Adding and Subtracting Positive and Negative Integers

Hello,

We are going to move on from measurement, and we are going to learn how to add and subtract positive and negative integers.  Basically, you just need to remember some basic rules and you will be fine.  

The following are rules that you should memorize, especially when you get into more advanced math, which requires you to remember adding and subtracting positive and negative numbers very quickly:

1.) positive + positive = positive; add the two numbers like you normally would

2.) Larger positive + smaller negative = positive; subtract the two numbers like you normally would

3.) Smaller positive + larger negative = negative; subtract the two numbers like you normally would

4.) negative + negative = negative; keep the negative and add the two numbers like you normally would

5.) positive - positive = positive; subtract the two numbers like you normally would

6.) positive - negative = positive + positive = positive; just add the two numbers like you normally would

7.) negative - negative = negative or a positive depending; subtract the two numbers like you normally would 

This may look extremely confusing, but let's try some examples and hopefully it will look less confusing!

Examples:  

1.) 8 + 2 = ?

2.) 5 + (-10) = ?

3.) 4 - 9 = ?

4.) (-6) + (-6) = ?

5.) (-7) - (-3) = ?

6.) 10 - 5 = ?

7.) (-2) + 14 = ?

8.) 8 - 12 = ?

9.) 1 + (-4) = ?

10.) 3 - (7) = ?

Solutions:

1.) 8 + 2 = 10

2.) 5 + (-10) = -5 ; the larger number has the negative, so we are using rule 3 from above; we keep the negative and subtract like normal.

3.) 4 - 9 = -5 ; this can also be written as 4 + (-9) and it becomes just like number 2; we keep the negative and subtract the two.

4.) (-6) + (-6) = -12 ; when we add two negatives, we keep the negative and add the two numbers together.

5.) (-7) - (-3) = (-7) + 3 = -4 ; a minus a negative is equal to a positive, and since the negative is with our bigger number, 7, we keep the negative and subtract the two.

6.) 10 - 5 = 5

7.) (-2) + 14 = 14 - 2 = 12

8.) 8 - 12 = 8 + (-12) = - 4

9.) 1 + (-4) = -3

10.) 3 - (7) = -4 

The following are links that help reiterate our lesson, and they will also help you practice:

1.) Reiteration of our lesson, with a practice at the bottom

2.) Another reiteration of how to add and subtract positive and negative integers

3.) Example problems with adding and subtracting positive and negative integers using a number line

4.) Another practice worksheet

I hope these help!