Definition/Procedure Example 4.6 Order Relations and Order of Operations Comparing Numbers with and The symbol means is greater than, and the symbol means is less than. We can use these symbols to compare the sizes of numbers. (p. 272) 9 4 is read as “9 is greater than 4.” 2 11 is read as “2 is less than 11.” Comparing Fractions As we move to the right on the number line, the numbers get larger. Therefore, when two fractions have the same denominator, the fraction with the larger numerator is the larger number. (p. 272) Fill in the blank with or . a) 5 2 _____ 3 2 b) 6 13 _____ 10 13 a) 5 2 3 2 5 2 is greater than 3 2 . b) 6 13 10 13 6 13 is less than 10 13 . Comparing Fractions with Unlike Denominators 1) Rewrite the fractions with the least common denominator. 2) Compare the numerators. The fraction with the greater numerator is the larger fraction. (p. 273) Fill in the blank with or : 3 4 _____ 5 7 Write each fraction with the LCD, 28. 3 4 7 7 21 28 5 7 4 4 20 28 Rewrite 3 4 _____ 5 7 as 21 28 _____ 20 28 . The numerator of 21 28 is greater than the numerator of 20 28 . Therefore, 21 28 20 28 or 3 4 5 7 . We can use exponents with fractions. (p. 274) Evaluate a 7 11 2 . b a 7 11 2 b 7 11 7 11 49 121 The Order of Operations 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 and square roots. 3) Multiply or divide, moving from left to right. 4) Add or subtract, moving from left to right. (p. 274) Simplify 1 2 8 9 a 3 4 3 . b 1 2 8 9 a 3 4 3 b 1 2 8 9 a 27 64 b Evaluate the exponent fi rst. 1 2 8 1 91 3 27 64 8 Multiply before adding; divide out common factors. 1 2 3 8 Multiply. 4 8 3 8 Get a common denominator. 7 8 Add. www.mhhe.com/messersmith CHAPTER 4 Summary 285
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