Transcript Slide 1

Multiplying Rational Numbers
5
 20
 5
13
  12
1
 112
high  1 ; low  11
Page 76 – 77 #18 – 58 even (#36 & #56 bonus) (19 problems – 19 points)
Multiplying Rational Numbers
Multiplication is repeated addition.
So, 3 7   7   7   7  21
By the Commutative Property of Multiplication,
3 7  73
This example suggests the following rule:
Multiplying Rational Numbers
Multiplying Two Numbers with Different Signs
The product of two numbers with different signs is negative.
Examples:
4 3  12
 34  12
Multiplying Rational Numbers
The product of two positive integers is positive.
What is the sign of the product of two negative integers?
Use the pattern to find (– 4)(– 1).
One positive and
one negative
factor: Negative
product
Two negative
factors:
Positive product
 42  8
 41  4
 40  0
 4 1  4
 4 2  8
4
4
4
4
Each
product is
4 more
than the
previous
product.
Multiplying Rational Numbers
This example suggests the following rule.
Multiplying Two Numbers with the Same Sign
The product of two numbers with the same sign is positive.
Examples:
43  12
 3 4  12
Multiplying Integers
Find (–8)(–6).
same signs  positive product
Answer: 48
Multiplying Integers
Find (10)(–11).
different signs  negative product
Answer: –110
Multiplying Integers
Find each product.
a. (–4)(8)
Answer: –32
b. (–6)(–12)
Answer: 72
You can simplify expressions by applying
the rules of multiplication.
Simplify Expressions
Simplify the expression
Associative Property ()
Substitution
Distributive Property
Answer:
Simplify.
Simplify Expressions
Simplify the expression
Answer: 3x
Multiplying rational numbers is similar to
multiplying integers.
Multiply Rational Numbers
Find
same signs  positive product
Answer:
Multiply Rational Numbers
Find
Answer:
Multiply Rational Numbers to Solve a Problem
Stocks The value of a company’s stock dropped by
$1.25 per share. By what amount did the total value of
the company’s stock change if the company has
issued 500,000 shares of stock?
To find the change in the total value of the company’s
stock, multiply the price lost per share by the number
of shares.
different signs  negative product
Answer: The total value of the company’s stock
changed by –$625,000.
Multiply Rational Numbers to Solve a Problem
Construction A construction project is stopped by a
winter storm. For every day that they are unable to
work, the company loses $35,000. If the storm keeps
them from working for 4 days, how much money do
they lose?
Answer: –$140,000
You can evaluate expressions that contain
rational numbers.
Evaluate Expressions
Substitution
Answer:
same signs  positive product
Evaluate Expressions
Answer:
Multiplying Rational Numbers
Multiplicative Property of – 1
The product of any number and – 1 is its additive inverse.
Examples:
 1a  a 1  a
 14  4 1  4
 1 2.3   2.3 1  2.3