Seventh Grade · Math · week 11

Multiplying and dividing negative numbers

Multiply and divide signed numbers using the rule that matching signs give a positive result and different signs give a negative result.

Multiplying and dividing signed numbers follows one clean rule: if the two signs MATCH (both positive or both negative), the answer is positive. If the signs are DIFFERENT, the answer is negative. This rule works exactly the same way for both multiplication and division.

A quick way to remember it: two negatives "cancel" to make a positive, just like two "nots" in a sentence cancel out. One negative and one positive cannot cancel, so the negative sign survives in the answer.

📋 For the teacher
Teach it (10–15 min):
  • Say the rule together every time before computing: "same signs, positive; different signs, negative."
  • Practice a mixed set of all four sign combinations back to back so the pattern, not just one example, sinks in.
  • Point out that this rule is the SAME for both multiplication and division -- one rule, two operations.
  • Use a real context, like a submarine descending (a repeated negative change), to make the rule feel concrete.
Talk about it:
  • What is the one rule for the sign of a product or quotient?
  • Why do two negative numbers multiply to a positive answer?
  • Does the sign rule change between multiplication and division?

Mastery looks like: They correctly multiply and divide any combination of signed numbers using the matching-signs rule.

Common stumbles: Assuming a negative times a negative stays negative; losing track of the sign when a problem has more than one negative.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →DivisionShare fairly and build equal groups.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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