Expression Builder

Pre-Algebra · Axiom Academy

Snap numbers and operators together, watch them evaluate, and find out why math needs one agreed order. An expression is a recipe — and it cooks down to one number An expression is just numbers stitched together with operations like + and ×. Build one and it has a single value hiding inside, waiting to be worked out. But the moment two different operations sit side by side, the "obvious" way to read it gets slippery — so let's watch one get assembled and evaluated. Watch the cards slide in and lock together into 2 + 3 × 4 . Then it evaluates the agreed way: the multiplication goes first (3 × 4 = 12), then the addition (2 + 12), folding the whole thing down to one number. Multiplication before addition isn't a trick — it's the rule everyone agrees to so the recipe means the same thing to everybody. Drop in the operators and watch it evaluate two ways Here's your sandbox: the numbers 2, 3, 4 are fixed, but YOU pick the two operators. The builder evaluates your expression two ways at once — the agreed order (do × and ÷ before + and −) and a naive left-to-right read. For most choices they match. Hunt for the ones where they don't . The two readings split exactly when a × (or ÷) lands to the right of a + or −. That clash is the whole reason an order of operations exists.

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