Order of Operations

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Student: If I have the problem 2 + 5 * 2 will the answer be the same if I start with 2+5 and if I start with 5*2?

Mentor: No, your answer will not be the same. By adding 2+5 you get 7 and then you are multiplying the number 7 by 2 to get 14. However, if you start by multiplying 5*2 then you get 10 and adding 2 would give you 12.

Student: I see how it can make a difference! Well, how do I know which way is the right way to solve the problem?

Student: The Order of Operations sets rules so that you know which operations you should do first.

Student: What operations are included in the Order of Operations?

Mentor: The Order of Operations tells you the order to do problems with exponents, problems with parentheses around specific operations, and problems that involve addition, subtraction, multiplication, and division.

Student: OK, how do I learn which to do first?

Mentor: Here is the order that you must work through a problem:

  1. First, you must do any operations that are in parentheses.
  2. Second, you must take care of the exponents.
  3. Third, you must do all the multiplication and division operations. (Start from the beginning of the math problem and work your way towards the end doing anything that is multiplication or division as you go. In other words, work from left to right.)
  4. Fourth, you must do all addition and subtraction operations. (Start from the beginning of the math problem and work your way towards the end doing anything that is addition or subtraction as you go. In other words, work from left to right.)

Student: That is a lot to remember! So if I were to represent the order using math symbols it would be:

  1. ( )
  2. ^
  3. x and ÷
  4. + and -

Mentor: That is right! There are also some fun ways to remember the order. One is to remember the rule as an acronym: P for parenthesis, E for exponents, M for multiplication, D for division, A for addition and S for subtraction. The acronym is PEMDAS.

Student: PEMDAS, I don't know if I can remember all of those letters.

Mentor: Another way to remember the order of operations is to memorize this saying: Please Excuse My Dear Aunt Sally. Each of those words begins with the letter of the acronym in the correct order.

Student: So, I guess now I can go back and figure out which method for solving 2+5*2 was correct.

Mentor: That is right, using the order of operations you can solve for the correct answer.

Student: OK, well the problem 2+5*2 includes multiplication and addition. According to the order of operations, multiplication comes before addition. Therefore, I should first multiply five by two (5*2=10) and then after doing that I should add two (10+2), which would equal 12.

Mentor:Great work! Let's do a more complicated one to make sure you understand all of the operations and their order. Solve:

19 - (3+1) ÷ 4 + 2^3 * 2.

Student:Wow, that problem looks hard.

Mentor:Just remember to go step by step and you'll do fine.

Student:OK, the first thing I should do is solve any problems that are in parentheses. There is a problem in parentheses: 3+1. I know that 3+1 = 4. Now the problem is:

19 - 4 ÷ 4 + 2^3 * 2

Next, I should solve any problems with exponents. There is a number with an exponent: 2^3. I know that 2^3 is 8. Now the problem is:

19 - 4 ÷ 4 + 8 * 2

Now I need to solve any problems that are multiplication or division. There are two problems that are multiplication and division: 4 ÷ 4 and 8*2.

Mentor: Remember, you should start with the operation at the beginning of the problem and then work your way towards the end so that you are working from left to right.

Student: Right, so first I would do 4 ÷ 4 since it is closer to the front. I know 4 ÷ 4 = 1. Now the problem is:

19 - 1 + 8 * 2

Next I will do the multiplication problem 8*2. I know 8*2=16. Now the problem is:

19 - 1 + 16

Mentor:It looks a lot better now!

Student: Lastly, I look for addition and subtraction problems. I see two. Since I am supposed to start at the beginning of the problem with these I will start with the subtraction problem 19 - 1. I know 19-1 = 18. Now the problem is:

18 + 16

This leaves only one operation left! I need to add 18 and 16. 18 + 16 = 34. Now there is nothing left of the problem. The final answer is 34!

Mentor:Great job! Just remember to always go step by step through the Order of Operations when you have a problem with multiple operations! You are now ready to practice using the Order of Operations Four Activity.

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