Question 1113332: What 2 factors of -1,920 add up to be -8
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Working with the negative numbers is confusing for most students. It is easier to find the answer if you modify the problem to say you are looking for two numbers whose product is POSITIVE 1920 and whose DIFFERENCE is 8.
I think the easiest way to do that is to start with one "easy" pair of factors of 1920 and look at their difference. If the difference is too large, the two numbers need to get closer together; if the difference is too small, the numbers need to get father apart.
Once you have found one pair of factors, an easy way to find another pair is to divide one of the numbers by some number and multiply the other by that same number. When you multiply one of the numbers by one number and divide the other by that same number, the product stays the same.
Here is what it might look like for your example....
1920 = 192*10. The difference is 182 -- way too big. Since 192 is even, divide it by 2 and multiply the other factor by 2.
192/2 = 96; 10*2 = 20.
1920 = 96*20. The difference is 76 -- still too big. 96 is again even, so divide by 2 and multiply the other factor by 2.
96/2 = 48; 20*2 = 40. The difference is 8 -- what we were looking for.
Now go back to the original problem. Without the signs, the two numbers are 48 and 40. With the signs, since you want the sum to be -8, the numbers you want are -48 and +40.
Answer: -48 and 40
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