This problem will review order of operations, i.e. rules of precedence or order in which mathematical operations are performed.

The rules are simple. Exponentiation is always done before multiplication and division, and multiplication and division are always done before addition and subtraction. (Mathematically we say exponentiation takes precedence over multiplication and division, etc.). For example what is 1+2*3? You can use parentheses (and also square brackets [ ] or curly braces $\lbrace \rbrace$) if you want to change the normal way operations work.

Note: You must compute this number before entering it into WeBWorK.

1+2*3 =

Note: You must compute this number before entering it into WeBWorK.

What is $2\cdot 3^2$?

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Now sometimes you want to force things to be done in a different way. This is what parentheses are used for.

Rule 1: Groups are simplified first. IE, Whatever is enclosed in parentheses (--), braces {--}, brackets [--], all in a numerator, all in a denominator, within an absolute value symbol |--|, or all under a radical $\sqrt{x}$ are done before anything else (and things in the inner most parentheses are done first).

For example, simplfy the following expression yourself, then enter the expression in the box below:

$$\frac {1+|9-3|}{2+\sqrt{49}}$$

Hint: This is a good place to use [ ]'s and also to use the "Preview" button. Also remember, |x| in standard notation is absolute value of x, so you must replace |x| with abs(x).

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Here are some more examples: (1+3)9 = 36, (2*3)**2 = 6**2 = 36, 3**(2*2) = 3**4 = 81, (2+3)**2 = 5**2 = 25, 3**(2+2) = 3**4 = 81

(Here we have used ** to denote exponentiation and you can also use this instead of a "caret" if you want). Try entering some of these and use the "Preview" button to see the result. The "correct" result for this answer blank is 36, but by using the "Preview" button, you can enter whatever you want and use WeBWorK as a hand calculator.

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Rule 2: The correct order of evaluation is > Roots and Powers (Exponents) > Division and Multiplication > Subtractions and Additiion Think! Correct order of operations goes from the hardest stuff (Roots) first to the easiest stuff (Addition) last.

There is one other thing to be careful about. Multiplication and division have the same precedence. For example, what does 2/3*4 mean? (Note that / is the "division symbol", which is sometimes written as a line with two dots. Don't think of / as the horizontal line in a fraction. Ask yourself what 1/2/2 should mean.)

Rule 3: Multiplication and divsion are evaluated from left to right.

Example: 2/3*4 means (2/3)*4 = 8/3, IT DOES NOT MEAN 2/12. If you want 2/(3*4) = 2/12, you have to use parentheses.

Rule 4: Addition and subtraction are evaluated from left to right.

Example: The same thing happens with addition and subtraction as with multiplication and division. Notice 1-3+2 = 0, but 1-(3+2) = -4.

This aare many situations where using parentheses might be a good idea, even if they are not needed

Example: Write (2/3)*4 rather than 2/3*4. This is also a case where previewing your answer can save you a lot a grief since you will be able to see what you entered.

Enter 2/3*4 and use the Preview button to see what you get.

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A Hand-in Assignment

Here's the link to the list of the functions which WeBWorK understands. WeBWorK ALWAYS uses radian mode for trig functions.

1. Click on the link. Print out this list and turn it in to your instructor before the due date of this assignment.

2. On the back of the list of functions, write the rules for the correct order of operations.

3. Also on the back of the page, calculate the following expression exactly. Show all steps as your apply order of operations.

$$\frac {3+|9-13|}{2+\sqrt{29-4}}$$

4. Look up the word "function" in your textbook. Write a defintion for "function" and provide a simple example of the concept.