Order of Operations

Order of operations is the agreed-upon sequence for solving a problem that has more than one kind of operation in it, so that everyone who solves 3 + 4 x 2 gets the same answer instead of two different ones depending on which direction they read the problem.

The order, and why it exists

Work parentheses first, then exponents, then multiplication and division together from left to right, then addition and subtraction together from left to right. Many classrooms teach this as an acronym like PEMDAS, but the acronym is just a memory hook for the rule, not the rule itself, and reciting it does not by itself tell a child why 3 + 4 x 2 is 11 and not 14.

The reason is simpler than the acronym makes it sound: multiplication is repeated addition, so "4 x 2" already means "two groups of four" before it ever meets the 3. Solve that grouping first, then add the 3 that was sitting outside it, and 3 + 4 x 2 becomes 3 + 8, which is 11. Skipping straight through left to right, the way you would read a sentence, throws that grouping away and gets 14 instead.

A steadier way to practice it

Instead of asking a child to recite the acronym, ask them to find the multiplication or division first and circle it, then the addition or subtraction, and solve in that order out loud. Picture a 6th grader, call him Devon (an illustrative example, not a real student): he stopped mixing up the order once he started circling before calculating instead of trying to hold the whole rule in his head at once.

Parentheses are worth calling out specifically: they exist to override the default order on purpose, so (3 + 4) x 2 is a genuinely different problem from 3 + 4 x 2, not a trick version of the same one.

To see this worked through step by step on a whiteboard, try the free Explanova demo: Coach Nova narrates each step instead of jumping to the answer.