved when 5200 pounds of paper are recycled? Write a verbal model of what you are comparing. Substitute in the values you are given. Use x to represent the quantity that you are looking for. Solve the proportion using cross products. 44.2 trees would be saved.

  8. Example #6 Jake can run 3.75 miles in 40 minutes. At this pace, how many minutes would it take him to run 7 miles? Round your answer to the nearest minute. Write a verbal model of what you are comparing. Substitute in the values you are given. Use x to represent the quantity that you are looking for. Solve the proportion using cross products. It would take Jake about 75 minutes to run 7 miles.