PEMDAS: The Order of Operations and 4 Mistakes to Avoid

Why multiplying comes before adding

PEMDAS can feel like a rule someone made up to trip you. There’s a reason behind it.

Multiplying is a shortcut for adding the same amount over and over. 3 × 6 means three sixes, like three cartons of six eggs. So 3 × 6 is one bundle, and you count the bundle before you add anything to it.

Exponents are the same idea one level up. 6² is a shortcut for 6 × 6, so it gets worked out before any multiplying. Parentheses go first because they’re how you say “do this part first” on purpose.

Bottom line: the order opens the biggest shortcuts first. Adding and subtracting come last.

Example 1: a receipt

Go left to right instead and you get 5 + 2 = 7, then 7 × 12 = 84. That’s the price of seven shirts. When a total looks too big for the story, check the order.

Example 2: splitting a bill

The catch? Parentheses aren’t the only way to group numbers. A fraction bar groups everything above it, and everything below it.

Skip the grouping and you’d work 54 + 12 ÷ 3, which is 54 + 4 = 58. That’s $58 each for a $66 bill.

Example 3: all four steps at once

A test-style question can pack every step into one line. Rewrite the line after each step, so nothing gets lost.

The division went first only because it came first. In 12 × 3 ÷ 2, you’d multiply first and get 18.

4 mistakes that cost points

Mistake 1: multiplying before every division

M and D are one step, worked left to right. In 24 ÷ 4 × 2, divide first to get 6 × 2 = 12 (multiplying first gives 24 ÷ 8 = 3, the wrong answer). A and S work the same way, so 10 − 4 + 2 is 8.

Mistake 2: adding before multiplying

Reading straight across, the way you read a sentence, adds too early. In 4 + 6 × 5, multiply first: 4 + 30 = 34. Left to right gives 50, a classic wrong choice.

Mistake 3: ignoring brackets and fraction bars

Brackets group numbers too, so work from the inside out. In 2[10 − (3 + 1)], that’s 4, then 6, then 2 × 6 = 12. On the calculator, type parentheses around the whole top and the whole bottom of a fraction.

Mistake 4: squaring a negative without parentheses

−3² means the negative of 3², which is −9. (−3)² means (−3) × (−3), which is 9. The TI-30XS reads it the same way, so type the parentheses when you mean a negative number squared.

Practice: 5 new questions

Every set is new. Check each answer as you go, and read the working on any you miss before the next one.

Want more? Practice all of number sense and operations (25 questions, every skill in the topic), or take the full GED math practice test.