BODMAS / PEMDAS — Order of Operations Explained

BODMAS, also called PEMDAS, tells you the order to use when an expression mixes operations. Work through brackets or parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

The common mistake is assuming multiplication always comes before division, or addition always comes before subtraction. That is not the rule. Each pair has the same priority, so you move left to right.

What BODMAS And PEMDAS Stand For

The letters stand for the same structure with slightly different vocabulary:

1. $B$ or $P$: Brackets or Parentheses
2. $O$ or $E$: Orders or Exponents
3. $D$ and $M$: Division and Multiplication
4. $A$ and $S$: Addition and Subtraction

They are not different systems. They are two mnemonics for the same order of operations.

How The Order Of Operations Works

Start by simplifying anything grouped together. If there is an exponent, handle that next. After that, work through multiplication and division as they appear from the left. Then finish addition and subtraction, again from the left.

If brackets are nested, start with the innermost one. A fraction bar also groups terms, so the whole numerator and denominator stay together until you simplify them.

Worked BODMAS Example

Evaluate

$$30 - 18 / 3 \times (2 + 1) + 2^3$$

First simplify the brackets:

$$30 - 18 / 3 \times 3 + 2^3$$

Now evaluate the exponent:

$$30 - 18 / 3 \times 3 + 8$$

Next do division and multiplication from left to right. Division comes first here because it appears first:

$$30 - 6 \times 3 + 8$$

Then multiply:

$$30 - 18 + 8$$

Now finish addition and subtraction from left to right:

$$12 + 8 = 20$$

So the value of the expression is $20$.

Common BODMAS Mistakes

Thinking Division Comes Before Multiplication

In $20 / 5 \times 2$, you divide first because that operation appears first from the left. The result is

$$4 \times 2 = 8$$

not $20 / 10 = 2$.

Thinking Addition Comes Before Subtraction

In $10 - 3 + 1$, work left to right:

$$10 - 3 = 7,\quad 7 + 1 = 8$$

Skipping The Rewrite Step

Most order-of-operations errors are not deep math errors. They are structure errors. Rewriting the expression after each stage makes it much easier to keep signs, exponents, and grouped terms in the right place.

When Order Of Operations Is Used

This rule matters whenever one expression mixes operations. That includes school arithmetic, algebra, spreadsheet formulas, calculator input, and many science formulas.

The condition is simple: if there is only one type of operation, the rule is not doing much work. It matters when different kinds of operations appear together and you need one consistent interpretation.

Try A Similar Problem

Try solving

$$24 / 4 \times (3 + 2) - 3^2$$

Write each stage on a new line and check whether you kept the left-to-right rule in the multiply-or-divide stage. A good self-check is to compare your intermediate lines, not just your final answer.