Section 1.3 Addition of Real Numbers 69 107. 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 36 4 3 Subtraction must be performed 9 3 36 4 3 32 3 108. If you use the acronym Please Excuse My Dear Aunt Sally to remember the order of operations, what must Multiplication or division is performed in order from left to right. you keep in mind about the last four operations? Addition or subtraction is performed in order from left to right. 109. Explain why the acronym Please Excuse Dr. Michael Smith’s Aunt could also be used as a memory device This is acceptable, provided division and multiplication are performed in order from left to right, for the order of operations. and subtraction and addition are performed in order from left to right. 1. Addition of Real Numbers and the Number Line Adding real numbers can be visualized on the number line. To do so, we locate the first addend on the number line.Then to add a positive number, we move to the right on the number line. To add a negative number, we 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 ( 5° F) at noon, and then drops 12° 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 1-3). The resulting temperature at 2:00 P.M. is 7°F. 15 10 7 5 0 5 10 15 Figure 1-3 Example 1 5 2 1 142 7 142 Start 6 5 4 3 2 1 0 1 2 3 4 5 6 Start 6 5 4 3 2 1 0 1 2 3 4 5 6 Start 3 2 1 0 1 2 3 4 5 6 7 8 9 5° 112°2. Using the Number Line to Add Real Numbers Use the number line to add the numbers. a. b. c. Solution: a. 5 2 3 Start at 5 , and count 2 units to the right. 1 142 5 b. Start at 1 , and count 4 units to the left. 7 142 3 c. Start at 7, and count 4 units to the left. Section 1.3 Skill Practice Use the number line to add the numbers. 5 4 3 2 1 0 1 2 3 4 1. 2 4 2. 3. 5 162 2 132 Classroom Examples: p. 74, Exercises 10 and 12 TIP: Note that we move to the left when we add a negative number, and we move to the right when we add a positive number. Answers 1. 2 2. 5 3. 1 Addition of Real Numbers Concepts 1. Addition of Real Numbers and the Number Line 2. Addition of Real Numbers 3. Translations 4. Applications Involving Addition of Real Numbers Division must be performed before multiplication. 27 before addition. 35 Writing Translating Expression Geometry Scientific Calculator Video
miller_introductory_algebra_3e_ch1_3
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