# Chapter 1: Foundations for Algebra Evaluate the Following:

– 8 – (-11)

3.5 – 10.4

7 – 7

-8 + 11 = 3

-6.9

0

Section 1-6: Multiplying and Dividing

Real Numbers

(+) * (+) = (+)

(- ) * (-) = (+)

(+) * (-) = (-)

(-) * (+) = (-)

Examples:

8 * 3 = 24

-6 * 3 = -18

-4 * -5 = 20

9 * -2 = -18

(+) / (+) = (+)

(- ) / (-) = (+)

(+) / (-) = (-)

(-) / (+) = (-)

Examples:

9 / 3 = 3

-6 / 3 = -2

-15 / -5 = 3

10 / -2 = -5

For every nonzero real number a, there is exactly one number

1 that 𝑎 ∗

1 𝑎 such 𝑎

= 1.

8 ∗

1

8

= 1

1 is called the reciprocal or multiplicative

Write the reciprocal of each number.

7 =

1

7

2

3

= 3

2

−4

=

3

−3

4

Another way to divide numbers is the multiply by reciprocals.

Example:

4

5

3

÷

10

=

Example:

5

9

÷ (−3) =

4

5

10

3

=

40

15

=

8

3

5

9

1

−3

=

5

−27

Let a represent any real number.

The product of any real number and zero is zero.

a * 0 = 0

Zero divided by any nonzero real number is zero to 0.

0 𝑎

= 0 where a is not equal

Division by zero is undefined (not possible).

Zero doesn’t have a reciprocal.

1-6 Worksheet:

1-11, 15-22, 26-34, 38, 40