1 3 Multiplying and Dividing Real Numbers Objectives

1 -3 Multiplying and Dividing Real Numbers Objectives Multiply real numbers. Divide real numbers. Holt Algebra 1

1 -3 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. Factors Product 3(5) Both positive 15 3(– 5) One negative – 15 – 3(– 5) Both negative This is true for division also. Holt Algebra 1 15 Positive Negative Positive

1 -3 Multiplying and Dividing Real Numbers Multiplying and Dividing Same Sign Numbers WORDS NUMBERS Multiplying and Dividing Numbers with the Same Sign If two numbers have the same sign, their product or quotient is positive. 4 5 = 20 – 15 ÷ (– 3) = 5 Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Multiplying and Dividing Diff. Sign Numbers WORDS NUMBERS Holt Algebra 1 Multiplying and Dividing Numbers with Different Signs If two numbers have different signs, their product or quotient is negative. 6(– 3) = – 18 ÷ 2 = – 9

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 1 a and 1 b Find the value of each expression. 1 a. 35 (– 5) – 7 The quotient of two numbers with different signs is negative. 1 b. – 11(– 4) 44 Holt Algebra 1 The product of two numbers with the same sign is positive.

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 1 c Find the value of each expression. 1 c. – 6 x for x = 7 – 6 x = – 6(7) = – 42 Holt Algebra 1 First substitute 7 for x. The product of two numbers with different signs is negative.

1 -3 Multiplying and Dividing Real Numbers Example 1: Multiplying and Dividing Signed Numbers Find the value of each expression. Top number times whole number, divided by bottom number A. – 5 The product of two numbers with different signs is negative. 12 The quotient of two numbers with the same sign is positive. B. Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Example 1 C: 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. Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers 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 Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Multiplicative inverses 10 ÷ 5 = 2 1 10 10 ∙ 5 = 2 Dividing by 5 is the same as multiplying by the reciprocal of 5, Holt Algebra 1 because 5 is really 5/1.

1 -3 Multiplying and Dividing Real Numbers Example 2 A: 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. Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 2 a Divide. Write as an improper fraction. To divide by and , multiply by have the same signs, so the quotient is positive. Holt Algebra 1 .

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 2 b Divide. Write the reciprocal of To divide by and . , multiply by have different signs, so the quotient is negative. Holt Algebra 1 .

1 -3 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, you can’t divide by 0. Therefore, dividing by zero is undefined (it doesn’t exist, there is no answer at all). Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Example 3: Multiplying and Dividing with Zero Multiply or divide. 0 A. 15 Zero is divided by a nonzero number. 0 B. – 22 0 undefined C. – 8(0) 0 Holt Algebra 1 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.