PSHS NCE Order of Operations Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Order of Operations

Know what to solve first so mixed-operation expressions do not turn into guessing games.

Grade 6–7 friendlyPEMDAS/BODMAS made simpleRegular practiceQuick Fire + Mastery

LearnFast MethodExamplesTry With MePracticeQuick FireMastery

MY STATUS

Order of Operations

Not yet started on this browser.

NOT STARTED

START HERE

Mixed operations have an agreed order

6 + 3 × 4

If you add first, you get 36. If you multiply first, you get 18. Only one can be correct.

Multiply first: 3 × 4 = 12, then 6 + 12 = 18.

Use PEMDAS:
P — Parentheses
E — Exponents
MD — Multiplication and Division from left to right
AS — Addition and Subtraction from left to right

DO IT FAST

Use P → E → MD → AS

1. P — Parentheses: Do anything inside grouping symbols first.
2. E — Exponents: Evaluate powers next. Example: 3² = 9.
3. MD — Multiply or Divide: Work from left to right.
4. AS — Add or Subtract: Work from left to right.
5. CHECK: PEMDAS does not mean multiplication always comes before division, or addition always before subtraction.

Important: PEMDAS does not mean “multiply before divide” or “add before subtract.” Those pairs are solved left to right.

WORKED EXAMPLES

Seven patterns you should recognize

1. Multiply before add

8 + 2 × 5

2 × 5 = 10, then 8 + 10 = 18.

18

2. Parentheses first

(8 + 2) × 5

8 + 2 = 10, then 10 × 5 = 50.

50

3. Exponents before multiplication

2 + 3² × 2

Exponent first: 3² = 9.
Then multiply: 9 × 2 = 18.
Then add: 2 + 18 = 20.

20

4. Division before subtraction

30 − 18 ÷ 3

18 ÷ 3 = 6, then 30 − 6 = 24.

24

5. Multiplication and division: left to right

24 ÷ 6 × 2

24 ÷ 6 = 4, then 4 × 2 = 8.

8

6. Addition and subtraction: left to right

20 − 7 + 3

20 − 7 = 13, then 13 + 3 = 16.

16

7. More than one layer

5 + 2 × (9 − 6)

Parentheses: 9 − 6 = 3.
Multiply: 2 × 3 = 6.
Add: 5 + 6 = 11.

11

TRY WITH ME

What should we do first?

18 ÷ 3 + 4 × 2

1. There are no parentheses.
2. Do division and multiplication before addition.
3. From left to right: 18 ÷ 3 = 6.
4. Then 4 × 2 = 8.
5. Now add 6 + 8.

14

COMMON TRAPS

Watch out for these

Going straight left to right.
Multiplication/division must happen before addition/subtraction.

Thinking multiplication always beats division.
They are equal priority. Go left to right.

Ignoring parentheses.
Grouping changes the order completely.

Doing too many steps in your head.
Write one clean step at a time on harder items.

REGULAR PRACTICE

Build the skill

Work one operation at a time. These start direct and become more mixed.

QUICK FIRE

Can you choose the first move fast?

Five short expressions. Keep the order straight.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Still unsure what to solve first?

Send Teacher Abi the expression that confused you and your result. I can show you the quickest clean order.

Message Teacher Abi

PSHS NCE REVIEW PATH

Choose your next step

Next competency: Integer and Signed-Number Reasoning

Previous: DecimalsPSHS NCE Student Hub