Section 1.4 Addition of Real Numbers 45 For Exercises 93–100, write the English phrase as an algebraic expression.Then evaluate each expression for (See Example 7.) x 4, y 2, and z 10. 93. Two times y cubed 94. Three times z squared 95. The absolute value of the difference of z and 8 96. The absolute value of the difference of x and 3 97. The product of 5 and the square root of x 98. The square root of the difference of z and 1 99. The value x subtracted from the product 100. The difference of z and the product of x and y of y and z Expanding Your Skills For Exercises 101–104, use the order of operations to simplify each expression. 101. 102. 103. 104. 105. Some students use the following common memorization device (mnemonic) to help them remember the order of operations: the acronym PEMDAS or Please Excuse My Dear Aunt Sally to remember Parentheses, Exponents,Multiplication,Division,Addition, and Subtraction.The problem with this mnemonic is that it suggests that multiplication is done before division and similarly, it suggests that addition is performed before subtraction. Explain why following this acronym may give incorrect answers for the expressions: a. 36 4 3 b. 36 4 3 106. If you use the acronym Please Excuse My Dear Aunt Sally to remember the order of operations, what must you keep in mind about the last four operations? 107. Explain why the acronym Please Excuse Dr.Michael Smith’s Aunt could also be used as a memory device for the order of operations. 04 0 2 22 1144 02 0 010 0 02 0 13 5 49 29 2 219 23 24 25 35 Addition of Real Numbers Section 1.4 1. Addition of Real Numbers and the Number Line Adding real numbers can be visualized on the number line.To do so, locate the first addend on the number line. Then to add a positive number, move to the right on the number line. To add a negative number, move to the left on the number line.The following example may help to illustrate the process. On a winter day in Detroit, suppose the temperature starts out at 5 degrees Fahrenheit ( F) at noon, and then drops two hours later when a cold front passes through. The resulting temperature can be represented by the expression On the number line, start at 5 and count 12 units to the left (Figure 1-7).The resulting temperature at 2:00 P.M. is 7°F. 15 10 7 5 0 5 10 15 Figure 1-7 5° 112°2. 5° 12° Concepts 1. Addition of Real Numbers and the Number Line 2. Addition of Real Numbers 3. Translations 4. Applications Involving Addition of Real Numbers
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