Order of Operations

Order of Operations in Math

If someone presented you with a series of numbers and no context, what would you do? Some may try to begin solving the problem based on its order; unfortunately, in the world of math, this isn’t an effective way to solve a problem.

In the past, the Romans and Greeks knew the importance of having a system in place to solve mathematical problems. This system helped navigate around the world, and helped astronomers map the sky. However, regardless of what it was, there was always a system.

It isn’t believed by many experts that the order of operations was “invented” per say. Instead, it became an accepted way of doing math because – well – it just made sense.

Math You’ll Use in the Future

The order of operations is an essential skill to have. Even if you aren’t aware of it, you will use this each day.

For example, when you go grocery shopping. Pretend almonds cost $4.00 per pound, and a bottle of water is $1.00. You get two pounds of almonds and one bottle of water.

How much are you going to have to pay?

Since one pound of almonds is $4.00 and you purchased two pounds, the almonds will cost $8.00. Add that to what you pay for the water ($1.00), and the total is $7.00.

Pretty simple right? Chances are you figured out this without any major issues. However, if you were presented the problem in a different way, for example, you may not solve it correctly.

For example, if you were given:

2 x 3 + 1

With this problem, you may have added the three and one first, then multiply the result by two. Solving this way provides an answer of eight, which is not equal to seven.

To arrive at the correct answer, you have to multiply first.

When making computations, always make sure to follow the rules of the order of operations.

Rule 1 – The Order

If any grouping symbols are present, such as parentheses, perform the operations inside the symbols first. Then, evaluate expressions with exponents. Next, multiply and divide from left to right. Last, add and subtract left from right.

Rule 2 – PEMDAS

No one expects you to just memorize the order of operations. It’s tedious and somewhat challenging for some. The good news is, there is a mnemonic that can help you.

PEMDAS – Please Excuse My Dear Aunt Sally

In PEMDAS, the “P” means parentheses, the “E” is for exponents, the “M” indicates multiplication, the “D” is for division, the “A” for adding, and “S” stands for subtraction.

You can use this even if you don’t see the operations successively in a problem.

Remember, if you see multiplication and division in a problem, you should do the operations from left to right.

If you don’t care for Please Excuse My Deal Aunt Sally to remember PEDMAS, then you may like “Popcorn Each Monday Drinks Always Saturday,” or “People Everywhere Made Decisions About Sums.” If none of those seem to work, make up your own. Once you remember the order of operations, you are ready to take the algebra world by storm.