1.5 S KM & PP 1

Multiplication ofReal Numbers

1.5 S KM & PP 2

Multiplicationab

In Algebra, MULTIPLICATION can

be written in several ways.

The PRODUCT of a and b could be represented by

any of the following:ab ba ba

ba ba ba

1.5 S KM & PP 3

Multiplication byZero

The product of zero and any real number is zero.

00a 0a0

0a00a This is sometimes called the

ZERO PRODUCT RULE

1.5 S KM & 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 S KM & PP 5

Multiplication:Real Numbers

1234 933 632 331 030 331 632 933 1234

1.5 S KM & 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 S KM & PP 7

Multiplication:Real Numbers

1234 933 632 331 030 331 632 933 1234

1.5 S KM & 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.

1234

1234 1234

1234

1.5 S KM & PP 9

Multiplication: Examples

Let’s look at some examples where there are more

than two numbers multiplied.

254 220

40

1.5 S KM & PP 10

Multiplication: Examples

What happens if three negative numbers are

multiplied?

235 215

30

1.5 S KM & PP 11

Multiplication: Examples

What happens if four negative numbers are

multiplied?

2355

275

150

2325

1.5 S KM & PP 12

Multiplication: Examples

What about five negatives?

13452

1340

120

13410

1120

1.5 S KM & PP 13

Multiplication: Examples

Let’s multiply six negatives!

134526

13460

720

134512

13240

1720

1.5 S KM & PP 14

Multiplication:Notice the Pattern?

The product of an even number of negative

numbers is a positive result.

3125

74 28

30

312521

60

1.5 S KM & PP 15

Multiplication:How About this

Pattern?

The product of an odd number of negative

numbers is a negative result.

315 15

32521 60

1.5 S KM & PP 16

Multiplication: Negative Numbers

Let’s see a few more examples!

45.32

31

54

154

28

312021 0

1.5 S KM & PP 17

What about x2 ?

Be very careful when working with variables.

It is always best to replace the variable

with parenthesis when you substitute.When you see

x2

think of it as ( )2.

1.5 S KM & PP 18

Evaluating x2

Evaluate x2 when x = -4 :

22 4x

44

16

1.5 S KM & PP 19

Evaluating x2

Evaluate x2 when x = 4 :

22 4x

44

16

1.5 S KM & PP 20

Evaluating -x2

Evaluate -x2 when x = 4 :

22 4x

44

16

1.5 S KM & PP 21

Evaluating -x2

Evaluate -x2 when x = -4 :

22 4x

44

16

1.5 S KM & PP 22

Evaluating (-x)2

Evaluate (-x)2 when x = -4 :

22 4x

24

44

16

1.5 S KM & PP 23

Evaluating (-x)2

Evaluate (-x)2 when x = 4 :

22 4x

24

44

16

1.5 S KM & PP 24

Comparingx2 , –x2 and (-x)2

So, for x = 4 :

22 4x 16

22 4x 16

22 4x 16

1.5 S KM & PP 25

Example 1

Evaluate -2x3 when x = 3:

3332 33 32x2

54

3332 33 32x2

54

Evaluate -2x3 when x = -3:

1.5 S KM & PP 26

Example 2

Evaluate (-2x)2 when x = -5:

22 52x2

210

100

1.5 S KM & PP 27

That’s All for Now!