What is negative 9 plus positive 20

Question

I dont know how to add negative Numbers and positive Numbers together

Answer 1

Another way to look at the problem is like this:

-9 + 20 is the same as 20 + (-9)

And when you add a negative, all you're doing is subtracting, so:

20 + (-9) is the same as 20 - 9, and that equals 12

Answer 2

-9 + 20

 

Maybe the best way to think about this problem is to visualize it on a number line:

 

-9     -8      -7     -6     -5      -4     -3     -2      -1      0       1       2       3      4       5       6      7       8     9       10   11 12

|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|____|

 

 

Now, simply count up 20 numbers on the line from -9. Remember, you're looking for the 20th number that is larger than -9 so you actually start counting at -8. That's all addition is - moving up the number line toward larger numbers. Subtraction is simply moving down toward smaller numbers.

 

REMEMBER: Just because -9 has a 9 in it, doesn't make it a larger number! That negative sign makes it smaller than say, a -8.

 

 

Once you've mastered this concept and maybe get a little tired of drawing things out on a number line, try switching the order of the numbers and the problem might look more familiar:

 

- 9 + 20 becomes:

20 - 9

 

But wait, what happened to the positive? It's still there - we just don't usually write it out!

 

+20 - 9

 

We can do this thanks to a thing called the commutative property which says that when dealing with binary operations (some fancy words that basically mean a math problem with only two numbers - okay, this is a little simplified but this definition will work for now) we can switch the order of the numbers without screwing up the answer.

 

for example:

 

3 + 4 = 4 + 3

Right? Both sides = 7.

 

 

BE CAREFUL THOUGH:

20 - 9 DOESN'T EQUAL 9 - 20

 

This is the commutative property applied wrongly! You must preserve the signs. The computation actually looks more like:

 

+20 - 9

SO

+20 - 9 = -9 +20

or just

20 - 9 = -9 + 20

 

 

 

 

Let me know if you have any questions!