Rules of Calculation

The rules about where to start inside an expression are settled here. Order is confirmed with mixed operations and with parentheses, the work moves on to smart calculation using the commutative, associative and distributive laws, and finally expressions using a box turn a situation directly into an expression.

The first hurdle is working strictly left to right, so multiplication never gets its turn and 6 + 2 × 3 comes out as 24. In a chain of multiplication and division the opposite happens, with 12 ÷ 2 × 3 read as 12 ÷ 6 and answered 2. With the distributive law, the number outside the parentheses gets multiplied into only one of the terms.

Parentheses join the toolkit, and this unit also spells out why reordering or regrouping numbers never changes the answer. Working through an expression that mixes addition and subtraction was already practiced in 3-Number Calculations in grade 2. The reasoning fixed here for whole numbers gets used the same way in grade 5, once Mixed Calculations with Decimals begins.