The Four Operations (Years 6–8) — Maths

Add, subtract, multiply and divide whole numbers and decimals using written methods.

Split a restaurant bill, work out change from a tenner, double a recipe, or check a phone contract adds up over the year — behind all of it are the four operations: addition (+), subtraction (−), multiplication (×) and division (÷). Master these and almost every other maths topic becomes readable.

Why this matters: these four moves are the alphabet of arithmetic. Every later topic — fractions, percentages, algebra, money — is really just these operations wearing different clothes. A wrong order or a slip in a written method is the single most common way answers go astray in exams.

BIDMAS — the order to work a calculation out

What each one really means

Dividing is sharing equally: 12 shared into 4 groups gives 3 in each.

It helps to picture each operation as a physical action rather than a symbol on a page:

+ — combine two amounts (pour two piles together).
− — take one amount away from another, or find the difference between them.
× — repeated addition: 4 × 3 means "four lots of three" = 3 + 3 + 3 + 3 = 12.
÷ — sharing equally, or "how many fit": 12 ÷ 4 means "share 12 into 4 equal groups" = 3.

They come in pairs: + and − undo each other, and × and ÷ undo each other — like a light switch that flicks both ways. That's why you can check 12 ÷ 4 = 3 by doing 3 × 4 = 12. Always use the opposite operation to check your work.

Written methods — keep the columns lined up

Splitting 24×13 into four easy parts: 200+40+60+12 = 312.

For adding and subtracting on paper, line the numbers up by place value (units under units) and work right to left, carrying or borrowing as needed. For multiplying a two-digit number, split it up: 24 × 13 = 24 × 10 + 24 × 3 = 240 + 72 = 312. This "partition" idea is the whole engine of long multiplication.

Order of operations — BIDMAS

When a calculation mixes operations, the order you do them in changes the answer — so everyone agrees to follow the same rule, BIDMAS. Think of it as a queue: some operations have priority and go first.

Brackets → Indices (powers) → Division & Multiplication → Addition & Subtraction.

Step	Do this	Example on 3 + 4 × 2
Scan for brackets	none here	—
Then × and ÷	4 × 2 = 8	3 + 8
Then + and −	3 + 8 = 11	11

3 + 4 × 2: multiplication comes before addition, so do 4 × 2 = 8 first, then 3 + 8 = 11. (Working blindly left-to-right would wrongly give 14.) For (7 + 3) × 2²: brackets first (10), then the index 2² = 4, then 10 × 4 = 40.

Common mistake: don't just work left to right. Always scan for brackets and ×/÷ before doing any +/−. Note too that D and M rank equally, as do A and S — when only those are left, work left to right.

Multiplying decimals

Multiply the whole numbers, then put back 2 decimal places: 0.3 × 0.6 = 0.18.

The trick is to ignore the decimal points, do easy whole-number multiplication, then put the point back at the end:

Ignore the points and multiply the whole numbers.
Count how many digits sit after the points in the question — the answer has that many too.

0.3 × 0.6: 3 × 6 = 18. There are 2 decimal places in the question (one in each number), so the answer has 2 → 0.18. Sense-check: a bit of a bit should be small, and 0.18 is indeed less than either number. ✓

Memory hook: know what each operation means, let BIDMAS decide the order whenever they're mixed, and check every answer with the opposite operation.