# Chapter 1: Foundations for Algebra

```
Evaluate the Following:

– 8 – (-11)
-8 + 11 = 3

3.5 – 10.4
-6.9

7–7
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,
1
there is exactly one number such
𝑎
1
that 𝑎 ∗ = 1.
𝑎
1
𝑎
is called the reciprocal or multiplicative
inverse of a.
Write the reciprocal of each number.
1
8∗ =1
8

7=
1
7

2
3
3
2

−4
3
=
=
−3
4
Another way to divide numbers is the multiply by reciprocals.

Example:
4
5
&divide;
3
10
=

4
5
∗
10
3
=
40
15
=




Example:
5
9
&divide; (−3)=
5
9
∗
1
−3
=
5
−27
8
3
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
```