Order of Operations — Safe Mustafa

The sequence is usually remembered as PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The part people get wrong isn’t the order of the letters — it’s treating M as strictly before D, and A as strictly before S. They’re not separate steps. Multiplication and division are the same tier, worked left to right in whatever order they appear. Addition and subtraction are the same tier, also worked left to right. PEMDAS is really four tiers, not six.

Evaluating 20 − 3² × 2 + (5 − 1)

A long expression isn't solved all at once — it's solved one tier at a time, in order, until only a single number is left.

Start with the expression

✓20 − 3² × 2 + (5 − 1)

Start with 20 − 3² × 2 + (5 − 1). Parentheses come first — simplify (5 − 1).

The left-to-right rule inside a tier matters more than it looks. 12 ÷ 3 × 2 is not the same as 12 ÷ (3 × 2) — division and multiplication aren’t interchangeable in the order you apply them, only in which tier they belong to. Work strictly left to right within a tier:

Worked example: 12 ÷ 3 × 2

= (12 ÷ 3) × 2

= 4 × 2

= 8

Common mistake

Doing all the multiplication first, then all the division — or all the addition, then all the subtraction — instead of working left to right within each tier. 12 ÷ 3 × 2 solved as 12 ÷ (3 × 2) gives 2, not 8. Same trap with 20 − 18 + 4: adding 18 + 4 first gives 20 − 22 = −2, the wrong answer — it has to be 20 − 18 = 2, then 2 + 4 = 6, strictly in reading order.

Question 1 of 9easy

Evaluate: 3 + 4 × 2