1.5 SKM & PP 1 Multiplication of Real Numbers

1.5 SKM & PP 2 Multiplication ab In Algebra, MULTIPLICATION can be written in several ways. The PRODUCT of a and b could be represented by any of the following:

1.5 SKM & PP 3 Multiplication by Zero The product of zero and any real number is zero. This is sometimes called the ZERO PRODUCT RULE

1.5 SKM & PP 4 Multiplication: Rules for Signs We already know that the product of two positive numbers is positive. Let’s look at a pattern to help us see that the product of a negative number and a positive number must be NEGATIVE.

1.5 SKM & PP 5 Multiplication: Real Numbers

1.5 SKM & PP 6 Multiplication: Rules for Signs The product of two positive numbers is positive. The product of a negative number and a positive number is negative. Let’s look at a pattern to help us see that the product of two negative numbers must be POSITIVE.

1.5 SKM & PP 7 Multiplication: Real Numbers

1.5 SKM & PP 8 Multiplication: Rules for Signs The product of two positive numbers is positive. The product of a negative number and a positive number is negative. The product of two negative numbers is positive.

1.5 SKM & PP 9 Multiplication: Examples Let’s look at some examples where there are more than two numbers multiplied.

1.5 SKM & PP 10 Multiplication: Examples What happens if three negative numbers are multiplied?

1.5 SKM & PP 11 Multiplication: Examples What happens if four negative numbers are multiplied?

1.5 SKM & PP 12 Multiplication: Examples What about five negatives?

1.5 SKM & PP 13 Multiplication: Examples Let’s multiply six negatives!

1.5 SKM & PP 14 Multiplication: Notice the Pattern? The product of an even number of negative numbers is a positive result.

1.5 SKM & PP 15 Multiplication: How About this Pattern? The product of an odd number of negative numbers is a negative result.

1.5 SKM & PP 16 Multiplication: Negative Numbers Let’s see a few more examples!

1.5 SKM & PP 17 What about x 2 ? Be very careful when working with variables. It is always best to replace the variable with parenthesis when you substitute. When you see x 2 think of it as ( ) 2.

1.5 SKM & PP 18 Evaluating x 2 Evaluate x 2 when x = -4 :

1.5 SKM & PP 19 Evaluating x 2 Evaluate x 2 when x = 4 :

1.5 SKM & PP 20 Evaluating -x 2 Evaluate -x 2 when x = 4 :

1.5 SKM & PP 21 Evaluating -x 2 Evaluate -x 2 when x = -4 :

1.5 SKM & PP 22 Evaluating (-x) 2 Evaluate (-x) 2 when x = -4 :

1.5 SKM & PP 23 Evaluating (-x) 2 Evaluate (-x) 2 when x = 4 :

1.5 SKM & PP 24 Comparing x 2, –x 2 and (-x) 2 So, for x = 4 :

1.5 SKM & PP 25 Example 1 Evaluate -2x 3 when x = 3: Evaluate -2x 3 when x = -3:

1.5 SKM & PP 26 Example 2 Evaluate (-2x) 2 when x = -5:

1.5 SKM & PP 27 That’s All for Now!