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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


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October 8th, 2017, 01:11 PM   #1
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Need a beginner Algebra book that teaches these ?

Prime factorization
LCM
GCF




I am trying to practice these

LCM of

Numbers
Fractions
Rational expressions

GCF of

Numbers
Fractions
Rational expressions

Quote:
LCM

1.
Find the prime factorization of each
number in the group.
2.
Make a list of ALL factors, raised
to the HIGHEST power that appears in
any factorization.
3.
Multiply out.

GCF

1.
Find the prime factorization of each
number in the group.
2.
Make a list of COMMON factors,
raised to the LOWEST power that
appears in any factorization.
3.
Multiply out
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October 8th, 2017, 01:38 PM   #2
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There are many books that discuss those topics. But there's no book you can read that will help with those problems past the basic definitions and some examples. Mostly you have to just think about it.

For example #1, finding the prime factors of a number. Say we needed to find the prime factors of 4584395435843584308. We have a calculator so that we don't actually have to do any arithmetic by hand.

How would we approach this problem? How about one prime at a time? The primes are 2, 3, 5, 7, 11, and so forth. So how about if we:

* Divide 4584395435843584308 by 2. If it can be done without leaving a remainder, then 2 divides 4584395435843584308.

* Now divide it by 3.

* Then divide it by 5.

* Etc.

In each case if the given prime divides our number evenly, it's a prime divisor. Else not.

Now how many primes do we have to try? You should convince yourself that we only have to check primes up to and including $\sqrt{4584395435843584308}$.

If you know any programming languages you can see that this is a very simple programming exercise. You could easily input a number and output its prime factors.

This is basically the style for these kinds of problems.

For specifics of LCM etc. you should start with Wiki. As far as general introductory algebra books good for self-study, I'm afraid I don't know, but I think there are a lot of MOOCs these days for discrete math, which is where these things are usually taught.

For the entire LCM procedure you should walk through it for simple pairs of numbers. What's the LCM of 15 and 25? 12 and 14? Work out some examples and you'll see what their procedure is doing.
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October 8th, 2017, 02:31 PM   #3
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Maschke

Thanks for the reply .

I was trying to learn this for some financial accounting studies i was doing .

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October 13th, 2017, 03:54 PM   #4
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For any two whole numbers, the product of the LCM and GCF is equal to the product of the two numbers. This is because, as Step Two of each procedure said, the LCM takes the higher exponent and the GCF takes the lower exponent. As an identity (an equation that does not depend on what the variables are), min(x, y) * max(x, y) = x * y. x and y would be the higher and lower exponent.

In case it needs explaining, Maschke's square root line is true because if x, y, and z are positive; x > the square root of z, and y > the square root of z, x * y > z. If x * y = z, then one of x and y is greater than the square root of z and the other is less than the square root of z, or the special case where x and y are equal and are the square root of z.
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