Why we need a rule
Take a single expression: 8 − 4 ÷ 2.
A student who reads strictly left to right computes 8 − 4 = 4,
then 4 ÷ 2 = 2. A student who knows division comes before
subtraction computes 4 ÷ 2 = 2, then 8 − 2 = 6. Same expression,
two different answers.
Same expression, two different answers
8 − 4 ÷ 2
✗ Naïve left-to-right
- 8 − 4 = 4
- 4 ÷ 2 = 2
= 2
Reading left-to-right looks fast — but it's the wrong answer.
✓ BEDMAS
- 4 ÷ 2 = 2
- 8 − 2 = 6
= 6
Division before subtraction. One real answer.
The math doesn't fix this on its own — it needs a convention. Mathematicians agreed centuries ago: resolve operations in this order, and only this order.
BEDMAS, in one ladder
The convention is named for its first letters: Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
Two pairs are tied: division and multiplication share a rung, and addition and subtraction share a rung. Within a tied rung, the left-to-right ordering breaks the tie. Everything else cascades.
See it / Try it
Tap the operator you think comes next. The expression resolves one step at a time.
Try it
Tap the next operation. BEDMAS picks the order.
Order of operations
No steps yet.
Brackets, Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right). One layer at a time. An expression rendered as a row of number tokens and tappable operator chips. The student taps the operator that BEDMAS demands next; correct taps log a step and rewrite the row, wrong taps print a transient hint about which operation BEDMAS prioritizes. Three preset expressions: an integer-only chain with an exponent, a fraction multiply-then-add, and a brackets-then-multiply with decimals.
The third preset hides nothing — (0.6 + 0.4) × 0.5. The brackets
force the addition first, even though × is normally above + on the
ladder. Brackets always win.
Equivalent forms can simplify the work
The curriculum makes a quiet point worth borrowing: equivalent forms of an expression can make evaluation easier. Take
A heavy approach: find a common denominator for 1/2 + 1/4 × 8 and
slog through fraction arithmetic. A lighter approach: do the
multiplication first (which BEDMAS demands anyway), turn 1/4 × 8
into the integer 2, and then 1/2 + 2 = 5/2. The second path is
shorter and cleaner — the order of operations plus a sense of
which form is easier saves work.
This shows up everywhere. 0.5 × (8 + 4) is 0.5 × 12 = 6, not a
muddle of decimal additions. Pick the form that makes the next step
easier.
Where it shows up in real life
A monthly power bill in Alberta has a fixed admin fee, a per-kWh charge for the first chunk of usage, and a different per-kWh charge above some threshold. The whole calculation collapses to one BEDMAS expression.
A power bill, one expression
total = 8.50 + 0.072 × 600 + 0.094 × (usage − 600)
= 8.50 + 0.072 × 600 + 0.094 × (750 − 600)
= 8.50 + 0.072 × 600 + 0.094 × 150
= 8.50 + 43.20 + 14.10
= 65.80
Numbers are illustrative — real Alberta utility rates change every quarter.
BEDMAS is what tells the student which terms collapse first. Without the convention, the bill could read four different totals depending on who computed it. With the convention, every cash register, every billing system, and every Grade 7 worksheet in the province lands on the same number.
Worksheet
These aren't graded. Try a few — the right approach is usually "what does BEDMAS demand?" before reaching for arithmetic.
Question 1 of 4
Try it
What is 5 + 2 × 3?
Multiple choice: what is five plus two times three? Four cards: eleven, twenty-one, fifteen, ten.Order of operations
- 1.BBrackets
- 2.EExponents
- 3.DDivision
- 4.MMultiplication
- 5.AAddition
- 6.SSubtraction
D and M tie — left-to-right. A and S tie — left-to-right.
Going further
Order of operations carries forward unchanged through every grade
that follows. Solving linear equations in the next strand
(MA.7.ALG.1) leans on BEDMAS to unwind an expression — addition
and subtraction first when isolating a variable, then multiplication
and division, then squares and roots.
In Grade 8, exponent laws fold into the same ladder. In Grade 9, the order of operations sits underneath every algebraic manipulation, even though no one writes it on the page anymore. The convention isn't a Grade 7 trick — it's the floor everything else stands on.