What PEMDAS Actually Means

PEMDAS is the mnemonic for the order of operations — the rule that tells us which part of a math expression to calculate first.

P — Parentheses (and other grouping symbols)
E — Exponents
M/D — Multiplication and Division (left to right)
A/S — Addition and Subtraction (left to right)

The most common mistake is treating multiplication as always before division, or addition as always before subtraction. It's not. Multiplication and division are at the same level — you do them left to right. Same with addition and subtraction.

Some curricula use GEMS or BODMAS instead of PEMDAS, but the rules are identical. The letters just vary.

Why the Order Matters

Without a shared order of operations, the expression 3 + 4 × 2 could equal 14 or 11 depending on who solves it. Math would collapse. PEMDAS is just a universal convention so everyone gets the same answer.

A Basic Example

Let's work 6 + 3 × 4 step by step:

No parentheses, so skip P
No exponents, so skip E
Multiplication: 3 × 4 = 12. Now we have 6 + 12.
Addition: 6 + 12 = 18.

Final answer: 18. (Not 36 — that's what you'd get if you went left to right ignoring PEMDAS.)

A Harder Example

Let's try 20 - 3 × (8 - 5) + 2²:

Parentheses first: (8 - 5) = 3. Now we have 20 - 3 × 3 + 2².
Exponents: 2² = 4. Now we have 20 - 3 × 3 + 4.
Multiplication: 3 × 3 = 9. Now we have 20 - 9 + 4.
Subtraction and addition, left to right: 20 - 9 = 11, then 11 + 4 = 15.

Final answer: 15.

Download the Grade 5 order of operations worksheet PDF for structured practice with expressions at this level — with answer keys so you can check work quickly.

Common Mistakes

Here's what goes wrong most often:

Doing addition before subtraction: 10 - 3 + 2 is 9, not 5. Work left to right.
Doing multiplication before division: 12 ÷ 4 × 3 is 9, not 1. Work left to right.
Skipping exponents: Kids sometimes forget to square before multiplying.
Ignoring nested parentheses: Work from the innermost set outward.
Forgetting that a fraction bar is a grouping symbol: Everything above and below the bar is grouped.

Grade-by-Grade Expectations

Order of operations shows up at different levels of difficulty across the grades:

Grade 5: Expressions with parentheses and the four operations
Grade 6: Expressions that include exponents
Grade 7: Expressions with integers and rational numbers
Grade 8: Expressions inside algebra problems

If your 6th or 7th grader is shaky, our Grade 6 pre-algebra worksheet PDF includes order of operations problems alongside other pre-algebra topics.

How to Practice

The most effective PEMDAS practice uses just a few problems at a time, worked completely. Don't race through 20 expressions — work through 5 with careful, labeled steps.

Have your child:

Write the expression
Underline or circle what they're doing first
Rewrite the expression after each step
Label which PEMDAS step they used

This builds the habit of pausing to identify the operation before jumping to answers.

Worksheets and Answer Keys

All our order of operations worksheets come with full answer keys. Free to print, no login needed.

Grade 5 Order of Operations PDF
Grade 6 Pre-Algebra PDF (includes order of operations)

Ten minutes a day for a week is usually enough to cement the basics. Add exponents, then negative numbers, and your child will be ready for anything algebra class throws at them.

PEMDAS Practice: Free Worksheets + Step-by-Step Examples