Page 76 – 77 #18 – 58 even (#36 & #56 bonus) (19 problems – 19 points) Math Pacing Multiplying Rational Numbers.

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Page 76 – 77 #18 – 58 even (#36 & #56 bonus) (19 problems – 19 points) Math Pacing Multiplying Rational Numbers

Multiplication is repeated addition. So, By the Commutative Property of Multiplication, 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:

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). Each product is 4 more than the previous product. One positive and one negative factor: Negative product Two negative factors: Positive 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:

Example 3-1a Find (–8)(–6). same signs  positive product Answer: 48 Multiplying Integers

Example 3-1b Find (10)(–11). different signs  negative product Answer: –110 Multiplying Integers

Example 3-1c Find each product. a. (–4)(8) b. (–6)(–12) Answer: –32 Answer: 72 Multiplying Integers

Example 3-2a Simplify the expression Associative Property (  ) Substitution Distributive Property Simplify. Answer: Simplify Expressions You can simplify expressions by applying the rules of multiplication.

Example 3-2b Answer: 3x Simplify the expression Simplify Expressions

Example 3-3a Find same signs  positive product Answer: Multiply Rational Numbers Multiplying rational numbers is similar to multiplying integers.

Example 3-3b Find Answer: Multiply Rational Numbers

Example 3-4a 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

Example 3-4b 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

Example 3-5a Substitution Answer: same signs  positive product Evaluate Expressions You can evaluate expressions that contain rational numbers.

Example 3-5b Answer: Evaluate Expressions

Multiplying Rational Numbers Multiplicative Property of – 1 The product of any number and – 1 is its additive inverse. Examples: