244 CHAPTER 5 Number Theory and the Real Number System In Section 5.2 we introduced the order of operations, which is used to simplify expressions. We will use the order of operations in the next example. denominator of 30. First, consider 13 15 . To obtain a denominator of 30, we must multiply the denominator, 15, by 2. If the denominator is multiplied by 2, the numerator must also be multiplied by 2 to obtain an equivalent fraction. Next, consider 5 6 . To obtain a denominator of 30, we must multiply the denominator, 6, by 5. Therefore, we must multiply both numerator and denominator by 5 to obtain an equivalent fraction. 13 15 5 6 13 15 2 2 5 6 5 5 26 30 25 30 1 30 − = ⋅ ⎛ ⎝ ⎞ ⎠ − ⎛ ⋅ ⎝⎜ ⎞ ⎠⎟ = − = b) In Example 6 of Section 5.1, we determined that the LCM of 36 and 90 is 180. Rewrite each fraction as an equivalent fraction using the LCM as the common denominator. 1 36 1 90 1 36 5 5 1 90 2 2 5 180 2 180 7 180 + = ⋅ ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎛ ⋅ ⎝ ⎞ ⎠ = + = 7 Now try Exercise 69 Example 15 Using the Order of Operations Evaluate the expression using the order of operations: − ÷ 13 15 14 45 7 9 Solution Since division is performed before subtraction, we begin by performing the division. To divide 14 45 by , 7 9 multiply by the reciprocal of , 7 9 which is . 9 7 13 15 14 45 7 9 13 15 14 45 9 7 13 15 14 45 9 7 13 15 2 5 13 15 2 5 3 3 13 15 6 15 7 15 2 7 5 9 = − ÷ = − ⋅ = − ⋅ = − = − ⋅ ⎛ ⎝ ⎞ ⎠ = − = ⋅ ⋅ Write 14 as 2 7⋅ and 45 as 5 9 ⋅ and cross out common factors Rewrite 2 5 with the LCD, 15. 7 Now try Exercise 81 Learning Catalytics Keyword: Angel-SOM-5.3 (See Preface for additional details.)
RkJQdWJsaXNoZXIy NjM5ODQ=