SECTION 2

.5

MULTIP

LICAT

ION O

F REAL

NUMBERS

OB

J EC

T I VE :

MU

LT I PLY R

E AL N

UM

BE R

S

US I N

G P

RO

P E RT I ES O

F MU

LT I PL I C

AT I ON

SUPPOSE THAT YOU BORROW $2500 PER YEAR TO ATTEND A 4-YEAR COLLEGE. ASSUME THAT YOU DO NOT PAY BACK ANY OF THE LOAN UNTIL AFTER GRADUATION AND THAT NO INTEREST IS DUE ON THE LOAN DURING THE TIME YOU ARE IN SCHOOL. HOW CAN YOU USE INTEGERS TO MODEL THE DEBT AT THE TIME OF GRADUATION?

MULTIPLYING REAL NUMBERS:

The product of two real numbers with the same sign is the product of their absolute values.

The product of two real numbers with different signs is the opposite of the product of their absolute values.

EX: FIND THE PRODUCT

1. 2.

3. 4.

5. 6.

9 3 18 6

2

33 1

2 3 52

4 x x x 4y

PROPERTIES OF MULTIPLICATION

COMMUTATIVE PROPERTY:

The order in which two numbers are multiplied does not change the product

ASSOCIATIVE PROPERTY:

The way you group three numbers when multiplying does not change the product

IDENTITY PROPERTY;

The product of a number and 1 is the number

PROPERTY OF ZERO:

The product of a number and 0 is 0

PROPERTY OF OPPOSITES:

The product of a number and -1 is the opposite of the number

EX: EVALUATE THE EXPRESSION

a)

b)

c)

2 when 7x x x

25 when 7

7x x

24 when 8a a a

EX: USING MULTIPLICATION IN REAL LIFE

After a recent flood, a store owner sells 294 cans of green beans at a reduced price because their labels were ruined. Because the price the store originally paid for the beans is more than the reduced price, the store loses $0.12 on each can of green beans sold. How much will the store lose if it sells 294 cans of beans?

HOW C

AN YOU D

ETERMIN

E IF

THE P

RODUCT OF

SEVERAL

NONZERO FACTO

RS WILL

BE

POSIT

IVE O

R NEGAT

IVE?

P. 9 6

1 6 – 5

6 EV

E NS ,

6 4 , 6 5 ,

7 4 , 8 3 ,

8 6 , 97