Online Math
Professor: Dr. Nancy C. Miller

How Do You Complete The Orientation?

Orientation for this course will be done by e-mail and phone or in person Thursday, Jan 19, at PIN campus from 5-6pm. Read through all of the course materials on these webpages and links.

• After you read the policies for your semester that are linked from http://www.austincc.edu/nmiller/ answer the questions below and e-mail them to Nancy Miller

MATD 0370 - You can call with your questions, or attend orientation Jan. 19 in person at   PIN campus. Pin Campus is on Highway 290 West, look for a tall building.   Call or e-mail me with your questions, after you read and study all our course web pages and answer the questions below.    

Please e-mail Nancy the information below by Jan. 18, nmiller@austincc.edu No attachments please.

1. Your name, mailing address, home phone number, work phone number, and/or cell phone number.

2. What is your ACC e-mail address, as most communication from Nancy from ACC Blackboard comes to this e-mail address and you need to read it each week?

3. Answers to the following questions about the course:

There isn't an easy way to enter standard math notation into e-mail to Nancy Miller. Here are some basic rules:

*
Use the following symbols:
o Multiplication: * (so 2*3)
o Division: / (so 5/7)
o Powers: ^ (so 3^2 = 9, or x^3)
o Absolute value: | (so |-7| = 7; you find this symbol on the \ key)
*
Use plenty of parentheses. This is especially true when writing fractions. Here are some examples:
o x - 4 / 7 isn't clear; does this mean x - (4/7) or (x-4)/7?
o 3x / (x-2)
o (2/3) - (-3/5)
* Add in some extra spaces around +, -, and =. It is just easier to read.

Examples: (These examples are from a Basic Math Skills course that I borrowed from Mary Parker, but the basic issues are the same. You probably won't need to show quite as many steps when you do your work. Think of it as a quick review of some Basic Math skills before your Elementary Algebra pretest)

In many cases there are easier and better ways to show the
work using paper and pencil. Use those easier and better
ways as you do homework and on the test.

Example 1: Factor 252 completely.

Solution:
252 = 2 * 126
= 2 * 2 * 63
= 2 * 2 * 7 * 9
= 2 * 2 * 7 * 3 * 3
= 2 * 2 * 3 * 3 * 7

Comments: Notice that, although the factor tree is a nice
way to find the factors, it is not convenient to put it into
an email message. And, on tests, sometimes students show
the factor tree, but neglect to show the final factored
form for the answer. So it is good to practice this.
Also, notice that it is not convenient to show exponential
notation using only text. You should be able to show
exponential notation when you take the test, of course.)

Example 2: Solve 4*5+7*10 = 4x + x

Solution:
4*5+7*10 = 4x + x
20+70 = 5x
90 = 5x
90/5 = 5x / 5
18 = x

Comments: Sometimes students prefer to skip steps.
On a test, you must show all steps to get full credit.
Even in working problems for practice, you should write
all the steps until you can see them in your mind so
clearly that you don't need to write them in order to see them.

Example 3: Multiplying fractions:
Do the indicated operation: (12/35)*(14/45)

Solution:
(12/35)*(14/45)
= (12*14) / (35*45)
= (2*6*2*7) / (5*7*9*5)
= (2*3*2*2) / (5*3*3*5)
= (2*2*2)/(5*3*5)
= 8/75

Comments: Many students actually multiply together the
two numerators and the two denominators in the first step.
They get large numbers and then have to reduce the
resulting fraction. Since the numbers are so large,
many students make mistakes in reducing. It is much
easier to indicate what should be multiplied and then
factor them before multiplying to get large numbers.
Then it is easy to see how to reduce the fraction.

Example 4: Adding fractions.
a. Find a common denominator for 28 and 42. Show all work.
b. Use that to add 11/28 + 5/42. Show the equivalent
fractions and your answer.

