1. Rules for Multiplication and Division
Chapter 1
Section 1.3

2. Objective
Students will multiply and divide real numbers. Students will also simplify expressions involving quotients.

3. Concept (multiplication)
When you multiply any given real number by 1, the product is equal to the given number. For example: 4 * 1 = 4 and 1 * 4 = 4 The identity element for multiplication is 1

4. Identity Property of Multiplication
There is a unique real number 1 such that for every real number a, a * 1 = a and 1 * a = a

5. Multiplicative Property of Zero
For every real number a: a * 0 = 0 and 0 * a = 0

6. Multiplication Property of -1
For every real number a:
a(-1) = -a and (-1)a = -a
Example: 4(-1) = (-1)+(-1)+(-1)+(-1) = -4
Multiplying any real number by (-1) produces the opposite of the number

7. Rules for Multiplication
If two numbers have the same signs, their product is positive
If two numbers have opposite signs, their product is negative
Even number of negatives is positive
Odd number of negatives is negative

8. Example
Multiply 4(7) (-5)8 6(-7) (-4)(-9)

9. Example
Simplify
4(-6)(-7)(-5)
(-2)(-8)(-7)(5)(-6)
(-9)(3)(0)(-5)

10. Example
Simplify
(-3x)(-4y)
-2(x – 3y)

11. Concept (division)
Two numbers whose product is 1 are called reciprocals, or multiplicative inverses, of each other. For example: 5 and 1/5 are reciprocals (5 * (1/5) = 1 4/5 and 5/4 are reciprocals (4/5 * 5/4) = and -0.8 are reciprocals (-1.25 * -0.8) = 1

12. Definition of Division
For every real number a and every nonzero real number b, the quotient a ÷ b, or a/b, is defined by: a ÷ b = a * 1/b To divide by a nonzero number, multiply by its reciprocal

13. Rules for Division
If two numbers have the same sign, their quotient is positive. If two numbers have opposite signs, their quotient is negative.

14. Example
Divide 24 ÷ 6 56 ÷ (-8) -24 ÷ (-3) -27 ÷ (-3)

15. Example
Divide 45x ÷ (-9) W ÷

16. Example
Divide 0 ÷ 5 5 ÷ 0

17. Concept
Dividing by 0 would mean multiplying by the reciprocal of 0. But 0 has no reciprocal. Therefore, division by 0 has no meaning in the set of real numbers.

18. Questions

19. Assignment
Worksheet