what do you do when the first negative number is less than the second

Question

When you have two negative numbers and you are subtracting them. I am confused with the part when the first negative number is less than the second. What then do  you do?

Answer 1

Jalen,

            There are at least two ways to keep these kinds of problems straight the first is intuitive and visual...if you picture the integers on a line starting way to the left say at -500 and continuing to the right by adding one each time then the next number would be -500+1 or -499. Ok so far? If we keep on doing this till we get to -1 then the next number will be 0 and then 1 and 2 and 3 and so on to very big numbers like 500. The point of all this is to illustrate that the numbers always increase as you go from left to right on the line. So -300 is greater than -400 even though it looks strange. But -400 is further to the left than -300 so -400<-300.

              The second way is non intuitive but a lot quicker. Say you want to subtract -10 from -7 or -7-(-10)  the two negative signs cancel in a way (-1*-1=+1) so the problem becomes -7+10=3. If you always follow the rule "the product of two negative numbers is always positive you will be ok. 

 

Jim

Answer 2

Subtracting a negative is the same as adding a positive (this is the rule that produces the rule that you have probably heard: negative x negative = positive). 

 

So A - (-B) is the same as A+B, regardless of the absolute values of the numbers.

 

For example, 3 - (-4) = 3 + 4,

                   -4 - (-2) = -4 + 2

                  -10 - (-20) = -10 + 20.

 

Once you've got rid of the double negative, now you can compare the numbers.  One will be positive and the other negative.  Remember that the sign will be that of the one with the greatest absolute value, and you subtract the absolute values to find the absolute value of the result.  (This kind of explanation is why they have everyone learn the meaning of "absolute value")  So for the above examples:

 

3 - (-4) = 3 + 4 = 7
-4 - (-2) = -4 + 2 = -2
-10 - (-20) = -10 + 20 = +10.

 

This rule for changing double negatives to positives is a general rule you can use everywhere.