What you should learn

To multiply rational numbers

NCTM Curriculm Standards

 

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

Scalar Multiplication

Introduction: Once called "the world's largest office building," the Pentagon, the five-story, five-sided defense building in Washington, D.C., was designed by G.E. Bergstrom to maximize space and efficiency. No two offices are more than a seven-minute walk from one another.

The building is made up of 10 corridors and five rings. There are 230 restrooms, 150 stairways, and 7748 windows. Each outside wall of the building is 921.6 feet in length, slightly longer than three football fields. The inner walls, also in the shape of a pentagon, are each 360.8 feet in length. What is the outer perimeter of the Pentagon?

One way to solve this problem is to use repreated addition.

An easier method would be to multiply 921.6 by 5

The perimeter of the Pentagon is 4608 feet.

Since this method would not work if you wanted to find the product of 2/3 and -2/5 or the product of -5 and -0.3, you can use the following patterns to discover a rule for multiplying rational numbers.

The examples above suggest the following rules.

Multiplying Two Rational Numbers: The product of two numbers having the same sign is positive. The product of two numbers having different signs is negative.

Exercise 1: Find each product.

a. (-9.8)4

(-9.8)4 = -39.2

b. (-3/4)(-2/3)

 

 

Sometimes you need to evaluate expressions that contain expressions that contain rational numbers.

Exercise 2: Evaluate a(5/6) if a = 2

a(5/6) = 2[(5/6)(5/6)] = 2(25/36) = 25/18

 

You may need to simplify expressions by multiplying rational numbers.

Exercise 3: Simplify each expression.

a. (2b)(-3a)

(2b)(-3a) = 2(-3)ab = -6ab

b. 3x(-3y) + (-6x)(-2y)

 

 

Notice that multiplying a number or expression by -1 results in the opposite of the number or expression.

Multiplicative Property of -1: The product of any number and -1 is its additive inverse. -1(a) = -a and a(-1) = -a.

 

To find the product of three or more numbers, you may want to first group the numbers in pairs.

Exercise 4: Find(-3/4)(-4 1/3)(3 2/5)(4)(-1).

(-3/4)(-4 1/3)(3 2/5)(4)(-1) = [(-3/4)(4)][(-4 1/3)(-1)](3 2/5)

= (-3)(-4 1/3)(3 2/5) = -221/5 or -44 1/5

 

 

You can multiply an matrix by a constant. This is called scalar multiplication. When scalar multiplication is performed, each element is multiplied by that constant and a new matrix is formed.

Scalar Multiplication of a Matrix:

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: 19 - 57 odd, 59 - 68

Alternative Homework: Enriched: 18 - 52 even, 54 - 68

Extra Practice: Students book page 760 Lesson 2-6

Extra Practice Worksheet: Click Here.

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