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For this exercise, you need
♥ INTERNET EXPLORER 6.0 and above, with MathPlayer installed.♥
AVERAGE OF TWO SIGNED NUMBERS
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.
For this section (and for many of the sections beyond!) you'll need to install MathPlayer so that
you can see correct mathematical notation.
The time has come to stop writing fractions as
a/b and instead write them in the preferred form, as the "horizontal fraction"
ab !
A teacher reports an average grade on a test.
You read about the average number of calories burned per hour for your favorite exercise.
What do these figures mean?
The purpose of this section is to discuss the concept, the computation, and some
important properties of averaging.
To average two numbers means to add the numbers together, and
then divide by 2 . Thus,
the average of a and b is
a+b2 .
Averaging two different numbers always gives the number exactly halfway
between, as illustrated below:
In this web exercise you will practice computing averages of two
numbers, where the numbers can be -10, -9, …, 9, 10 .
You should be able to do this exercise without a calculator!
It is good practice with mental arithmetic, and will reinforce your skills with addition of signed numbers.
There are several key ideas to keep in mind:
- If the two numbers being averaged are close to each other, just visualize the number line and
picture the number that is exactly halfway between.
- If the numbers being averaged are far enough apart that you can't easily decide which number is
halfway between, then do the arithmetic.
Add the two numbers and divide by 2 .
Clearly, the formula
a+b2
gives some number; but how do we know that
the number given by this formula is really, always, halfway between
a and b ? Although repeated trials
(with lots of different numbers) is pretty convincing, it is of
course impossible to check every pair of real numbers.
To see a proof, read the text!
EXAMPLES:
The average of -3 and -5 is -4 .
The average of 7 and 10 is 8.5 .
You must write your answers in decimal form (as needed).
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.