Adding, subtracting, multiplying and dividing negative numbers, with the negatives written in brackets so the signs stay readable.
Grade 6–Grade 9 · every refresh draws a new set · answer key included
Integers worksheets
Work out each answer. Watch the signs.
Integers worksheets — answer key
Work out each answer. Watch the signs.
24 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
Negative numbers break every rule of thumb a pupil has built up over six years: subtracting can make a number bigger, multiplying two numbers can give a positive from two negatives, and the sign in front of a bracket is not the same as the operation between two terms. This page separates adding and subtracting from multiplying and dividing, because the rules are genuinely different and mixing them in a first lesson guarantees confusion. Negatives are printed in brackets, which is the convention that keeps two signs in a row readable.
Grade 6 to Grade 9, ages eleven to fifteen. Adding and subtracting integers is Grade 6 and 7 work, multiplying and dividing follows in Grade 7, and all four mixed together belongs at the end of that sequence or as revision before algebra.
Do adding and subtracting on its own page first, and use a number line alongside it — the rule that subtracting a negative moves right is much easier to believe when it is seen. Move to multiplying and dividing once the additive rules are automatic. The all four setting is a revision sheet, not a teaching one, because the two rule sets look alike and pupils apply the wrong one under time pressure.
The famous error is treating two signs in a row as one: 5 − (−3) answered as 2. The second is carrying the multiplication rule into addition — assuming that two negatives added give a positive. Both are worth naming out loud when marking, because they are not slips; they are rules the pupil has invented from a half-remembered pattern.