What you should learn

To solve equations by using multiplication and division

NCTM Curriculm Standards 2, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Multiplication Property of Equality

Division Property of Equality

Introduction: In 1990, Congress passed into law the Americans with Disabilities Act. One of the provisions of that law has to do with ramps installed on buildings to give people with disabilities access to those buildings. The law states that for a rise of 1", there should be at least 12" of run. The maximum rise is 30".

If a contractor wants to build a ramp that has a 180-inch run, what is the greatest rise that the ramp can have?

In the table above, the pattern suggests that the run is always 12 times the rise. Let x represent the number of inches in the rise. Then 12x represents the number of inches in the run . Write an equation to represent the situation.

To solve equations with multiplication and division, you will need new tools. Equations of the form ax = b, where a and/or b are fractions, are generally solved by using the multiplication property of equality.

Multiplication Property of Equality: For any numbers a, b, and c, if a = b, then ac = bc.

 

Exercise 1: Solve

(g/24) = (5/12)

24 (g/24) = 24(5/12)

g = 2(5) or 10

Check:

(10/24) = (5/12)

(5/12) = (5/12)

The solution is 10.

Exercise 2: Solve each equation.

a. (3 1/4)p = 2 1/2

b. 40 = -5d

The equationin Example 2b, 40 = -5d, was solved by multiplying each side by -1/5. The same result could have been obtained by dividing each side by -5. This method uses the division property of equality. It is often easier to use than the multiplication property of equality.

Division Property of Equality: For any numbers a, b, and c, with c0, if a = b, then (a/c) = (b/c)

Exercise 3: Refer to the application at the beginning of the lesson. Solve 12x = 180.

12x = 180

(12x)/12 = 180/12

x = 15

Check: 12x = 180

12 (15) = 180

180 = 180

This rise of the ramp could be at most 15 inches.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 15 - 41 odd, 42, 43, 45, 46 - 53

Alternative Homework: Enriched: 14 - 40 even, 42 - 53

Extra Practice: Students book page 762 Lesson 3-2

Extra Practice Worksheet: Click Here.

Return to Chapter 3