Solving PEMDAS Problems

PEMDAS Problems

PEMDAS problems are a common challenge for anyone using math – especially when you're learning PEMDAS in school for the first time, and without much real-life context. PEDMAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It's a set of rules that tell you the order to follow when solving a math problem to get the right answer, and an answer which mathematicians can agree on internationally.  PEDMAS is the term in the US; BODMAS is the term used pretty much everywhere else.  I can't help wondering if this is going to end badly.

• Parentheses always come first. You must calculate everything inside the parentheses before moving on.
• Exponents (like squares, cubes, or square roots) are next.
• After that, it's the arithmetic functions: Divide, Multiply, Add, Subtract.  In BODMAS, Division always comes first.  For some strange reason I have not been able to fathom, in PEMDAS, you just do everything from left to right.  It's sure to cause confusion, and a quick look at social media will tell you that.  How can it not, if 3 *4 /3+2 is PEMDAS does 3*4 and then divide by three, and then add two?  If it's BODMAS then you do the division first, even though it's not on the left.  Let's leave that for a whole other discussion.

Why is PEMDAS Important?

Imagine you have this expression: 3 * 4 - 2

• Without PEMDAS, it's unclear whether you should multiply 3 by 4 first, or subtract 2 from 4.
• PEMDAS helps avoid confusion and makes sure everyone gets the same answer.
  

Image from Hotpot

Let's Look at Some Examples:

1. (3 * 4) - 2

   • Parentheses first: 3 * 4 = 12
   • Subtraction: 12 - 2 = 10

2. 3 * (4 - 2)

   • Parentheses first: 4 - 2 = 2
   • Multiplication: 3 * 2 = 6

3. 4 * (6 - 2²)

   • Parentheses first:
     • Exponents: 2² = 4
     • Subtraction: 6 - 4 = 2
   • Multiplication: 4 * 2 = 8

Why Does PEMDAS Sometimes Cause Trouble?

• Tricky Online Problems: Some people intentionally write confusing problems (like 1 + 7 * 3) to see if others can solve them correctly.  There is a correct answer, but the ambiguity is a bigger problem than the math.
• Everyday Math: Even simple situations can involve PEDMAS. For example:
  • If each car has 4 wheels and is towing a caravan with 2 wheels, how many wheels are there in total for 4 cars?
    • Correct: 4 * (4 + 2) = 24 wheels 
    • Incorrect: (4 * 4) + 2 = 18 wheels.  Four wheels on four cars, and two for a caravan is not enough.

PEMDAS helps us avoid these kinds of mistakes and ensures we get the correct answer every time!

Image by Hotpot