Counting the Negatives
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 30 of 60.
A long product is worked one pair at a time, left to right. (-4) × 2 × (-1) × (-3): first (-4) × 2 is -8, giving -8 × (-1) × (-3). Then -8 × (-1) is 8, giving 8 × (-3). Then -24.
You can know the sign before doing any of that. Each negative factor flips the sign, and two flips cancel. So count the negative factors: an even number of them gives a positive product, an odd number gives a negative one. The example has three, so the answer had to be negative.
That splits the job in two: count the negatives for the sign, and multiply the sizes for the number. 4, 2, 1 and 3 multiply to 24, and three negatives make it -24. It is also a quick way to check your last line.
Challenge
Work out (-2) × 5 × (-3) × (-1), one pair at a time, left to right.
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