Order of Operations

The Rules of the Road for Math

When you see a math problem like `3 + 4 × 2`, how do you know what to do first? Do you add 3 and 4, then multiply by 2? Or do you multiply 4 and 2, then add 3? Depending on the order, you get two different answers (14 or 11).

To make sure everyone gets the same, correct answer, mathematicians have agreed on a standard order of operations. It's a set of rules that tells you the correct sequence for solving a problem. A common mnemonic to remember this order is PEMDAS.

PEMDAS

Please Excuse My Dear Aunt Sally

This stands for:

Step 1: Parentheses

Always solve what's inside parentheses or other grouping symbols first. If there are nested parentheses, work from the inside out.

Step 2: Exponents

Next, solve any exponents or roots. An exponent tells you how many times to multiply a number by itself (e.g., 3² = 3 × 3 = 9).

Step 3: Multiplication and Division

After parentheses and exponents, perform all multiplication and division. This is a very important rule: you do them as they appear from left to right. Division does not always come after multiplication; they are on the same 'level'.

Step 4: Addition and Subtraction

Finally, perform all addition and subtraction, again, working from left to right. They are also on the same level.

Let's Solve Some Problems

Problem 1: `3 + 4 × 2`

Problem 2: `(5 + 3)² ÷ 4 - 2`