# Thread: Missing Basic Algebar Rules

1. ## Missing Basic Algebar Rules

Since I've been in Accounting & Finance classes, I've realized I must have missed a lot in Algebra back in the day.

Let me give you an example (it's Finance, but needs Algebra)...

Say you have:

Return on Assets = Net Income / Total Assets

You've been given:

6% = Net Income / $90 Ok, so to find net income you take .06 X$90. Why?

The idea is to get Net Income by itself? Other problems seem to use division instead of multiplication after you get the 'missing' portion by itself.

Does this make any sense?? Know what I mean?

When would you divide instead of multiply? (Probably an extremely thick question) but is the denominator always on the bottom no matter what case if you're dividing or rearranging a problem in this manner?

Thanks for any help.

2. Originally Posted by matius
Since I've been in Accounting & Finance classes, I've realized I must have missed a lot in Algebra back in the day.

Let me give you an example (it's Finance, but needs Algebra)...

Say you have:

Return on Assets = Net Income / Total Assets

You've been given:

6% = Net Income / $90 Ok, so to find net income you take .06 X$90. Why?

The idea is to get Net Income by itself? Other problems seem to use division instead of multiplication after you get the 'missing' portion by itself.

Does this make any sense?? Know what I mean?

When would you divide instead of multiply? (Probably an extremely thick question) but is the denominator always on the bottom no matter what case if you're dividing or rearranging a problem in this manner?

Thanks for any help.
ok, first of all i asume you know why 6% = 0.06, ok, let me not assume anything.

"Percentage" is a fancy word for "/100" or "out of 100," so basically a percentage is a fraction where the denominator is 100

so 25% = 25/100 = 0.25, 5% = 5/100 = 0.05, 6% = 6/100 = 0.06 etc.

Now, what you are asking about is solving an equation. Basically you have an expression with an equal sign, where one thing is unknown, and your objective is to get that unknown on one side of the equal sign by itself. basically, if there is anything else with the unknown on the same side, you do the opposite operation that thing is doing. since there is an equal sign, you have to maintain the equality by doing the same thing on the other side.

example:

5 = x + 2
we want to get x on one side by itself, but there is a +2 beside it, so we do the opposite operation, that is, we minus 2. however, to maintain the equality, we have to minus 2 from the other side as well. so we get:

5 - 2 = x + 2 - 2
5 - 2 = x
3 = x
therefore, x = 3

a similar concept applies when multiplying and dividing.

25 = x/5
we want x on one side, but there is a 5 dividing it, so we do the oppostie, we multiply by 5, so that will cancel out the 5 that is there. since it is an equation, we must do the same thing on the other side. so,

25 * 5 = x/5 * 5
5 = x
therefore, x = 5

what if the x was on the bottom of the fraction, well, there are two typical ways to deal with that.

5 = 25/x
ok, we can follow the same principle we have been using the whole time. since we have a 25 on top, we can divide by 25, or multiply by 1/25, that is where 25 is on the bottom to cancel the one on top. but be careful, when doing this we don't end up with x on one side, we end up with 1/x

5/25 = 25/x /25
5/25 = 25/x * 1/25
5/25 = 1/x
now flip both sides
25/5 = x
therefore, x = 5

or, we could move the x first.

5 = 25/x ..........multiply by x on both sides
5 * x = 25/x * x
5x = 25 .......now we have a 5 times x, so do the opposite, divide by 5
5x / 5 = 25/5
x = 5

another method is we can cross multiply. that is, we take the denominator of one side times the numerator of the other side, and put that answer on one side of the equal sign, then do the same thing with the numerator and denominator on the opposite side.

5 = 25/x
5/1 = 25/x
5*x = 1*25
x = 25/5
x = 5

so there are general patterns here, that you get familiar with the more you do them. if you do enough problems, you will be able to do these automatically without even thinking of the rules.

Let's say in all the following, we want to solve for a. i will try to put a in every possible position you may come across it in.

a + b = c
=> a = c - b

a - b = c
=> a = c + b

a/b = c/d
=> a = b*c/d

b/a = c/d
=> a = b*d/c

and we can mix these up:
example

a/b + c = d
a/b = d - c
a = b*(d - c)

you can try some others.

So now to do your problem:

6% = Net Income / \$90

=> 0.06 = NetIncome/90 .......we have 90 dividing, so multiply by it on both sides
=> 0.06 * 90 = NetIncome/90 * 90
=> 5.4 = NetIncome

Try to grab an algebra book and practice some of these problems, or practice a lot of them in your finance text book, come back here with your solutions and we'll tell you your mistakes...if you make any

3. Can't tell you how much that helps me. Thank you!

It's very clear to me how this works now, but you're right, will need to practice before it really sets in.

4. Originally Posted by matius
Can't tell you how much that helps me. Thank you!
good! glad to be of service

It's very clear to me how this works now, but you're right, will need to practice before it really sets in.
yes, practice is necessary, even for people who are good with math (unless you're Guass reincarnated). you can always come back here to check the work that you have done