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October 19th, 2017, 08:52 AM   #1
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Reducing fractions to its simplest form ( with exponents)

Hello! I'd like some help with a few problems that I have with reducing certain fractions to its simplest form. I already know the answers since they are written down in my book; what I need help with is how to think, explanation. Here are the problems:

a) 3AB^3/18A^3B

b) 10X^3/15X^2

c) 2X+2/2X

Thanks.

Last edited by skipjack; October 19th, 2017 at 09:02 AM.
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October 19th, 2017, 09:18 AM   #2
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In each fraction, identify any factor (other than 1) of every term of the numerator that is also a factor of every term of the denominator, then remove that factor from both the numerator and the denominator (this amounts to dividing every term by the factor).

(c) 2X + 2 and 2X have 2 as a common factor. To remove 2 from the second term of the numerator, replace that term with 1. Hence the result is (X + 1)/X. This assumes that the original fraction was intended to be (2X + 2)/(2X).

Having removed a common factor, repeat the process if another common factor still exists.

Is that sufficient explanation?
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October 19th, 2017, 10:36 AM   #3
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Quote:
Originally Posted by A9810A View Post
a) 3AB^3/18A^3B

b) 10X^3/15X^2

c) 2X+2/2X
Hmmm... Seems I'm doing the "pet peeve" thing today.

Warning! Warning!! Pet peeve alert! Warning!

a) (3AB^3)/(18A^3B)

b) (10X^3)/(15X^2)

c) (2X + 2)/(2X)

The parentheses are important. For example, using order of operations:
a) 3AB^3/18A^3B = (3AB^3/18 ) * A^3B = (3AB^3 * A^3B)/18

which is not at all what you were trying to say. See here: Order of operations.

Pet peeve ended. I'm all better now!

-Dan
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