1. Objectives
Multiply real numbers.
Divide real numbers.

2. Factors Product When you multiply two numbers, the signs of the
numbers you are multiplying determine whether
the product is positive or negative.
Factors
Product
3(5) Both positive
15 Positive
3(–5) One negative
– Negative
–3(–5) Both negative
Positive
This is true for division also.

3. Multiplying and Dividing Same Sign Numbers
WORDS
Multiplying and Dividing Numbers with the Same Sign
If two numbers have the same sign, their product or quotient is positive.
NUMBERS
4  5 = 20
–15 ÷ (–3) = 5

4. Multiplying and Dividing Diff. Sign Numbers
WORDS
Multiplying and Dividing Numbers with Different Signs
If two numbers have different signs, their product or quotient is negative.
NUMBERS
6(–3) = –18
–18 ÷ 2 = –9

5. Check It Out! Example 1a and 1b
Find the value of each expression.
1a. 35  (–5)
The quotient of two numbers
with different signs is negative. –7
1b. –11(–4)
The product of two numbers
with the same sign is positive. 44

6. Check It Out! Example 1c
Find the value of each expression.
1c. –6x for x = 7
–6x = –6(7)
First substitute 7 for x.
The product of two numbers with different signs is negative.
= –42

7. Example 1: Multiplying and Dividing Signed Numbers
Find the value of each expression.
Top number times whole number, divided by bottom number
The product of two numbers
with different signs is negative. A. –5 B.
The quotient of two numbers
with the same sign is positive. 12

8. Example 1C: Multiplying and Dividing Signed Numbers
Find the value of the expression.
First substitute for x.
Whole number times top number,
divided by bottom number.
The quotient of two numbers
with different signs is negative.

9. Two numbers are reciprocals if their product is 1
Two numbers are reciprocals if their product is 1. (At least one of the numbers will be a fraction).
Dividing fractions is the same as
Flip the Second Fraction and Multiply

10. Multiplicative inverses1 10
10 ÷ 5 = 2
10 ∙ = = 2 5 5
Dividing by 5 is the same as multiplying by the
reciprocal of 5, because 5 is really 5/1.

11. Example 2A: Dividing by Fractions
Example 2 Dividing by Fractions
Divide.
To divide by , multiply by
Multiply the numerators and multiply the denominators.
and have the same sign,
so the quotient is positive.

12. Check It Out! Example 2a
Divide.
Write as an improper fraction.
To divide by , multiply by
and have the same signs, so the quotient is positive.

13. Check It Out! Example 2b
Divide.
Write the reciprocal of
To divide by , multiply by
and have different signs, so the quotient is negative.

14. No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, you can’t divide by 0. Therefore, dividing by zero is undefined (it doesn’t exist, there is no answer at all).

15. Example 3: Multiplying and Dividing with Zero
Multiply or divide. 15 A.
Zero is divided by a nonzero number.
The quotient of zero and any nonzero
number is 0.
B. –22  0
A number is divided by zero.
undefined
Division by zero is undefined.
C. –8(0)
A number is multiplied by zero.
The product of an number and 0 is 0.