factoring problems?

Question

thanks everyone for answering my last question
but I still don't get some problems, can you PLEASE help me and explain to me how you got that answer?

1.) 48 - 4m ; would that equal -12m?
2.) 1/3m - 2/3n - 5/3 ; those / signs mean over (like a fraction) I don't understand that, can someone give me the answer and explain?
3.) 9h - 63j ; would that equal -7hj?
thanks a lot for your help guys :D

Answer 1

1.) 48 - 4m

4(12 - m) {12 and m are not like terms, and cannot be combined}

2.) 1/3m - 2/3n - 5/3

The fractions can be combined like the ones we learned in elementary school, only here the LCD is 3mn

n/3mn - 2m/3mn - 5mn/3mn

(n - 2m - 5mn)/3mn

3.) 9h - 63j

Again, these are not like terms, so they cannot be combined. We can factor a 9 from the numeric portions

9(h - 7j)

Answer 2

You need someone to help you 'catch-up' because math will come at you fast in future grades, and your success depends on how well you know the basic stuff.

The / sign is that dividing bar in a fraction yes---it functionally means 'divide'.

Look at the following:

3cats + dog -2bats -2cats + 3dogs -55
Using algebraic symbols it could look like so:
3c + 1d - 2b -2c + 3d - 55
rearranging and simplifying
3c - 2c + d +3d -2b -55
collecting like terms
c+4d-2b-55

Notice that you can only add up things that are of the same 'species' ! My explanation is not very good but I am trying to convey the message that math is really quite simple. It's just a bunch of simple things and ideas put together in a giant puzzle that only looks difficult.

Looking at 2] above, you have three terms which are all different animals, if you will, and you cannot do any 'collecting'

(1/3)m -(2/3m) -5/3 is way different than what you have written by the way. Using brackets and parentheses is a good idea for numerous reasons.

Also, get used to fractions as they are sometimes far easier to work with than their 'decimal' equivalents.

Let's look a little closer at multiplying: I will use the X to show multiplication for this example only:
3a X 4b = whatever
This equation means the same as:
3 X a X 4 X b = whatever
And because it doesn't matter in which order you multiply, all this could be rewritten this way:
3 X 4 X a X b = whatever
Now you can see we can only proceed with the two similar 'animals'--the NUMBERS.
3 X 4 is 12
Because the 'a' and 'b' are different animals they cannot be ' simplified' or 'worked -out'

So the farthest we can go would look like so:
12XaXb=whatever
And, removing those ugly and confusing 'X' signs denoting 'times' we finish with the following simplified equation:

12ab = whatever

Consider rational expressions and terms now:

(2/5)x + (1/5)y

We can't do anymore 'simplifying'
here because the two terms are different creatures.

However, If you had two similar creatures:
(2/5)k + (1/5)k these could be simplified into one term:
Add the two coefficients as you would add fractions in grade 6 or 7:

2/5 + 1/5 = 3/5 and so,
(3/5)k is our simplification.

It might help to show that (3/5)k can also be expressed the following ways:
3k/5
(3k)/5
3k/(5)
or even
(1/5)(3k)
but never:
3/5k

This tutorial could go on for another 1000 lines but I do not know at what level your understanding is---I don't know all that you know. And, though I don't know much more, I like to help others----PASS IT ON (helping others that is).

Answer 3

48 = 4x12, and 4m = 4xm
so factoring means that that same number out
48 - 4m = 4(12 - m)

1/3m - 2/3n - 5/3 = 1/3(1/m - 2/n -5)

9h - 63j = 9(h - 7j)