When you see 1 + 1, you know you need to add. With 845 · 952, your product may be messy, but it's clear that you need to multiply.
So what happens when you see 4 2 (17 – 15) / (3 + 1) – 5 ? What do you do first? This song will help you remember the order of operations, and soon evaluating an expression like this one will be no sweat.
First you need to evaluate everything inside the parentheses. That's these guys:
If there are multiple operations to be completed inside the parentheses, they also follow the order of PEMDAS.
2. Exponents & Roots
After you complete parentheses, it's time for exponents. Reminder: don't multiply the base by the exponent. Multiply the base by itself, as many times as the exponent says. If your expression has any roots, this is also the time to solve them.
3. Multiplication & Division
Next up? Multiplication and division. If you have a few numbers or terms to multiply and divide, the order you multiply or divide them in doesn't matter. So a good rule of thumb is just to go from left to right to make sure you didn't miss any. And always divide from left to right.
4. Addition & Subtraction
The final step includes the operations you probably learned first: addition and subtraction. At this point in your evaluation process, you should only have to add and subtract the remaining terms. If there are any other operations left--like a stray parenthesis or something to multiply--you missed a step. If you have multiple terms to add or subtract, solve from left to right to make sure you don't forget any.
The mnemonics PEMDAS or Please Excuse My Dear Aunt Sally can help you remember the order of operations. But often the best mnemonics are the ones you make up yourself.
Can you think of your own phrase to help remember the order of operations?
Phelps Earned Mucho Dinero After Swimming? Picky-Eating Monsters Don't Allow Sardines? You try!
Even if your expression doesn't have every type of operation, the order of operations is still the same. If it is missing one, just skip it and move on to the next operation. No parentheses in your equation? Skip the P and use EMDAS. No addition? Have we got a PEMDS for you!