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Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.
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Multiplying and Dividing Real Numbers
1.7 Multiplying and Dividing Real Numbers
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Multiplying Real Numbers
1. The product of two numbers with the same sign is a positive number. 2. The product of two numbers with different signs is a negative number.
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Examples Multiply. a. 4(–2) = –8 b. ‒7(‒5) = 35 c. 9(‒6.2) = ‒55.8 d.
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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
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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
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Example Evaluate. a. (–2)4 = (–2)(–2)(–2)(–2) = 16
b. ‒72 = ‒(7 ·7) = ‒49
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Finding Reciprocals Reciprocal or Multiplicative Inverse
Two numbers whose product is 1 are called reciprocals or multiplicative inverse of each other. Quotients Involving Zero The number 0 does not have a reciprocal.
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Example Find the reciprocal. a The reciprocal is b.
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Quotient of Two Real Numbers
If a and b are real numbers and b is not 0, then 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.
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Example Divide. a. b. c.
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Examples a. Find the quotient. b. Find the quotient.
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Division Involving Zero
If a is a nonzero number, then If a and b are real numbers, and b 0, then
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Evaluating Expressions
Example: Evaluate the expression (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. = – 3 Evaluate the exponent. = 85 – 3 Add. Subtract. = 82
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Example Use order of operations to evaluate each expression. a. b.
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