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§ 1.7 Multiplying and Dividing Real Numbers Multiplying Real Numbers The product of two numbers with the same sign is a positive number. Example: Multiply. –75 × (– 3) –75 × (– 3) = 225 Example: 5 2 Multiply. 12 3 The result will always be positive. 5 5 2 5 2 12 3 2 2 3 3 18 Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Multiplying Real Numbers The product of two numbers with different signs is a negative number. Example: Multiply. – 6(4) – 6(4) = – 24 Example: Multiply. 12(– 9) 12(– 9) = – 108 The result will always be negative. Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Zero as a Factor If b is a real number, then b · 0 = 0. Also 0 · b = 0. Example: Multiply. – 6 · 0 –6·0=0 Example: Multiply. 0 · 125 0 · 125 = 0 Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Evaluating Exponents Example: Evaluate ( 3)3. ( 3)3 = ( 3)( 3)( 3) = 27 Odd exponent: Negative result Example: Evaluate ( 2)4. ( 2)4 = ( 2)( 2) ( 2) ( 2) = 16 Even exponent: Positive result Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Quotient of Two Real Numbers If a and b are real numbers and b is not 0, then a 1 a b a b b The product or quotient of two numbers with the same sign is a positive number. The product or quotient of two numbers with different signs is a negative number. Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 Multiplying or Dividing Real Numbers Example: 36 Find the quotient. 12 36 36 (12) 3 12 Example: Find the quotient. 3 1 2 6 3 5 3 6 3 6 33 2 9 2 6 2 5 25 25 5 Martin-Gay, Beginning and Intermediate Algebra, 4ed 7 Zero as a Divisor or Dividend 1. The quotient of any nonzero real number and 0 is undefined. In symbols, if a a 0, 0 is undefined. 2. The quotient of 0 and any real number except 0 is 0. In symbols, if 0 a 0, 0. a Example: Divide. – 6 ÷ 0 There is no answer because division by 0 is undefined. Martin-Gay, Beginning and Intermediate Algebra, 4ed 8 Evaluating Expressions Example: Evaluate the expression 4 + (42 – 13)4 – 3. 4 + (42 – 13)4 – 3 = 4 + (16 – 13)4 – 3 Evaluate the exponent inside the parentheses. = 4 + (3)4 – 3 Work inside the parentheses. = 4 + 81 – 3 Evaluate the exponent. = 85 – 3 Add. = 82 Subtract. Martin-Gay, Beginning and Intermediate Algebra, 4ed 9