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Proportions and solving problems with ratios

Learn how to use proportions to solve problems involving ratios and discover the properties of proportions. Practice examples included.

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Proportions and solving problems with ratios

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  1. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 4-3b Objective Use proportions to solve problems

  4. Example 4-3b Vocabulary Proportion An equation stating that two rates are equivalent 1 2 = 2 4

  5. Example 4-3b Vocabulary Property of Proportions The cross products of a proportion are equal a/b = c/d then ad = bc a c = b d

  6. Example 4-3b Vocabulary Cross products Multiplying the denominator of one ratio by the numerator of the equivalent ratio a c = b d

  7. Lesson 4 Contents Example 1Identify a Proportion Example 2Solve a Proportion Example 3Use a Proportion to Solve a Problem

  8. Determine whether the ratios form a proportion. Example 4-1a Write the proportion Cross multiply Multiply the numerator of one ratio with the denominator of the other ratio = 12  18 9  27 243 = 216 Multiply 9  27 Multiply 12  18 Products are not equal Answer: The ratios do not form a proportion. 1/3

  9. Determine whether the ratios form a proportion. Example 4-1b Answer: The ratios form a proportion 1/3

  10. Solve Example 4-2a Write the equation. Find the cross products. Bring down 20x = 20x = 4(7) Multiply 4  7 20x = 28 Ask “what is being done to the variable?” Variable is being multiplied by 20 Do the inverse on both sides of the equal sign 2/3

  11. Solve Example 4-2a Bring down 20x = 28 Divide 20x by 20 Divide 28 by 20 20x = 4(7) Combine “like” terms 20x = 28 Use Identify Property to multiply 1  x 1  x = 1  x = 1.4 x = 1.4 Answer: x = 1.4 2/3

  12. Solve Example 4-2b Answer: x = 2.75 2/3

  13. Example 4-3a COOKINGA recipe serves 10 people and calls for 3 cups of flour. If you want to make the recipe for 15 people, how many cups of flour should you use? 10 people and calls for 3 cups of flour 15 people how many cups of flour people served 10 Write first ratio cups of flour 3 Write second ratio keeping units in same location people served 15 cups of flour x Write a proportion with the first ratio equal to the second ratio 10 15 = 3 x 3/3

  14. Example 4-3a people served 10 15 Cross multiply = Bring down = cups of flour 3 x Cross multiply 10x = 3(15) 10x 10x = Bring down 10x = 10x = 10x = 45 Multiply 3  15 Ask “what is being done to the variable?” Variable is being multiplied by 10 Do the inverse on both sides of the equal sign 3/3

  15. Example 4-3a Do the inverse on both sides of the equal sign people served 10 15 = Bring down 10x = 45 cups of flour 3 x Divide 10x by 10 10x 10x = 10x = 3(15) Divide 45 by 10 10x = 10x = 45 Combine “like” terms 10x = 45 Use Identify Property to multiply 1  x 10 10 Add dimensional analysis 1  x = 1  x = 4.5 Answer: cups of flour x = 4.5 3/3

  16. Example 4-3b * COOKINGA recipe serves 12 people and calls for 5 cups of sugar. If you want to make the recipe for 18 people, how many cups of sugar should you use? Answer: x = 7.5 cups of sugar 3/3

  17. End of Lesson 4 Assignment

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