In this video we use algebra tiles to explain how to add integers.

In the video above, we added integers using Algebra tile, another way to thing about adding integers is by using a number line.   Remember: if a number does not have a sign it is positive, so ${^-5} + 3$ is the same as saying negative 5 plus positive 3.

A negative number plus a positive number:

Ex. 1    Lets look at the problem ${^-5} + 3$.

To do this problem lets pretend that you are walking along a number line.   First you would start by standing on the first number (in this case ${^-5}$.)

Because this is an addition problem you will be facing as if you were to walk toward the positive numbers.

Since the $3$ is positive, you would move forward $3$ spaces.

A positive number plus a negative number:

Ex. 2    $5 + {^-3}$

First you would start by standing on the first number
(in this case ${^+5}$)   Because this is an addition problem you will be facing as if you were to walk toward the positive numbers.
Since the $3$ is negative, and a negative sign can mean “take the opposite”, you would move backwards $3$ spaces.

A negative number plus a negative number:

Ex. 3    ${^-5} + {^-3}$.
First you would start by standing on the ${^-5}$. Because this is an addition problem you will be facing as if you were to walk toward the positive numbers.
Since the $3$ is negative you would move backwards $3$ spaces.

A positive number plus a positive number:
Ex. 4    I am sure we all remember that $5 + 3 = 8$.

Try the problem $7 + {^-8}$ on your own then check your answer with the video below.