The order of operations (PEMDAS)

One expression, one answer

Ask a few people to evaluate \(8 + 2 \cdot 5\) and some will say \(50\) (adding first) while others say \(18\) (multiplying first). Math can't allow two answers to the same question, so everyone agrees on a fixed order. The correct answer is \(18\).

PEMDAS

Many students remember the order with the word PEMDAS:

Some people use the sentence "Please Excuse My Dear Aunt Sally". In other countries you might see BODMAS or BEDMAS: same rule, different letters.

Grouping symbols

Parentheses \((\;)\) are the most common grouping symbol, but you'll also see brackets \([\;]\) and braces \(\{\;\}\). They all mean the same thing: do what's inside first. When groups are nested, start with the innermost one and work outward.

A number written right next to a grouping symbol means multiplication: \(2[\dots]\) means \(2 \cdot [\dots]\).

Fraction bars group too

A fraction bar acts like a pair of parentheses around the top and another around the bottom. Simplify each one completely before dividing.

Habits that prevent mistakes

• Copy the whole expression on every line, changing only the part you just worked on.
• Do one step at a time until the order feels automatic.
• Underline the operation you'll do next before you do it. It forces you to check that it really is next.

Practice