Adding Integers

There are two rules that you must follow when adding integers. You must look at the signs of each number that you are adding to determine which rule to use!


Rule #1: Adding Integers with the Same Signs

When adding integers with signs that are the same, ADD the numbers and keep the sign.


Examples

Negative + Negative = Negative

-3 + (-2) = -5   I added the numbers 3 + 2 to get 5, and then

kept the negative sign, so my answer is -5.

-8 + (-2)= -10   I added the numbers 8 + 2 to get 10, and then

kept the negative sign, so my answer is -10.


Ok... pretty easy stuff, so far! Let's see what happens when the signs are different!


Rule #2: Adding Integers with Signs that are Different

When adding integers with signs that are DIFFERENT, SUBTRACT the numbers and keep the sign of the number with the largest absolute value.


Examples

4 + (-2) = 2     I SUBTRACTED 4 - 2 to get 2 and then kept the sign of the 4 (positive) because it has the larger absolute value.

-7 + 2 =  -5   I SUBTRACTED 7 - 2 to get 5 and then kept the sign of the -7 (negative) because it has the largest absolute value.

8 + (-9) =  -1   I SUBTRACTED 9 - 8 to get 1 and then kept the sign of the -9 (negative) because it has the largest absolute value.

-5 + 11 = 6   I subtracted 11 - 5 to get 6 and then kept the sign of the 11 (positive) because it has the largest absolute value.

Do those two rules for Adding Integers make sense? Keep those rules handy for your next set of review problems! Ok.. your turn!


Let's Practice Adding Integers

1. -5 + (-8) = ________

2. 9 + (-14) = _________

3. -16 + 5 = ______

4. 10 + (-4) = _____

5. -12 + (-10) = ______

6. 15 + (-9) = ________

7. -12 + 3 = ________

8. 16 + (-16) = _______

9. 14 + (-7) = _______

10. -8 + (-8) = ________

Pretty easy? Let's challenge yourself a little more! Ready?

11. -5 + (-7) + 3 = _______

12. 13 + (-5) + 8 = ________

13. -4 + 6 + (-8)= _______

14. 10 + (-15) + 3 = ______

15. -12 + (-7) + (-5) = ________

Ok...., so how did you do?


Answers to Let's Practice Adding Integers

1.  -13   Signs are the same:

5+8 = 13 and keep the negative.


2.  -5    Signs are different:

14 - 9 = 5 and 14 has the larger absolute value so the
answer is -5.


3.  -11  Signs are different:

16  -5=11 and 16 has the larger absolute value so the
answer is -11.


4.  6    Signs are different:

10 - 4 = 6 and 10 has the larger absolute value so the
answer is positive 6.


5.  -22  Signs are the same:

12 + 10 = 22 and then keep the negative sign.


6.  6  Signs are different:

15 - 9 = 6 and 15 has the larger absolute value so the
answer is positive.


7.  -9  Signs are different:

12 - 3 = 9 and 12 has the larger absolute value so the
answer is -9.


8.  0  Signs are different:

16 -16 = 0


9.  7  Signs are different:

14 - 7=7 and 14 has the larger absolute value so the
answer is positive.


10.  -16  Signs are the same:

8 + 8=16 and the answer remains negative.


11.  -9   Break the problem into 2 parts:

-5 +(-7) = -12


   -12 + 3 = -9


12.  16   Break the problem into 2 parts:

13 + (-5) = 8

   8 + 8 = 16


13.  -6   Break the problem into 2 parts:

-4 + 6 = 2

   2 + (-8) = -6


14.  -2   Break the problem into 2 parts:

10 + (-15) = -5

   -5 + 3 = -2


15.  -24   Break the problem into 2 parts:

-12 + (-7) = -19

   -19 + (-5) = -24




Did you get them all correct? If so, Congratulations - and it's time to move on to subtracting integers or multiplying and dividing integers.




If you missed a few, go back and review your answers and the two Adding Integer Rules. Try Again - you can do it!



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