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Proportions and Ratios: Math Lesson for Solving Problems

Learn how to identify and solve proportions in this interactive math lesson. Practice writing proportions, finding cross products, and determining if ratios form a proportion. Clear examples and step-by-step solutions provided.

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Proportions and Ratios: Math Lesson for Solving Problems

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 3-4b Objective Solve proportions

  4. Example 3-4b Vocabulary Proportion When two ratios are equivalent

  5. Example 3-4b Vocabulary Cross product The product of the numerator of one ratio and the denominator of the other ratio

  6. Lesson 3 Contents Example 1Identify a Proportion Example 2Identify a Proportion Example 3Solve Proportions Example 4Solve Proportions

  7. Determine whether and form a proportion. Example 3-1a Write a proportion. Find the cross products. 8(3) =? 12(2) Multiply. 24 = 24 Check to see if equation is equal The cross products are equal Answer: The ratios form a proportion 1/4

  8. Determine whether and form a proportion. Example 3-1b Answer:The ratios do not form a proportion 1/4

  9. Determine whether and form a proportion. Example 3-2a Write a proportion Find the cross products. 5(32) =? 8(18) Multiply. Check to see if equation is equal The cross products are not equal Answer: The ratios do not form a proportion 2/4

  10. Determine whether and form a proportion. Example 3-2b Answer:The ratios form a proportion 2/4

  11. Solve Example 3-3a Write the proportion. Find the cross products. Multiply. Ask “what is being done to the variable?” The variable (n) is being multiplied by 3.5 Do inverse on both sides Combine “like” terms 1  n 1  n = 24 3/4

  12. Solve Example 3-3a Use the Identity Property to multiply 1  n 1  n = 24 Answer: n = 24 3/4

  13. Solve Example 3-3b Answer:x = 25 3/4

  14. length →width → length →width → length →width → Example 3-4a FLAGSAccording to specifications, the ratio of the length of the U.S. flag to its width must be 1.9 to 1. How long must a U.S. flag be if it is designed to have a width of 2.5 feet? Write a proportion. Find the cross products. Multiply. Add dimensional analysis Answer:L = 4.75 feet 4/4

  15. Example 3-4b * SCHOOLThe ratio of boys to girls at Blue Hills Middle School is 4 to 5. How many girls attend the school if there are 96 boys? Answer: x = 120 girls 4/4

  16. End of Lesson 3 Assignment

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