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Today’s Agenda

Learn how to solve proportions and apply them to various problems. Explore the concept of cross-multiplication and practice writing and solving proportions. Homework included.

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Today’s Agenda

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  1. Today’s Agenda 1. Lesson: Proportions • Quiz 7 back • Homework

  2. 6-2 Proportions Objectives: • Solve proportions • Use proportions to solve problems

  3. Understanding Proportion • A Proportion is an equality of two ratios. • The proportion a/b = c/d is read as “a is to b as c is to d.” • A proportion has two cross products a * d, and b * c. The process of forming cross products is called cross multiplying.

  4. Write the verbal description as a proportion • The proportion a/b = c/d is read as “a is to b as c is to d.” Write • 7 is to x as 14 is to 20 • n is to 9 as 10 is to 18 • 35 is to 25 as p is to 5

  5. Use cross products to tell whether the two ratios are equal 2 and 12 4 and 6 3 16 16 21

  6. Solve the Proportion • In many proportion problems, one of the numerators or one of the denominators is a variable. Here is an example: 8/x = 2/3 • To solve this, you use the cross multiplication • Solve the proportion 8/x = 2/3 • Write the original problem • Use cross multiplying • Divide each side by 2 • Simplify

  7. Solve the Proportion Solve x/12 = 18/27

  8. Solve the Proportion Solve 4/3 = b/21

  9. Solve the Proportion Solve x/12 = 18/27

  10. Solve the Proportion Solve 7/9 = j/22.5

  11. 6-3 Writing Proportions • Here, you will read a word problem and come up with your own proportions. Then, you will solve the proportion as learned yesterday. • You must make sure that proportion is written in the correct order. • Three posters cost $9.60. At that rate, how many posters can you buy for $48?

  12. Writing and Solving Proportions • At the Copy Shoppe, 18 copies cost $1.08. At that rate, how much will 40 copies cost?

  13. Writing and Solving Proportions • A microchip inspector found three defective chips in a batch containing 750 chips. At that rate, how many defective chips would there be in 10,000 chips?

  14. HW 23: Text P. 286-287 #19-29 Odd, 39-45 Odd, 53, and 55

  15. 6-2 Proportions Objectives: • Solve proportions • Use proportions to solve problems

  16. Solve the Proportion • Solve the proportion x/12 = 1/4 • Write the original problem • Use cross multiplying • Divide each side by the number before the variable 4. Simplify

  17. Writing and Solving Proportions • When wheel B turns 2 revolutions, wheel A turns 5 revolutions. When wheel A turns 40 revolutions, how many revolutions does wheel B turn?

  18. Writing and Solving Proportions • It takes a machine 12 minutes to fill 200 bottles of soda. At this rate, how many minutes will it take the machine to fill 500 bottles of soda?

  19. Writing and Solving Proportions • A car gets 24 miles per gallon of gasoline. How many gallons of gasoline would the car need to travel 144 miles?

  20. Writing and Solving Proportions • Jerry read a 200-page book in 10 hours. At that rate, how long will it take him to read a 320-page book?

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