Due to math content, this page has special requirements (including JavaScript) for full functionality.
With your current viewing scenario, it is not appearing and behaving as it is supposed to!
Please visit Dr. Carol J.V. Fisher's Homepage (link at left) to learn what this site has to offer.
Watch the "Welcome" video to get started—hope to see you back here soon!
Dr. Carol J.V. Fisher's Homepage
ADDITION
Jump right to the exercises!
See the best ALGEBRA PINBALL time for this exercise
The concepts for this exercise are summarized below; for a complete discussion,
read the text.
With the trend towards more and earlier calculator usage,
some people have lost a comfort with basic arithmetic operations like 5 · 7 = 35 and 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 2x means " 2 times x " which is a shorthand for the addition problem x + x .
Similarly, the expression 3y means " 3 times y " which is a shorthand for the addition problem y + y + y , and so on.
Thus, for example, 2x + 3x = 5x and 8t + 9t = 17t .
Note that x means 1x , so that
x + 7x means 1x + 7x which is 8x .
Also, an expression like 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 , (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 (say) (1 + 2) + 3 and 1 + (2 + 3) would give different results,
so you'd always have to specify which way it should be done.
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 , 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.
EXAMPLE:
Evaluate 2x + 3 when x is 5 .
SOLUTION:
2x + 3 = 2(5) + 3 = 10 + 3 = 13
EXAMPLE:
Evaluate 2x + 3y when x = 1 and y = 7 .
SOLUTION:
2x + 3y = 2(1) + 3(7) = 2 + 21 = 23
Word/story problems on this web site will often 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.
In this exercise, you will practice addition problems of the form "x + y"
where x and y can be any of these numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 .
Follow the instructions below, and time yourself.
If you average less than 3 seconds per problem, then you'll get an online reward!
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.