Today’s Agenda1. Lesson: Proportions

2. Quiz 7 back

3. Homework

6-2 Proportions

Objectives:

1.Solve proportions

2.Use proportions to solve problems

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.

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

Use cross products to tell whether the two ratios are equal

2 and 12 4 and 63 16 16 21

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 = 2/31.Write the original problem2.Use cross multiplying3.Divide each side by 24.Simplify

Solve the Proportion

Solve x/12 = 18/27

Solve the Proportion

Solve 4/3 = b/21

Solve the Proportion

Solve x/12 = 18/27

Solve the Proportion

Solve 7/9 = j/22.5

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?

Writing and Solving Proportions

• At the Copy Shoppe, 18 copies cost $1.08. At that rate, how much will 40 copies cost?

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?

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

6-2 Proportions

Objectives:

1.Solve proportions

2.Use proportions to solve problems

Solve the Proportion

• Solve the proportion x/12 = 1/41.Write the original problem2.Use cross multiplying

3.Divide each side by the number before the variable

4. Simplify

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?

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?

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?

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?