How do I use PEMDAS?

Question

When using PEMDAS, it is important to understand the "steps" that go into it. Let's use this problem for example: 2³ + (12 x 2) - 9 ÷ 1

P- Parentheses

E- Exponents

MD- Multiplication OR Division- whichever comes first

AS- Addition OR Subtraction- whichever comes first

First, is the P (Parentheses). This means that if the problem contains parentheses, you must solve whatever is inside of the parenthesis first before you do any other part of the problem. I also like to keep my answer in parenthesis until the end, just so I know that is what used to be inside the parentheses. Using the example problem, we would solve 12 x 2 before we solve anything else.

So the updated problem would look like this: 2³ + (24) - 9 ÷ 1

Next, we have E, which represents exponents. f the problem has exponents, this is when you solve them. If not, you simply skip this step.Exponents are the tiny number in the upper right hand corner of a number. The tiny number tells you how many times you multiply the big number by itself, not the exponent (explained more below). In our problem, the first value is an exponent, so we want to solve that using the updated problem from solving P- that looks like this: 2³ + (24) - 9 ÷ 1. That first value of 2³ is an exponent. This means that we are going to multiply 2 by itself (2) 3 times, so it will look like 2 x 2 x 2. Exponents do NOT mean that we multiply the big number by the exponent (for example we would NOT multiply 2 x 3, even though in some cases you get the same answer). So now we know that 2 x 2 x 2 = 8, so I would update my expression to reflect this answer: 8 + (24) - 9 ÷ 1.

Then, we have MD. A lot of students think this means multiplication and then division, but it actually means multiplication OR division, whichever comes first in a problem. We read problems left to right, just like we read a book. Other than whatever operation is inside the parentheses, we have to solve them in this order. So we start reading the problem from left to right and whatever operation (multiplication or division) we hit first, is what we solve first. In this case, we do not hit multiplication at all (we already solved it in the parentheses, so all we have to do is the division of 9 ÷ 1, which equals 9. So we plug that update into the expression once again to look like this: 8 + (24) - 9.

Finally, we have AS, which means addition or subtraction whichever comes first. Again, we read the problem left to right and solve whichever comes first. In this case, we hit addition first with 8 + 24. So, 8 + 24 = 32. Then, we plug in the answer to update the problem: 32 - 9. Now, we read the problem again and solve the subtraction in it, since that is the only operation left- so, 32-9 = 23.

I hope this helps and if you need any additional help or questions, please contact me to set up a quick phone call or virtual meeting for instant help!

Answer 1

2^3 + (12x2) -9/1

= 2^3 + 12x2 - 9/1

= 8 + 12x2 -9/1

= 8 + 24 -9/1

= 8 + 24 - 9

= 32 - 9

= 23

the parentheses are unnecessary or redundant