Problems like
$(2) + (3) = 5$
and
$\,(3) + 5 = 2\,$ are easy for some people and hard for others.
If they're easy for you, then try a few problems below, and then
jump right to the exercises.
Otherwise, read on—and keep in mind that explaining something simple, in words, often ends up sounding
very complicated!
Click the ‘New Problem’ button to practice adding signed numbers. Type your answer, then press ‘enter’. 




The phrase signed numbers refers to numbers that can be
either positive (like
$\,5\,$) or negative (like
$\,5\,$).
That is, signed numbers are allowed
to have a minus sign.
Every real number can be interpreted in two ways:
The number
$\,3\,$ can mean:
go to position
$\,3\,$ on the number line.
The number
$\,3\,$ can mean:
go to position
$\,3\,$ on the number line.
Positive numbers can indicate movement to the right.
For example,
$\,3\,$ can mean:
move
$\,3\,$ units to the right.
Negative numbers can indicate movement to the left.
For example,
$\,3\,$ can mean:
move
$\,3\,$ units to the left.
When you add a negative number, you should put it in parentheses, unless it comes first.
For example, the sum of
$\,3\,$ and
$\,1\,$ should be written as
$\,3 + (1)\,$.
(Recall that the word sum refers to an addition problem.)
If you want, you can optionally put that first negative number in parentheses, too:
$\,(3) + (1)$.
Every number has a size (its distance from zero).
Every nonzero number has a sign (positive or negative).
For example:
The number
$\,3\,$:
its size is
$\,3\,$, and its sign is positive.
The number
$\,3\,$:
its size is
$\,3\,$, and its sign is negative.
In the movement interpretation of a real number,
the size tells us how far to move, and
the sign tells us which direction to move.
Now we're ready to combine the position and
movement ideas in an addition problem.
The process is illustrated
first with an example:
Consider the problem:
$\,2 + (3) + 5\,$
Or, you can always start at zero!
That is, write
$2 + (3) + 5$ as
$0 + 2 + (3) + 5$ .
The first number indicates position, and the remaining numbers indicate movement.
Start at
$\,0\,$, move
$\,2\,$ to the right,
$\,3\,$ to the left, and
$\,5\,$ to the right, ending up at
$\,4\,$.
You should understand both interpretations, but in practice you can use whichever is more natural to you.
The start at zero interpretation is used in the following discussion.
You probably don't want to be drawing number lines every time you need to do an
addition of signed numbers problem.
The good news is that every problem—no matter how many numbers are involved—boils down to either
a twonumber addition problem, or a twonumber subtraction problem, which can then be done efficiently in your head.
Keep reading!
When you add numbers with the same signs (both positive or both negative),
then in your head you do an addition problem.
Here are two examples:
When you add numbers with different signs (one positive, one negative),
then in your head you do a subtraction problem.
Here are two examples:
When you add two signed numbers, you can follow this five step process.
As you read through these steps, think of applying these questions to the problem
$\,2 + (3)\,$:
If there are more than two numbers being added,
just turn it into a twonumber problem in the first step,
by combining the positive and negative numbers separately, like this:
Here, you will practice addition problems of the form "$\,x + y\,$"
where $\,x\,$ and $\,y\,$ can be any of these numbers:
$\,10, 9, 8, \ldots, 1, 0, 1, \ldots, 8, 9, 10\,$.
About half of the problems will involve variables!
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
