Two Negatives
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 29 of 60.
What is (-3) × (-1)? Repeated addition cannot answer that, so look at a pattern instead. (-3) × 2 is -6, (-3) × 1 is -3, and (-3) × 0 is 0. Each time the second factor drops by 1, the product grows by 3.
Keep the pattern going, and the next product must grow by 3 again: (-3) × (-1) is 3, and (-3) × (-2) is 6. A negative times a negative is positive.
Why does that make sense? Multiplying by a negative number flips the sign, just as a minus sign means 'the opposite of'. Flip once and you land on the negative side; flip a second time and you are back on the positive side. So multiply the sizes, and two negatives give a positive answer.
Challenge
Work out (-8) × (-9).
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Numbers & Operations
1Working on the Board
Your First AnswerType the Next LineOne Line at a TimeDots and BarsFriendly ProductsRecap: Board Work4Adding Integers
Adding Two NegativesDifferent SignsZero PairsAdding Several IntegersRecap: Adding Integers2Order of Operations
Multiply Before AddingLeft to RightParentheses FirstBrackets Inside BracketsThe Fraction Bar GroupsRecap: Order of Operations5Subtracting Integers
Add the OppositeSubtracting a NegativePlus and Minus in a RowDistance Between NumbersRecap: Subtracting Integers6Multiplying and Dividing
Negative Times PositiveTwo NegativesCounting the NegativesDividing IntegersZero in DivisionRecap: Multiply and Divide