Solution:
a. 28=2*2*7 and 42=2*3*7, so denom = 2*2*3*7 = 84
b. 11/28 + 5/42
= 11/(2*2*7) + 5/(2*3*7)
= (11*3)/(2*2*7*3) + (5*2)/(2*2*3*7)
= 33/84 + 10/84
= (33+10)/84
= 43/84

Comments:
Students often want to find the common denominator by
"inspection." That doesn't work in all cases. It's a
good idea to use a method that will always work. And,
of course, remember that you only need to find a common
denominator when adding or subtracting fractions,
NOT when multiplying or dividing fractions.

Example 5: Solving percent problems.
To find the selling price of a TV, the dealer multiplies
the wholesale price by 130%. If the selling price of a
particular TV was $195, what is the wholesale price of the TV?

Solution: Let x = the wholesale price

Wholesale price / wholesale percent = original price / original percent
x/100 = 195/130
x*130 = 195*100
(x*130)/130 = (195*100)/130
x = 150
So the wholesale price is $150.

Comments: There are several different ways to correctly
write the ratios needed here, but there are also some
incorrect ways.

Example 6: Order of operations: Perform the indicated
operations and simplify.
16 + 20 / 5 * 2 - (-7)
= 16 + 4 * 2 - (-7)
= 16 + 8 - (-7)
= 24 + ( +7)
= 31

Comments: Sometimes students can get the correct answer
while doing more than one operation per step. But almost
no one can reliably get them correct in that fashion.
Show all steps, one at a time. Also, students often do
not notice that the rule says "multiplications and divisions,
in order, from left to right." In this problem, that means
the division comes before the multiplication, since the
division comes first.

Example 7: Adding positive and negative numbers
Simplify: -13 - (-4) - 8 + (-6)

Solution:
-13 - (-4) - 8 + (-6)
= -13 + (+4) + (-8) + (-6)
= -9 + (-8) + (-6)
= -17 + (-6)
= - 23

Comments: Students who try to do problems like these
in any fashion less well-organized than this almost
always miss some of them on tests.
1. Replace each subtraction with addition of the opposite.
2. Keep each step equivalent to the one before it.
3. Do one operation in one step.
4. Keep doing steps until you have done all the operations.

Example 8: Convert 30 miles per hour to feet per second.

Solution: Need miles / hour = feet / second
So we need to divide by miles and multiply by feet
to get the length done. That's 5280 feet / 1 mile.

And we need to multiply by hours and divide by seconds.
We can do that in one step or two steps.
Here's how to condense two steps to one:
(hours / minutes) * (minutes / seconds)
So we have: (1 hours / 60 minutes) * (1 minutes / 60 seconds)
= 1 hour / 3600 seconds (canceling out the minutes.)

So

(30 miles) / 1 hour
= (30 miles / 1 hour ) * (5280 feet / 1 mile) * (1 hour / 3600 seconds)
= (30 * 5280 * 1) / (1 * 1 * 3600) (feet / seconds)
= ( 5280) / (120) feet/second
= 44 feet/second

Example 9: Solve 0.2x + 1.8 = 3.2

Solution:
0.2x + 1.8 = 3.2
0.2x + 1.8 - 1.8 = 3.2 - 1.8
0.2x = 1.4
0.2x / 0.2 = 1.4 / 0.2
x = 7

Example 10: The measurement of the second angle of a triangle is 30 degrees
more than the measurement of the first angle. The measurement of the third angle
is 22 degrees less than twice the measurement of the first angle. What are the
measurements of all three angles?

Solution: Let x = measurement of the first angle
Let x + 30 = measurement of the second angle
Let 2x - 22 = measurement of the third angle
first + second + third = 180
x + x + 30 + 2x - 22 = 180
4x + 8 = 180
4x + 8 - 8 = 180 - 8
4x = 172
4x / 4 = 172/4
x = 43
So the first angle is 43 degrees.
Second: x + 30 = 43 + 30 = 73 degrees
Third: 2x - 22 = 2(43) - 22 = 86 - 22 = 64 degrees

Check: Since the three angles of a triangle must sum to 180, we add these and see what it equals. 43 + 73 + 64 = 180.
So it checks!
Answer: The triangle has angles of 43 degrees, 73 degrees, and 64 degrees.

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