7,17,19,8,14,16,9,10,12,__,__,__?
10, 5 and 7
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
One Easy Rule for Dividing and
Multiplying Integers
This last rule for dividing and multiplying integers is the easiest of all.
One simple rule to remember regarding the sign and everything else is just as
you learned it in 4th grade!
Multiplying and Dividing Integers
If the signs are the SAME, then the answer is POSITIVE.
If the signs are DIFFERENT, then the answer is NEGATIVE
That's it - multiply and divide as you normally would and then apply these rules
to determine the sign!
Ready for a few examples?
Examples for Multiplying and Dividing
Integers
1. 7(-6) = -42 The signs are different (positive 7 and negative 6), so the answer
is negative.
2. -4(-5) = 20 The signs are the same (negative 4 and negative 5), so the answer
is positive.
3. -4/2= -2 The signs are different (negative 4 and positive 2), so the answer
is negative.
Yes, it really is that easy! Just check your signs to make sure that your final
answer is correct.
Just remember:
Same sign - answer is positive.
Different signs - answer is negative.
