The Order Matters

Algebra 1 · Axiom Academy

A formal introduction to PEMDAS/BODMAS — the universal rulebook that gives every expression exactly one answer. Without a standard set of rules, a simple expression could have multiple answers. Consider this expression: If we just work left to right, we get one answer. If we do the multiplication first, we get another. Which one is correct? Play the animation to watch both readings race to their answers. PEMDAS is the acronym for the agreed priority order. (In many countries the same convention is called BODMAS — different letters, identical rules.) Play the animation to watch the priority ladder assemble from the top rung down. Evaluate inside grouping symbols ( ), [ ], first. If they are nested, work from the inside out. BODMAS: Brackets. Next, handle powers and roots. BODMAS: Orders. These are partners at the same rank : perform them from left to right , in the order they appear. Also partners at one rank: perform them from left to right , in the order they appear. Let's apply the full ladder to one expression. On every pass, find the highest-priority operation still remaining and do that one next. Play the animation to reduce it one rung at a time — the active rule lights up on each line. 4. The Left-to-Right Rule is Critical A very common mistake is to always do multiplication before division, or addition before subtraction. They are partner operations : solve them from left to right, as you encounter them.

This is the written version of the interactive lesson above. See the full Algebra 1 course.