The Real Number System and Order of Operations


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Original Response
1. Describe the order of operations and explain how it is used to simplify expressions. Explain specifically the order in which mathematical operations must be performed to correctly simplify an expression.
2. Provide an example of a real life situation where a specific order of steps is necessary for a proper end result. What will happen if the proper order is not followed? (Humor and creativity are encouraged.)
3. Develop an original mathematical expression which must be simplified using order of operations. Include addition, subtraction, multiplication, division, an exponent, and at least one set of parentheses. Simplify the expression incorrectly, showing each step as you simplify. You do not have to include the reasons for each step.
Below is how the actual layout should be:
1. Describe the order of operations and explain how it is used to simplify expressions. Explain specifically the order in which mathematical operations must be performed to correctly simplify an expression. Label this part your answer as “PART 1”. Next, in your own words, describe the order of operations (in general terms) and what it is used for. Then, list the actual order of the operations (i.e., what operation goes first, what operation goes second, etc.)
2. Provide an example of a real life situation where a specific order of steps is necessary for a proper end result. What will happen if the proper order is not followed? (Humor and creativity are encouraged.) Label this part of your answer as “Part 2”.
Think of a real life, non-math situation where you need to perform certain steps in a specific order to achieve the desired results. First list the steps in the correct order and label them “correct order”; then rearrange the steps in a different order and label them “incorrect order”; and describe what would likely happen if you don’t follow the steps in the proper order.
3. Develop an original mathematical expression which must be simplified using order of operations. Include addition, subtraction, multiplication, division, an exponent, and at least one set of parentheses. Simplify the expression incorrectly, showing each step as you simplify. You do not have to include the reasons for each step. Label this part of your answer as “Part 3”.
Create a numerical expression that includes: addition, subtraction, multiplication, division, an exponent and at least one set of parentheses; simplify it INCORRECTLY! This means you are NOT going to follow the correct order of operations. Show each step of your incorrectly simplified numerical expression on a separate line and do NOT explain your steps.
example:
Part 3:
Simplify
12 – 8(15/3 + 22 * 5)
= 4(15/3 + 22 * 5)
= 4(15/3 + 102)
= 60/3 + 102
= 20 + 100
= 120 THIS IS AN EXAMPLE ONLY PLEASE USE ORIGINAL MATHEMATICAL EXPRESSION
Keep the following in mind as you complete this part of the discussion question. We are not covering equations in this unit. Be sure that you understand the difference between an equation and a numerical expression.
Next, Simplify the numerical expression using the correct order of operations. Explain each step and tell us why the original step is incorrect. Write each step on a separate line.
3³ – 7² + (8-2) ÷ 2 x 3
3³ – 7² + 6 ÷ 2 x 3
81 – 49 +6 ÷ 6
32 + 6 ÷ 6
32 + 1
33
next
Find and comment on at least one classmate’s correction of an expression. Make sure your comments are substantive and advance the Discussion. If the expression is not simplified correctly, tactfully identify the error and simplify the expression correctly.
Begin your post with, “This is my second response to a classmate”. Here is the problem to comment on:



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