PEMDAS tricks and shortcuts

PEMDAS tricks and shortcuts

PEMDAS tricks and shortcuts

You know the rule. But applying it under exam pressure is another thing. Here are the mental shortcuts that save time and prevent mistakes.

Trick 1: "Spot the × or ÷ first"

Before you put pen to paper, scan the expression for × or ÷ symbols. They're the first thing to compute (after brackets). Marking them mentally helps you see the structure.

12 + 3 × 5 − 2

Spotted: × in the middle. So this is really `12 + (3 × 5) − 2`, even though the parentheses aren't written.

100 − 8 + 4 × 2

Spotted: × at the end. So this is really `100 − 8 + (4 × 2)`.

Trick 2: "If there are no × or ÷, just go left to right"

When the expression has only + and −, there's no priority puzzle — just go left to right. Same when it has only × and ÷.

50 − 20 + 8 = 30 + 8 = 38. Easy.

60 ÷ 5 × 2 = 12 × 2 = 24. Easy.

Trick 3: "Brackets shout 'me first!'"

The moment you see `(`, that's your starting point. Compute inside the brackets, write down the result, and rewrite the expression without them.

3 × (8 + 2) − 5

Inside: 8 + 2 = 10. Rewrite: 3 × 10 − 5. Continue: × first, 3 × 10 = 30. Then 30 − 5 = 25.

Trick 4: "Show your steps"

A pencil costs nothing. Write the expression below each transformation:

   2 × (4 + 5) − 3
=  2 × 9 − 3
=  18 − 3
=  15

This is the single most reliable way to avoid mistakes. Each line is one step.

Trick 5: "Watch for the trap multiplications"

These are the most common error patterns:

  • `a + b × c`: it's `a + (b × c)`, not `(a + b) × c`.
  • `a − b × c`: it's `a − (b × c)`, not `(a − b) × c`. (Easy to forget.)
  • `a ÷ b × c`: left to right, not `a ÷ (b × c)`.

Trick 6: "Hidden brackets in fractions"

In a written fraction, the top and the bottom act like they're each in brackets, even if no brackets are visible.

12 / (3 + 1)

Mental parentheses: `(12) / (3 + 1) = 12 / 4 = 3`. With a typed `12 / 3 + 1`, the answer would instead be `(12/3) + 1 = 4 + 1 = 5`.

A self-check: "if I read this differently, do I get a different answer?"

Whenever you compute an expression, ask yourself: "Would a different reading give a different answer?" If yes, double-check that you used the rule.

Worked traps

Trap 1

20 − 5 × 2

Wrong way: 20 − 5 = 15, then 15 × 2 = 30. Wrong.

Right way: 5 × 2 = 10, then 20 − 10 = 10.

Trap 2

24 ÷ 4 × 2

Wrong way: 4 × 2 = 8, then 24 ÷ 8 = 3. Wrong.

Right way: left to right within level 2. 24 ÷ 4 = 6, then 6 × 2 = 12.

Trap 3

(3 + 2) × (4 − 1)

Each set of brackets first: 5 × 3 = 15. Don't try to "distribute" — Year 5 doesn't need that.

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