Positive and negative multiplication plus#

This is essentially the same explanation given above, just with a few White, Community College on October 3, 1997:Ībout that question: why is a negative number times a negative number After this demonstration, students used negative numbers in their algebra with understanding.įrom my experience at Cosumnes River Elementary Schoolĭo you have a place to make comments like these?īuzz you for your comments I have placed them as followup commentsįollowup question by Ms. Again the students cheered realizing that subtracting 2 red checkers three times was like adding six to the balance sheet.

I then subtracted 2 red checkers three times from the next student. After just one example, all the students cheered in unison with the joy of understanding subtracting negative numbers. For each red checker (-$1) subtracted, the students realized their balance increased by $1. After each example, I had the student recalculate their balance. I went from student to student, taking back (subtracting) n red checkers. I then advised the students that my accounting had been wrong and I had incorrectly given each student more red checkers than I should have given them. They excitedly calculated their respective balances. I owed them a dollar, and for each red checker they owed me a dollar. The red checkers represented (hypothetically) their wrong answers. I announced that the blacks (hypothetically) represented each correct answer the student had given during the class. I randomly handed students each a bunch of red and black checkers. This is a comment on your answer to the question: 'Why is a negative number times a negative number a positive number?' As a volunteer teacher for a pre-algebra class of sixth graders, I addressed the same question with the following practical demonstration. Property that the product of two negative things is positive stillįollowup Comment by Buzz Breedlove on May 9, 1997: Even in such general, non-numerical contexts, the Only covered in a junior or senior level undergraduate universityĬourse) which studies the properties of operations on numbers inĬomplete generality, even in contexts that have nothing to do with University level: there is a subject called Abstract Algebra (usually Know that more advanced versions of this question are studied at a However, as an aside, he may be interested to

(and should, in my opinion, be explained as part of every student'sĪrithmetic classes). The answer to this question is accessible to a 7th grader Related to the fact that the inverse of the inverse of a positive number The fact that the product of two negatives is a positive is therefore In other words, the inverse of in other words, 12. Therefore, is the inverse of the inverse of 12 Itself (by similar reasoning) the inverse of. Them and use the distributive law, you get

When you add them (and use the fact that multiplication needs to Of (something) × (something else), because (-something) × (something else) is the inverse Of the factors in a product, you change the sign of the product: To put it another way, if you change sign twice, you get back to the (because 3 is the number which, when added to -3, gives zero). Number back again: '-(-3)' means 'the inverse of -3', which is 3 Note that when you take the inverse of an inverse you get the same Negative numbers were introduced: so that each positive number wouldįor example, the inverse of 3 is -3, and the inverse of -3 is 3. To it (a sort of 'opposite' number), which when added to the (which I am both surprised and sorry that he has not been able to findĮach number has an 'additive inverse' associated Your 7th grader's question is an important and fundamental one 'subtraction', 'multiplication', and 'division'). Properties of operations on numbers (the notions of 'addition', The answer has to do with the fundamental Remember it's a 7th grader who wants to understand, not to mention I won't feel bad if you don't answer this.

Positive and negative multiplication plus#

Minus equals a plus he says WHY? (sorry about yelling). I'm helping a 7th grader with things like: a plus times a plusĮquals a plus, a minus times a plus equals a minus, and a plus timesĪ minus equals a minus. Why is the Product of Negative Numbers Positive? Asked by an anonymous poster on March 18, 1997: Question Corner - Why is the Product of Negative Numbers Positive? Navigation Panel: (These buttons explained below)