Objectives Multiply real numbers. Divide real numbers.

Factors Product When you multiply two numbers, the signs of the numbers you are multiplying determine whether the product is positive or negative. Factors Product 3(5) Both positive 15 Positive 3(–5) One negative –15 Negative –3(–5) Both negative 15 Positive This is true for division also.

Multiplying and Dividing Same Sign Numbers WORDS Multiplying and Dividing Numbers with the Same Sign If two numbers have the same sign, their product or quotient is positive. NUMBERS 4  5 = 20 –15 ÷ (–3) = 5

Multiplying and Dividing Diff. Sign Numbers WORDS Multiplying and Dividing Numbers with Different Signs If two numbers have different signs, their product or quotient is negative. NUMBERS 6(–3) = –18 –18 ÷ 2 = –9

Check It Out! Example 1a and 1b Find the value of each expression. 1a. 35  (–5) The quotient of two numbers with different signs is negative. –7 1b. –11(–4) The product of two numbers with the same sign is positive. 44

Check It Out! Example 1c Find the value of each expression. 1c. –6x for x = 7 –6x = –6(7) First substitute 7 for x. The product of two numbers with different signs is negative. = –42

Example 1: Multiplying and Dividing Signed Numbers Find the value of each expression. Top number times whole number, divided by bottom number The product of two numbers with different signs is negative. A. –5 B. The quotient of two numbers with the same sign is positive. 12

Example 1C: Multiplying and Dividing Signed Numbers Find the value of the expression. First substitute for x. Whole number times top number, divided by bottom number. The quotient of two numbers with different signs is negative.

Two numbers are reciprocals if their product is 1 Two numbers are reciprocals if their product is 1. (At least one of the numbers will be a fraction). Dividing fractions is the same as Flip the Second Fraction 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, because 5 is really 5/1.

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

Check It Out! Example 2a Divide. Write as an improper fraction. To divide by , multiply by . and have the same signs, so the quotient is positive.

Check It Out! Example 2b Divide. Write the reciprocal of . To divide by , multiply by . and have different signs, so the quotient is negative.

No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, you can’t divide by 0. Therefore, dividing by zero is undefined (it doesn’t exist, there is no answer at all).

Example 3: Multiplying and Dividing with Zero Multiply or divide. 15 A. Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. B. –22  0 A number is divided by zero. undefined Division by zero is undefined. C. –8(0) A number is multiplied by zero. The product of an number and 0 is 0.