PEMDAS Unveiled

Pre-Algebra · Axiom Academy

The fixed order that tells us which calculation to do first — watch an expression collapse one operation at a time down to a single number. PEMDAS is the agreed order for evaluating an expression. You don't read left to right — you read by rank . The two pairs at the bottom are special: Multiplication and Division share one rank , and Addition and Subtraction share the next . Within a shared rank you go strictly left to right . Picture the operations as a stack of ranks. The top rank is settled first, then the next, and so on down. When two operations sit on the same rank, neither outranks the other — so you simply take them in reading order , left to right. Reading left to right would tempt you to add 2 + 3 first — but multiplication outranks addition. Watch the higher-rank operation resolve first, then the addition, until a single number is left. Now a longer expression. Parentheses come first, then the M/D rank (the and the are equals — take them left to right), and finally the subtraction. Four folds collapse it to one number. (8+2)=10 → then on the M/D rank, left to right: , then → finally 30 - 2 = 28 . 5. What Goes Wrong Without PEMDAS Here is exactly why the order matters. The same expression is worked two ways. Watch the strict left-to-right path and the PEMDAS path split apart and land on different numbers. You've seen the order of operations not as a rule to memorize, but as a sequence of folds — each operation collapsing in rank order until one number remains.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.