# Thread: Sign of Integer Product/Quotient

1. ## Sign of Integer Product/Quotient

We know that when we multiply two integers with the same sign together, the sign of the product is positive. When we multiply to integers with differing signs together, the sign of the product is negative. Similar rules apply to division (presumably because of the inverse relationship of the two operations). By viewing the process of multiplication as being equivalent to successive additions, I can see why the product of two positive numbers is a positive and why the product of a positive number and a negative number is a negative. I'm having trouble wrapping my mind around the sign of the product of two negative numbers. Can someone please guide me as to how I would deduce that result?

Thanks for any input.

... doug

2. ## Re: Sign of Integer Product/Quotient

$(-2)(-3)=-[2(-3)]=-[-3-3]=-[-6]=6$

3. ## Re: Sign of Integer Product/Quotient

$1\times{1}=1$

...Change a sign:

$1\times{-1}=-1$

And change a sign again:

$-1\times{-1}=1$

Let's say I am losing £ $300$ a month as a result of a business venture. So I am gaining £ $-300$ per month.

Now let's say, for a year, the company decides to pay for me. How much money would I gain?

£ $-300\times{12}=-3600$, so in a year, if I paid myself, I'd lose £ $3600$

However, I have lost the need to pay for $12$ months, so, the equation for the amount I'd be paying would be:

£ $-300\times{-12}$ and as I'm not losing money, the answer is that I will save +£ $3600$

4. ## Re: Sign of Integer Product/Quotient

Thanks to all who contributed in this thread.

Generally speaking, after receiving help (as in this thread), it has been my policy to express my gratitude in a concluding thank-you message. However, because of the "bumping" effect of so doing and because of the policy of this forum against bumping, I have decided that in the future I will not post concluding messages that merely express my gratitude for help that I have received. Accordingly, in the future, please just assume that I am always grateful for any and all help that I receive. Thanks.

... doug

5. ## Re: Sign of Integer Product/Quotient

Originally Posted by ddjolley
Thanks to all who contributed in this thread.

Generally speaking, after receiving help (as in this thread), it has been my policy to express my gratitude in a concluding thank-you message. However, because of the "bumping" effect of so doing and because of the policy of this forum against bumping, I have decided that in the future I will not post concluding messages that merely express my gratitude for help that I have received. Accordingly, in the future, please just assume that I am always grateful for any and all help that I receive. Thanks.

... doug
If you want to express your thanks, press the "Thanks" link at the bottom of each useful post.

6. ## Re: Sign of Integer Product/Quotient

"Thanks" is in the bottom left of each reply.

Also, there is a thread option in the top right of the PAGE, where you (the OP) can mark as "solved".