1. 1-3
Purpose
Multiply real numbers.
Divide real numbers.

2. Positive + , + + , - or - , + Negative - , - Positive Factors Product
This is true for division also.

3. Multiplication Division (3)(10) = 30 (-12)(-2) = 24
Multiplying & Dividing signed numbers
Multiplication
Division
Same Signs answer is +
(3)(10) = 30 (-12)(-2) = 24
Different Signs answer is -
(-9)(2) = -18 (7)(-4) = -28

4. Find the value of each expression.
Example 1
Find the value of each expression. A.
The product of two numbers
with different signs is negative. –5 B.
The quotient of two numbers
with the same sign is positive. 12

5. Example 1C: Multiplying and Dividing Signed Numbers
Find the value of the expression.
First substitute for x.
The quotient of two numbers
with different signs is negative.

6. You can use multiplicative inverses when dividing fractions!
Reciprocal: Two #’s when multiplied together give you 1. EX: 4(1/4) = 4/4 = 1
Multiplicative Inverse: A number and it’s reciprocal. EX: 4 is the mult. inv. of 1/4
You can use multiplicative inverses when dividing fractions!

7. Flip the 2nd term and multiply!
Multiplicative inverses 1 10
10 ÷ 5 = 2
10 ∙ = = 2 5 5
Dividing by 5 is the same as multiplying by the
reciprocal of 5, .

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

9. Flip the 2nd # and multiply!!
You Try!
Divide.
Flip the 2nd # and multiply!!
Write as an improper fraction.
To divide by , multiply by
and have the same signs, so the quotient is positive.

10. (1/2)0 = 0 0(-17) = 0 a(0) = 0 0(a) = 0 Properties of zero
Number Example
Algebra Example
Multiplication by zero
(1/2)0 = 0 0(-17) = 0
a(0) = 0 0(a) = 0
Zero Divided by a number
Division by zero or or or or
Undefined
Undefined

11. Example 3: Multiplying and Dividing with Zero
Multiply or divide. A. 15
Zero is divided by a nonzero number.
The quotient of zero and any nonzero
number is 0.
B. –22  0
undefined
A number is divided by zero.
C. –8.45(0)
Division by zero is undefined.
A number is multiplied by zero.
The product of an number and 0 is 0.

12. You Try! Divide: 3b. 0 ÷ 0 Any number divided by 0 is undefined.
3c. (–12.350)(0)
The product of any number and 0 is 0.
(–12.350)(0) = 0

13. Example 4: Recreation Application
The speed of a hot-air balloon is 3 mi/h. It travels in a straight line for 1 hour before landing. How many miles away from the liftoff site does the balloon land? 1 3 4
Find the distance traveled at a rate of 3 mi/h for 1 hour.
To find distance, multiply rate by time. 3 4 1
rate
times
time 3 4 1 3  1 3

14. Example 4: Recreation Application3 4 • 1 = 15
Write and as improper fractions. 3 4 1
15(4)
4(3) = 60 12
Multiply the numerators and
multiply the denominators. 3 4
and have the same sign, so
the quotient is positive. 1
= 5
The hot-air balloon lands 5 miles from the liftoff site.

15. Exit Task
Find the value of each expression. 1. 35 –7 –5
2. 2x for x = –6
– 12
Multiply or divide if possible.
undefined
3. –3 ÷ 1 3 4
(0)
4. –2 1 3 – 12 7
5. –
 0 3 4