What is order of operations (pemdas)?

Why it matters

Without an agreed order, the same expression could equal different things. Order of operations is how we make sure everyone solves 3 + 4 × 2 the same way — and it underpins every algebra problem from middle school onward.

Worked example

Evaluate: 3 + 4 × (2 + 5) − 6 ÷ 2

1. 1

   Parentheses first: (2 + 5) = 7. The expression becomes 3 + 4 × 7 − 6 ÷ 2.

   Always do what’s inside parentheses before anything else.

2. 2

   No exponents to handle, so move to multiplication and division — left to right. First: 4 × 7 = 28. Then: 6 ÷ 2 = 3. The expression becomes 3 + 28 − 3.

   Multiplication and division share the same step — do them in the order they appear from left to right, not multiplication first.

3. 3

   Now addition and subtraction, left to right: 3 + 28 = 31, then 31 − 3 = 28.

Common mistakes

• •Always multiplying BEFORE dividing (or adding before subtracting) instead of going left to right within each step.
• •Forgetting to handle what’s inside parentheses first — jumping straight to multiplying.
• •Doing the easy operation first because it’s easy ("I’ll add 3 + 4 because it’s simple") instead of following the order.
• •Treating PEMDAS as 6 separate steps instead of 4 (P, E, MD together, AS together).

How Briveli teaches order of operations (pemdas)

Briveli introduces order of operations in Grade 5 with parentheses-only problems first, then adds exponents and multi-step expressions in Grade 6 alongside one-step algebraic equations.