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