Mixed Operations with Negative Integers
25 problems on two pages that mix adding, subtracting, multiplying, and dividing with integers, mostly between −20 and 20, like 13 − (−13) and −17 × (−17). Use it with 7th graders after the rules for each operation have been taught on their own.
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Two sets of sign rules
Multiplying and dividing follow one simple rule: same signs give a positive answer, different signs give a negative. So −17 × (−17) = 289, and −3 × 9 = −27.
Adding and subtracting don't follow that rule, and mixing the two up is the usual mistake on this sheet. −7 + (−9) is −16, not 16. Subtracting a negative means adding, so 13 − (−13) = 26. A number line helps: adding a negative moves left, and subtracting a negative moves right.
Have students name the operation before applying a rule. If it's too much at once, go back to adding and subtracting negative integers or multiplying negative integers first.
Frequently Asked Questions
Is a negative times a negative always positive?
Yes. Same signs multiply to a positive, and that includes two negatives: −9 × (−7) = 63. Division follows the same rule.
Why is subtracting a negative the same as adding?
Subtracting a number moves left on the number line, and subtracting a negative reverses that and moves right. So 7 − (−18) is 7 + 18, or 25.
What grade learns operations with negative numbers?
6th grade introduces negative numbers on the number line, and 7th grade covers all four operations with them.