Page 76 – 77 #18 – 58 even (#36 & #56 bonus) (19 problems – 19 points)

Multiplying Rational Numbers

5 5

20 121

1213 1

11;1 lowhigh

Multiplying Rational Numbers

Multiplication is repeated addition.

So, 2177773

By the Commutative Property of Multiplication,

3773

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:

12431234

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).

824 4

4

4

4

Each product is 4 more than the previous product.

One positive and one negative factor: Negative product

Two negative factors: Positive product

414 004 414 824

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:

12431234

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)

b. (–6)(–12)

Answer: –32

Answer: 72

Multiplying Integers

Simplify the expression

Associative Property ()

Substitution

Distributive Property

Simplify.Answer:

Simplify Expressions

You can simplify expressions by applying the rules of multiplication.

Answer: 3x

Simplify the expression

Simplify Expressions

Find

same signs positive product

Answer:

Multiply Rational Numbers

Multiplying rational numbers is similar to multiplying integers.

Find

Answer:

Multiply Rational Numbers

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

Multiply Rational Numbers to Solve a Problem

Substitution

Answer: same signs positive product

Evaluate Expressions

You can evaluate expressions that contain rational numbers.

Answer:

Evaluate Expressions

Multiplying Rational Numbers

Multiplicative Property of – 1

The product of any number and – 1 is its additive inverse.

Examples:

aaa 11

41441

3.213.23.21