Definition/Procedure Example Negative Signs in Fractions When a fraction is negative, the negative sign is usually written in front of the fraction. However, we can write other, equivalent forms of the fraction. If a fraction has a negative sign in front of it, we can rewrite the fraction with the negative sign in the numerator or the denominator but not both. (p. 744) Write two equivalent forms of 5 8 by moving its negative sign. Solution We can write 5 8 5 8 . We can also write 5 8 5 8 . Using Exponents with Negative Numbers We can use an exponent to represent repeated multiplication of a negative number. In this case, the negative number must be in parentheses. (p. 748) Write 8 (8) (8) (8) using an exponent. Solution 8 (8) (8) (8) (8)4 4 factors of 8 Order of Operations The order of operations applies to signed numbers. Simplify expressions in the following order: 1) If parentheses or other grouping symbols appear in an expression, simplify what is in these grouping symbols fi rst. 2) Simplify expressions with exponents or square roots. 3) Multiply or divide, moving from left to right. 4) Add or subtract, moving from left to right. (p. 749) ⎛ ⎝ ⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪ Simplify each expression. a) (4)2 b) 42 c) 6 33 (3) (5 7)3 Solution a) (4)2 4 (4) 16 The base is 4. b) Notice that 42 does not contain parentheses. The order of operations tells us to evaluate exponents fi rst. 42 1 42 1 16 16 c) 6 33 (3) (5 7)3 6 33 (3) (2)3 Simplify inside parentheses fi rst. Evaluate the exponential expression. Divide. Add and subtract from left to right. Add. 6 33 (3) (8) 6 (11) (8) 5 (8) 13 10.5 The Order of Operations Chapter 10: Review Exercises (10.1) Represent the number in each statement as a signed number. 1) The British luxury passenger liner Titanic was found approximately 13,000 ft below the ocean’s surface. (www.britannica.com/titanic) 2) The Badwater area in Death Valley National Park is the lowest point in North America and is 282 ft below sea level. (www.nps.gov) Graph each group of numbers on the number line. 2524232221 0 1 2 3 4 5 3) 1, 5, 1, 3, 2 4) 4, 2, 5, 3, 2 5) 2 1 5 , 3, 3 4 , ˇ1 1 2 , 5 6 6) 2, 3 1 4 , 7 8 , ˇ 7 8 , 4 1 2 7) 0.7, 5, 3.6, 0.9, 2 8) 1.1, 1.1, 0, 4.5, 3.9 Fill in the blank with or to compare each pair of numbers. 9) 45 _____ 44 10) 4 11 _____ 5 12 11) 3 2 3 _____ 3 5 6 12) 0.01 _____ 0.009 Use the number line below for Exercises 13–16. Fill in the blank with or to make the statement true. a b 0 c d 13) c a 14) b 0 15) b a 16) 4 a 760 CHAPTER 10 Signed Numbers www.mhhe.com/messersmith
messersmith_power_basic_college_1e_ch4_7_10
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