Expressions that only come out right if the operations are done in the correct order, with brackets switched on or off and every answer a whole number.
Grade 4–Grade 8 · every refresh draws a new set · answer key included
Order of operations worksheets
Work out each answer. Mind the order of operations.
Order of operations worksheets — answer key
Work out each answer. Mind the order of operations.
20 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
The order of operations is a convention, not a discovery, and pupils who treat it as an opinion get every question on this page wrong in the same way: left to right, whatever the signs say. Each expression here is chosen so that reading left to right gives a different answer from the correct one — an expression where both routes agree teaches nothing and just pads the page. Brackets can be switched off while multiplication before addition is being established, and on once it is.
Grade 4 to Grade 8, ages nine to fourteen. Two operations without brackets suit Grade 4 and 5; brackets arrive in Grade 5 and 6; the same skill resurfaces in Grade 7 and 8 wherever expressions have to be evaluated before an equation can be solved.
Start with brackets off, so every question is about multiplying and dividing before adding and subtracting. Turn them on once that is automatic — bracketed expressions are not harder arithmetic, they are a second rule layered on the first. Keep the largest number modest: this page is about the order, and three-digit products only make it slower to mark.
Working strictly left to right is the error the page exists to expose, and it is worth marking as one mistake rather than as a wrong answer — the arithmetic is usually fine. The second pattern is doing multiplication before division when both appear, rather than taking them left to right as equals. The third is applying the number outside a bracket to only the first term inside it.