Holt McDougal Algebra Multiplying and Dividing Real Numbers Warm Up Multiply or divide. 1. 6(7) ÷ Write as an improper fraction Write as a mixed number.

Holt McDougal Algebra Multiplying and Dividing Real Numbers

Holt McDougal Algebra Multiplying and Dividing Real Numbers To multiply and divide real numbers. Objectives

Holt McDougal Algebra Multiplying and Dividing Real Numbers reciprocal multiplicative inverse Vocabulary

Holt McDougal Algebra Multiplying and Dividing Real Numbers When you multiply two numbers, the signs of the numbers you are multiplying determine whether the product is positive or negative. FactorsProduct 3(5)Both positive 3(–5)One negative –3(–5) Both negative 15Positive –15 Negative 15 Positive This is true for division also.

Holt McDougal Algebra Multiplying and Dividing Real 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 Signed Numbers

Holt McDougal Algebra Multiplying and Dividing Real 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 Multiplying and Dividing Signed Numbers –18 ÷ 2 = –9

Holt McDougal Algebra Multiplying and Dividing Real Numbers Find the value of each expression. –5–5 The product of two numbers with different signs is negative. Example 1 A. 12 The quotient of two numbers with the same sign is positive. B.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Find the value of the expression. The quotient of two numbers with different signs is negative. Multiply. = –2 C. Example 2

Holt McDougal Algebra Multiplying and Dividing Real Numbers Find the value of each expression. –7–7 The quotient of two numbers with different signs is negative. Say out loud… 1a. 35  (–5) 44 The product of two numbers with the same sign is positive. 1b. –11(–4)

Holt McDougal Algebra Multiplying and Dividing Real Numbers Find the value of each expression. Say Out Loud… –6(7) = – 42 The product of two numbers with different signs is negative.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse. Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number. WRITE THIS DOWN

Holt McDougal Algebra Multiplying and Dividing Real Numbers 10 ÷ 5 = 210 ∙ = = Multiplicative inverses Dividing by 5 is the same as multiplying by the reciprocal of 5,.

Holt McDougal Algebra Multiplying and Dividing Real Numbers You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. Helpful Hint

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 2 Dividing by Fractions Example 3 Divide. To divide by, multiply by. Multiply the numerators and multiply the denominators. and have the same sign, so the quotient is positive.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 4 Divide. Write as an improper fraction. To divide by, multiply by. and have different signs, so the quotient is negative.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 5 Divide. Write as an improper fraction. To divide by multiply by. The signs are different so the quotient is negative.

Holt McDougal Algebra Multiplying and Dividing Real Numbers No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, division by 0 is not possible. We say that division by zero is undefined.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Properties of Zero WORDS NUMBERS ALGEBRA Multiplication by Zero The product of any number and 0 is · 0 = 0 0(–17) = 0 a · 0 = 00 · a = 0

Holt McDougal Algebra Multiplying and Dividing Real Numbers Properties of Zero WORDS NUMBERS ALGEBRA Zero Divided by a Number The quotient of 0 and any nonzero number is = 0 0 ÷ a = 0 0 ÷ 2323 = 0 0a0a

Holt McDougal Algebra Multiplying and Dividing Real Numbers Properties of Zero WORDS NUMBERS ALGEBRA Division by Zero Division by 0 is undefined. a ÷ 0 a0a0 12 ÷ 0 Undefined –5 0 Undefined

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 6 Multiply or divide. A B. –22  0 undefined C. –8.45(0) 0 Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. A number is divided by zero. Division by zero is undefined. A number is multiplied by zero. The product of an number and 0 is 0. 0

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 7 Divide: Zero is divided by a nonzero number. The quotient of zero and any nonzero number is zero.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Example 8 Divide: 3b ÷ ÷ 0 = undefined Any number divided by 0 is undefined. 3c. (–12.350)(0) ( – )(0) = 0 The product of any number and 0 is 0.

Holt McDougal Algebra Multiplying and Dividing Real Numbers Find the value of each expression –7 –52. 2( – 6) – 12 Exit Card Multiply or divide if possible. 3. –3 ÷ (0) 4. – –  – undefined 15 miles 6.A cyclist traveled on a straight road for 1 hours at a speed of 12 mi/h. How many miles did the cyclist travel? 1414