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July 7th, 2018, 07:02 AM   #1
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Complex Fractions and Beginning Algebra

Hello all,

I'm starting a "beginning algebra" class (that's what my school calls it). It's been a while since I've had a math class and have been reviewing everything from fractions to pre-algebra. In addition to using Khan Academy I purchased a workbook so I could get used to showing my work on problems. In my fraction section of my workbook there are a lot of complex fractions. They seem really complicated (as most math does to me) but I never saw them in any section of KA I've used, again I've only gone as far as pre-algebra.

I was wondering if I should take some initiative and try to learn this on my own or if they're beyond what I'll need to know to get started "beginning algebra" or if I'll even need to know them at all for where I'm right now?

The topics included in beginning algebra will be signed numbers, algebraic terminology, basic operations on algebraic expressions and exponents, solution of linear equations and inequalities, simple factoring, algebraic fractions, and word problems.

Thank you!
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July 7th, 2018, 08:57 AM   #2
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Can you post some of the fractions you mentioned, so that the appropriate part of Khan Academy can be identified (or another site, if necessary)?
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July 7th, 2018, 09:51 AM   #3
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As example, can you solve 2x + x/4 = 45 ?
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July 7th, 2018, 10:32 AM   #4
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Quote:
Originally Posted by bleach3759 View Post
Hello all,

I'm starting a "beginning algebra" class (that's what my school calls it). It's been a while since I've had a math class and have been reviewing everything from fractions to pre-algebra. In addition to using Khan Academy I purchased a workbook so I could get used to showing my work on problems. In my fraction section of my workbook there are a lot of complex fractions. They seem really complicated (as most math does to me) but I never saw them in any section of KA I've used, again I've only gone as far as pre-algebra.

I was wondering if I should take some initiative and try to learn this on my own or if they're beyond what I'll need to know to get started "beginning algebra" or if I'll even need to know them at all for where I'm right now?

The topics included in beginning algebra will be signed numbers, algebraic terminology, basic operations on algebraic expressions and exponents, solution of linear equations and inequalities, simple factoring, algebraic fractions, and word problems.

Thank you!
First, I am not sure what you mean by complex fractions. You might mean fractions containing complex numbers such as

$\dfrac{4 + 5i}{3 + 4i}, \text { where } i^2 = -\ 1.$

You might mean fractions containing algebraic expressions such as in

$\dfrac{x^2 - x - 6}{x + 2} = x - 3.$

Or you might mean fractions containing fractions such as

$\dfrac{\dfrac{1}{x}}{\dfrac{1}{y}}.$

In the US, I would not expect fractions of the first type during first year high-school algebra. I would expect fractions of the latter two types.
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July 7th, 2018, 12:22 PM   #5
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The topics mentioned would seem to correspond literally to "beginning algebra", rather than a high school algebra class.

Last edited by skipjack; July 7th, 2018 at 12:26 PM.
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July 7th, 2018, 12:25 PM   #6
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Here are 2 examples from my book
1) 5/x-1 - 3/x+1
2) 6y-7/6xy - 4x-3/15xy
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July 7th, 2018, 12:53 PM   #7
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If the examples had been
(1). $\displaystyle \frac{5}{7 - 1} - \frac{4}{7 + 1}$, and

(2) $\displaystyle \frac{6*3 - 7}{6*2*3} - \frac{4*3 - 7}{6*3*5}$ (where "*" means "multiplied by"),

would you have been able to obtain the answers?

If so, precisely how? If not, what exactly in those examples causes you difficulty?
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July 7th, 2018, 02:54 PM   #8
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Skipjack, I'm trying to brush up on my math skills by doing a review of pre-algebra before starting my "beginning algebra" or algebra 1 class. I'm just wondering if I should take the initiative and familiarize myself with problems like this for the level I'm at.
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July 7th, 2018, 10:23 PM   #9
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The direct answers are "yes - you should review pre-algebra", "maybe - you could take the initiative if you are able to", and "no, you shouldn't familiarize yourself with problems like those you posted, because they are covered in Khan Academy under Algebra 2 (Subtracting rational expressions: unlike denominators) and your time would be better spent on much earlier topics.

If you've struggled a bit with the reviewing you've already done, you may need to revise basic arithmetic first. There are quite a few things in basic arithmetic that should be learnt by heart, else you may end up counting on your fingers while you're supposed to be learning algebra.
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July 8th, 2018, 06:20 AM   #10
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Math Focus: Wibbly wobbly timey-wimey stuff.
By definition a complex fraction is a fraction where the numerator and/or the denominator have a fraction in them. (I prefer the term "compound fraction" as the word "complex" usually refers to complex numbers.)

So we have something like
$\displaystyle \frac{ \frac{5}{6} }{ 1 + \frac{1}{3} }$

The first step is the multiply the numerator and denominator of the "large" fraction by the LCM of the "small" fractions. In this case this would be LCM(3, 6) = 6. So:

$\displaystyle \frac{ \frac{5}{6} }{ 1 + \frac{1}{3} } \cdot \frac{6}{6}$

$\displaystyle = \frac{ \frac{5}{6} \cdot 6 }{ \left ( 1 + \frac{1}{3} \right ) \cdot 6}$

$\displaystyle = \frac{5}{6 + 2} = \frac{5}{8}$

-Dan
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