Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Representation and Calculation - Chapter Summary, Review, and Test - Review Exercises - Page 244: 24



Work Step by Step

This is an order of operations problem. The original problem is: -40$\div$ 5 x 2 (except the text used a dot for the multiplication symbol. Many times the order of operations isn't taught correctly early on and causes problems for students as they progress through their math careers. The first step is to work all expressions that are within grouping symbols (we usually just say parentheses, but grouping can include many other things: braces, brackets, absolute value bars, fraction bars, etc:. This problem has not grouping, so we move to step 2, exponents. There are not exponents, so we can move to step 3. Step 3 is actually stated: Multiply and Divide left to right as you to come to the operation. In other words, if division comes before multiplication, we divide first. So for our problem:, -40 $\div$ 5 x 2 Division is the first operation we see, so we divide -40 by 5. This gives us -8. Now, we have -8 x 2. We may now multiply and get the final answer for the expression: -16. Note: Be careful when working order of operations. Step 4 (if we had to use it, is a lot like step 3). It actually states that we add and subtract left to right as we come to it....this means we might subtract prior to adding. Too many teachers use "PLease Excuse My Dear Aunt Sally" to teach this concept. While it is fine in the early grades, it really causes a lot of confusion and missed problems in the upper levels of math.
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