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# Algebra

How does this = a/b-5/12b third line down? I figured out the -5/12b part, because 12b is the common factor when subtracting -3/4b+1/3b. It looks like they are trying to add a/2b + a/2b.

a/2b + a/2b = 2a/2b not a/b. This can't be reduced can it because the numerator and denominator have different letters?

How do they get a/b? Thanks.
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2 Solutions

Commented:
First and third terms in 2nd line:    a/(2b) +   a/(2b)  = 2 [ a/(2b) ] =  a/b

leaving 4th and 2nd terms:   1/(3b) - 3/(4b)

Is that clearer?
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Commented:
2a/(2b) = (2/2)* (a/ b)
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Commented:
because
1/(2b) = (1/2)*(1/b)

and

(2a)/b = 2*(a/b)

putting it together:

(2a)/(2b) = 2*[ a/(2b) ] = 2*a*[ 1/(2b) ] = 2*a*[ (1/2)*(1/b) ] = 2*a*(1/2)* [ (1/b) ] =
= a* [ (1/b) ] = a/b
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Author Commented:
= 2 [ a/(2b) ] =  a/b

2 * a = 2a
2 * 2b = 4b

=2a/4b

doesn't it?
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Commented:
= 2 [ a/(2b) ] =  a/b
=2a/4b

Your above 2 lines show the Right Hand Side of the = sign. It is important that you have a both a RHS and a LSH when writing an = sign.

What are the LHS's of the = sign?
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Commented:
2 [ 1/2 ] = 1/1, not 2/4
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Author Commented:
I don't understand what your getting at.

= 2 [ a/(2b) ] =  a/b  here 2*a and 2*2b = 2a/4b. or so I thought.
=2a/4b
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Author Commented:
Ok. ozo clued me in. I now understand how you get 2a/2b.

But still how to get from there to a/b?
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Commented:
2 [ 1/2 ] = 1/1
true.
===
I don't understand what your getting at.

= 2 [ a/(2b) ] =  a/b  here 2*a and 2*2b = 2a/4b. or so I thought.
=2a/4b
===
2 [ a/(2b) ] =

2            a
------  * --------
1           2b

One 2 is in the numerator; the other is in the denominator, so they cancel out.
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Commented:
2            a
------  * -------- =
1           2b

2            a
------  * -------- =
2            b

1            a
------  * -------- =
1            b

a
--------
b
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Author Commented:
I looks like your saying that it's OK to separate the number from the variable in order to reduce the number and then reattach the number to the variable in this case it's just a one over one 1/1 so you get when multiplied back to a/b = a/b.
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Author Commented:
I thought 2a/2b was like comparing apples to oranges and the 2a could not be divided into the 2b in order to reduce the fraction to just a/b.
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Commented:
The more general form is described in the Fundamental Principle of Fractions:

It helps to plug in numbers as a check:
Let a = 36 and b = 4

Is (2a)/(2b) = (a/ b)  ?

(2a)/(2b) = (2*36)/(2*4) = 72/8 = 9

a/b = 36/4 = 9
So, at least for that a and b, it checks out OK.
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Author Commented:
Thanks for your help once again.
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Commented:
One more step. Keep on stepping!
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Author Commented:
Thanks for that link. I will check it out.
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RetiredCommented:
Here is another approach:

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