BASIC ADDITION PRACTICE

With the trend towards more and earlier calculator usage,
some people have lost a comfort with basic arithmetic operations like [beautiful math coming... please be patient] $\;5\cdot 7 = 35\;$ and [beautiful math coming... please be patient] $\;8 + 6 = 14\;$.
It is a waste of valuable time to use your calculator for problems such as these.
In this section, your basic addition skills are brought "up to speed"
so you won't be wasting mental energy on arithmetic and will be able to concentrate on higher-level ideas.

Algebra uses letters to represent numbers. (LOTS more on this later on!)
The expression [beautiful math coming... please be patient] $\;2x\;$ means ‘$\,2\,$ times $\,x\,$ ’. This is a shorthand for the addition problem $\;x + x\;$.
Similarly, the expression [beautiful math coming... please be patient] $\;3y\;$ means ‘$\,3\,$ times $\,y\,$’. This is a shorthand for the addition problem [beautiful math coming... please be patient] $\;y + y + y\;$.
Thus, for example, [beautiful math coming... please be patient] $\;2x + 3x = 5x\;$ and [beautiful math coming... please be patient] $\;8t + 9t = 17t\;$.

Note that [beautiful math coming... please be patient] $\;x\;$ means [beautiful math coming... please be patient] $\;1x\;$, so that [beautiful math coming... please be patient] $\;x + 7x\;$ means [beautiful math coming... please be patient] $\;1x + 7x\;$, which is [beautiful math coming... please be patient] $\;8x\;$.
Also, an expression like [beautiful math coming... please be patient] $\;2x + 5t\;$ cannot be simplified.

To commute means to change places.
The Commutative Property of Addition states that for all numbers $\,x\,$ and $\,y\,$, $\;x + y = y + x\;$.
That is, you can change the places of the numbers in an addition problem, and this does not affect the result.

If you're a sociable person, then you probably like being in groups;
i.e., you like to associate with other people.
In mathematics, associative laws have to do with grouping.

The Associative Property of Addition states that for all numbers $\,x\,$, $\,y\,$, and $\,z\,$, [beautiful math coming... please be patient] $\;(x + y) + z = x + (y + z)\;$.
Notice that the order in which the numbers are listed on both sides of the equation is exactly the same; only the grouping has changed.
The Associative Property of Addition states that in an addition problem, the grouping of the numbers does not affect the result.

Thanks to the associative property, we can write things like $\;1 + 2 + 3\;$ without ambiguity!
Think about this—if the grouping mattered, then $(1 + 2) + 3$ and $1 + (2 + 3)$ would give different results,
so you'd always have to use parentheses to specify which way it should be done.
(That would be a real nuisance.)

Adding zero to a number does not change it.
In other words, adding zero preserves the identity of the original number.
That is, for all numbers $\,x\,$, [beautiful math coming... please be patient] $\;x + 0 = 0 + x = x\;$.
For this reason, the number $\,0\,$ is called the additive identity.

When an expression involves a variable, then you will often be asked to evaluate the expression for a given value.
This means to substitute the given value for the specified variable, and then simplify the result.
The phrase can be used with more than one variable.

EXAMPLES:
Question: Evaluate [beautiful math coming... please be patient] $\;2x + 3\;$ when [beautiful math coming... please be patient] $\;x\;$ is $\;5\;$.
Solution: [beautiful math coming... please be patient] $2x + 3 = 2(5) + 3 = 10 + 3 = 13$
Question: Evaluate [beautiful math coming... please be patient] $\;2x + 3y\;$ when [beautiful math coming... please be patient] $\;x = 1\;$ and [beautiful math coming... please be patient] $\;y = 7\;$.
Solution: $2x + 3y = 2(1) + 3(7) = 2 + 21 = 23$
Master the ideas from this section
by practicing both exercises at the bottom of this page.

When you're done practicing, move on to:
Multiplication

 
 

In this exercise, you will practice addition problems of the form [beautiful math coming... please be patient] $\;x + y\;$,
where $\,x\,$ and $\,y\,$ can be any of these numbers: $\;0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10\;$.

    
(an even number, please)
CONCEPT QUESTIONS EXERCISE:

Word/story problems on this web site may involve an imaginary unit of money, the moncur.
An apple might cost $\,1\,$ moncur. An orange might cost $\,2\,$ moncur.
(Think: MONey/CURrency)
In this way, web exercises won't get outdated due to inflation.

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
Stuff I want to move!
(MAX is 25; there are 25 different problem types.)