Learn · Grades 6–8

Order of Operations (PEMDAS), Step by Step

When an expression has more than one operation, everyone must work them in the same order, or the same problem would have different answers. The order is remembered as PEMDAS (or BODMAS in some countries).

Try it with your own problem ↓

The steps

  1. Parentheses: work inside parentheses and brackets first, innermost first.
  2. Exponents: then powers and roots, such as 6².
  3. Multiplication and Division: next, left to right, whichever comes first. They share one level.
  4. Addition and Subtraction: last, left to right. They share one level too.
  5. Rewrite the whole expression after each step so you can see what is left.

A worked example

Work out 3 + 4 × (8 − 2)² ÷ 6.

  1. Parentheses: 8 − 2 = 6. The expression is 3 + 4 × 6² ÷ 6.
  2. Exponents: 6² = 36. The expression is 3 + 4 × 36 ÷ 6.
  3. Multiply and divide, left to right: 4 × 36 = 144, so we have 3 + 144 ÷ 6. Then 144 ÷ 6 = 24, so we have 3 + 24.
  4. Add: 3 + 24 = 27.

3 + 4 × (8 − 2)² ÷ 6 = 27.

Try it with your own problem

Open the free The Order Stack with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 3 + 4 * (8 - 2)^2 / 6Opens The Order Stack with this example

Or try these

Common mistakes

Questions people ask

Is PEMDAS the same as BODMAS or BEDMAS?

Yes. They are different names for the same order: brackets/parentheses, then orders/exponents, then division and multiplication, then addition and subtraction.

Does multiplication always come before division?

No. They have equal rank and are done left to right. The same goes for addition and subtraction.

What if there are parentheses inside parentheses?

Start with the innermost pair and work outward.

Keep learning

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