Adding integers is easy if you know the basic patterns.  We will break up integer addition into a few cases, just to keep everything straight.

Case 1: Adding positive to positive:

• This is the case we know from everyday math.  You have done this since you were a toddler.
• We simply add the values of the numbers together.
• Example: 3+4 = 7
• Example: 5+10 = 15
• Example: 2+6=8
• Example: 1+77 = 78

Case 2: Adding negative to negative:

• Remember that a negative number just means that you owe someone else that many items.  For example, if you have -3 pencils, you don't have any pencils...but you owe someone else 3 pencils.

• So, if we have a negative number and we add to this another negative number, then we just owe someone else, for example, more pencils.

• When adding a negative number to another negative number, we just add the absolute value of the numbers together, and we put a negative sign in front of the final answer.

• Example: (-3)+(-4) = -7    We originally owed someone 3 pencils, but we borrowed 4 more pencils.  So in the end, we owe 7 pencils total.  The negative sign in the answer tells us that we in total owe 7 pencils.

• Example: (-2)+(-4) = -6    We originally owed someone 2 apples, but we borrowed 4 more apples.  So in the end, we owe 6 apples total.

• Example: (-10)+(-7) = -17   We add the absolute values of the numbers together, and put a negative in front of the final answer.

• Example: (-3)+(-9) = -12   We add the absolute values of the numbers together, and put a negative in front of the final answer.

• Example: (-20)+(-10) = -30  We add the absolute values of the numbers together, and put a negative in front of the final answer.

Case 3: Adding negative to positive:

• Focus initially only on the absolute value of the numbers you have.

• Subtract the absolute values of the numbers.  Take the larger absolute value and subtract the smaller one.

• The sign of the answer can be either negative or positive.  The sign of the answer will always be the same as the sign as the larger absolute value number in your problem.

• Example: (-3)+5 = 2.     We subtract the absolute values: 5-3=2.  The sign is positive because the number with the larger absolute value in our original problem (5), was positive.

• Example: (-3)+2 = -1.    We subtract the absolute values: 3-2=1.  The sign for the answer negative because the number with the larger absolute value in our original problem (-3), was negative.  So, the final answer is: -1.

• Example: (-10)+5 = -5.   We subtract the absolute values: 10-5=5.  The sign for the final answer is negative because the number with the larger absolute value in our original problem (-10), was negative.  So, the final answer is: -5.

• Example: 7+(-5) = 2.   We subtract the absolute values: 7-5=2.  The sign for the final answer is positive because the number with the larger absolute value in our original problem (7), was positive.  So, the final answer is: 2.

• Example: (-8)+1 = -7.  We subtract the absolute values: 8-1=7.  The sign for the final answer is negative because the number with the larger absolute value in our original problem (-8), was negative.  So, the final answer is: -7.

• Example: (-2)+2 = 0.   We subtract the absolute values: 2-2=0.  Zero is neither positive or negative so we leave the answer as zero.

• Example: 17+(-10) = 7   We subtract the absolute values: 17-10=7.  The sign for the final answer is positive because the number with the larger absolute value in our original problem (17), was positive.  So, the final answer is: 17.