Order of Operations — PEMDAS / BODMAS Rules

Order of operations tells you what to do first in a math expression so everyone gets the same answer. For PEMDAS or BODMAS, the rule is: simplify grouping symbols first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

If you remember only one thing, remember this: multiplication and division share one level, and addition and subtraction share one level. Within each level, move left to right.

PEMDAS And BODMAS Mean The Same Rule

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BODMAS uses Brackets and Orders instead of Parentheses and Exponents. The rule behind them is the same.

The confusing part is the middle of the acronym. Multiplication and division are one priority level, so you do whichever comes first from the left. Addition and subtraction are also one priority level, so you again work from left to right.

That means PEMDAS does not say "always multiply before dividing." It says "finish the multiply-or-divide stage in order."

Order Of Operations In 4 Steps

1. Simplify inside grouping symbols such as parentheses.
2. Evaluate exponents.
3. Do multiplication and division from left to right.
4. Do addition and subtraction from left to right.

If grouping symbols are nested, start with the innermost part and work outward. A fraction bar also acts like grouping, because the whole numerator and denominator stay together.

Worked Example: Apply PEMDAS Step By Step

Evaluate

$$24 / 3 \times (1 + 3) - 2^2$$

Start with the parentheses:

$$24 / 3 \times 4 - 2^2$$

Now evaluate the exponent:

$$24 / 3 \times 4 - 4$$

Next, do division and multiplication from left to right:

$$24 / 3 = 8$$

so the expression becomes

$$8 \times 4 - 4$$

Then multiply:

$$32 - 4$$

Finally subtract:

$$28$$

So

$$24 / 3 \times (1 + 3) - 2^2 = 28$$

This example shows the main trap clearly. If you multiplied $3 \times 4$ first, you would be changing the left-to-right rule inside the multiplication-and-division stage.

Common Mistakes With Order Of Operations

One common mistake is reading PEMDAS as a strict top-to-bottom ladder. In $20 / 5 \times 2$, you divide first because that operation appears first from the left, so the result is $8$, not $2$.

Another mistake is treating addition as if it must happen before subtraction, or subtraction before addition. In $10 - 3 + 1$, you work left to right and get $8$.

Students also often skip the rewrite step. That makes it easy to drop a sign, miss an exponent, or perform an operation too early. Writing the expression again after each stage is slow for a few seconds, but it prevents many errors.

When You Use This Rule

You use order of operations whenever an expression mixes operations. That includes school arithmetic, algebra, science formulas, spreadsheet calculations, and calculator input.

Programming languages also use operator precedence, but the exact symbols can differ by language or tool. The core idea is the same: some operations are grouped before others so expressions are interpreted consistently.

A Quick Check Before You Move On

After you finish, ask two questions:

1. Did I clear grouping symbols and exponents before the basic operations?
2. Inside the multiply-or-divide stage and the add-or-subtract stage, did I move left to right?

If the answer to both is yes, your structure is probably correct.

Try A Similar Problem

Try

$$30 / 5 \times (2 + 1) + 3^2$$

Solve it one stage at a time and check whether you divide before you multiply. If you want to verify your steps afterward, try your own version in the solver and compare the intermediate lines, not just the final answer.