Lesson Eight: Part One: Algebra
So I finally finished my practice tests. According to the grades I made, I probably shouldn't be teaching you math or science, but as I'm going by a book, I think I wont do too bad if I keep teaching.
I also went to attempt to register for my GED test but they were already full, so I'll be going April 9th to register for a test on the 16th and 17th instead.
(I hope that this makes sense, if it doesn't, feel free to email me at [email protected] and i'll try to make more sense out of it for you, simply make the subject line Lesson Eight: Part One: Algebra.)
Some credit goes to GED Success 2004.
So here's the first lesson on Algebra!
Signed Numbers and Absolute Value:
Numbers that drop below zero can be measured by using signed numbers. Signed numbers just show how far a number is from 0.
Any number less than zero is a negative (-) number, and any number higher than zero is a positive number (doesn't need a sign to it)
Imagine a number line, the numbers start at -10, and as you move to the right, it slowly increases by 1.
-10, - 9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
A B C D E
If someone asked you what the value of point B was, you'd say it was -4.
However, if someone asks you what the ABSOLUTE value of B is, the answer would be a simple 4.
The difference between value and absolute value is just that value means the exact number.
Absolute value is how many places it is away from 0.
Well B isn't -4 places away from 0, right? Right, it is simply 4 places away from 0.
To Add and Subtract Signed Numbers:
Subtracting:
EX: It was 8 degrees at 1pm, within 6 hours, the temperature had dropped 9 degrees. What was the temperature once it had dropped?
Well 'dropped 9 degrees' is just the same as saying '-9'
So 8 degrees and -9 degrees.
Now look at the number line written above, and start at 8.
Then move to the left 9 points.
The temperature was -1 degree.
EX: In Dallas, it's 10 degrees outside, but in Los Angeles it is -3 degrees. What is the difference between the two temperatures?
There are two ways you can do this, firstly you could easily use the number line above to solve it, by starting at 10 and counting to the left until you get to -3 to see how many places you move.
Or you can do it this way.
10 - (-3)
When you have a - (- such as you have after the 10, that becomes a + sign and the first number to the right of your minus sign also becomes positive. So 10 - (-3) becomes 10 + 3.
The difference between the two temperatures is 13 degrees.
Adding: -4 + (-2) = ______
In order to add numbers with the same sign (both of these have negative signs so they're same sign obviously), take the absolute values of both the numbers, add them together, and then keep the original sign.
-4 + (-2) = 4 + 2 = 6 = -6
EX: -8 + (-4) = -12
8 + 4 = 12
5 + 6 = 11
-5 + (-6) = -11
In order to add numbers who have different signs, here's what you do:
6 + (-8)
Step 1: Subtract the absolute values.
8 - 6 = 2
Step 2: In the original problem, whichever of the numbers has the greater absolute value is the sign in which you'll use.
-8 has the greatest absolute value, so you'll use a negative sign as the sign for your answer.
6 + (-8) = -2
EX:
9 + (-13) =
13 - 9 =
4 =
and since 13 is the highest value, you use its sign
Multiplying and Dividing Signed Numbers:
Step 1, simply multiply and divide as if the numbers were all positive
Step 2, figure out the sign of the answer. If the signs are different, it's a negative and if the signs are the same, it's a positive.
EX:
4(-2) =
In multiplication, different signs mean you'll have a negative answer.
So multiply as if they were all positive (4 x 2 =8) and then make it negative since the signs in the problem are different.
4(-2) = -8
EX:
-16/-2 =
Same signs yield a postive answer, so -16 divided by -2 would equal 8.
EX:
-18/3
Different signs make negative answers.
18/3 = 6
Make it negative, so its -6
EX:
-3(-4)
Same signs make positive answers.
-3 x -4 = 12
If you have more than two negatives being multiplied together, try and remember this small shortcut:
An even number of negatives multiplied together will give off a positive number.
Even = Positive
An odd number of negatives multiplied together will give you a negative number.
Odd = Negative
