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MATH · GRADE 7Number

Order of Operations

Without a convention, the same expression has two answers.

Grade 7
3 + 4 × 214left to right…11× first…?only one can be right…
In this lesson

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

  1. 8 − 4 = 4
  2. 4 ÷ 2 = 2

= 2

Reading left-to-right looks fast — but it's the wrong answer.

✓ BEDMAS

  1. 4 ÷ 2 = 2
  2. 8 − 2 = 6

= 6

Division before subtraction. One real answer.

The math itself doesn't choose between the two answers. That takes 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.

Order of operations

  1. 1.BBrackets
  2. 2.EExponents
  3. 3.DDivision·MMultiplication
  4. 4.AAddition·SSubtraction

Steps 3 and 4 each pair two operations — resolve left-to-right.

Two pairs are tied: division and multiplication share a rung, and addition and subtraction share a rung. Within a tied rung, left-to-right breaks the tie. Everything else cascades.

Resolve one step at a time

Tap the operator BEDMAS picks first.

Try it

Tap the next operation. BEDMAS picks the order.

8423

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.

In (0.6 + 0.4) × 0.5, brackets are the highest priority on the ladder, so the addition runs first even though × would normally beat +.

Worksheet

The right approach is usually "what does BEDMAS demand?" before reaching for arithmetic.

Practice · Not graded

MA.7.NUM.4

Practice the idea

01 / 04

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. 1.BBrackets
  2. 2.EExponents
  3. 3.DDivision·MMultiplication
  4. 4.AAddition·SSubtraction

Steps 3 and 4 each pair two operations — resolve left-to-right.

Show common mistakes

Student says

“5 + 2 × 3 = 21. I added first because + comes first in the expression.”

What it reveals

Reading the expression left-to-right and applying operators in that order. Position in the expression doesn't decide priority. BEDMAS does.

Targeted response

Multiplication outranks addition on the BEDMAS ladder. 2 × 3 = 6 first, then 5 + 6 = 11. Position in reading order doesn't matter.

Student says

“8 − 4 ÷ 2 = 2. I worked left to right.”

What it reveals

Strict left-to-right evaluation. The student treated subtraction and division as if they shared a rung.

Targeted response

Division outranks subtraction. 4 ÷ 2 = 2 first, then 8 − 2 = 6. Left-to-right only breaks ties between operations on the same rung (× and ÷; or + and −).

Student says

“12 ÷ 4 × 3 = 1. I did the multiplication before the division because M comes before D in 'BEDMAS'.”

What it reveals

Read 'BEDMAS' as a strict alphabet (B, then E, then D, then M…) instead of a tied-pair ladder. D and M share a rung; you go left-to-right within the rung.

Targeted response

Division and multiplication share priority. Read left-to-right: 12 ÷ 4 = 3 first, then 3 × 3 = 9. Same rule for + and −: tied, left-to-right.

Going further

Order of operations applies in every grade that follows. Solving linear equations in the next strand (MA.7.ALG.1) uses BEDMAS in reverse to isolate a variable: addition and subtraction first, then multiplication and division, then squares and roots.

In Grade 8, exponent laws fit into the same ladder. In Grade 9, the order of operations governs every algebraic manipulation, even though most expressions don't write the convention out explicitly anymore.