Simply multiplying and simplifying fractions

[lydiamay19]

Hey!

I'm doing a pre-calc review packet this summer and there is one page that is just multiplying and simplifying complex fractions. I just don't remember the rules about it.

One example: (6s^2/5t^3)*(10st/6s^3)

So I just multiply it so it looks like (6s^2)(10st)/(6s^3)(5t^3) right? Then how do I simplify it?

 

[pka]

Any factor present in BOTH numerator and denominator can be cancelled.

\(\displaystyle \dfrac{6s^2}{5t^3} * \dfrac{10st}{6s^3} = \dfrac{60s^3t}{30s^3t^3} = \dfrac{2 * 30}{30t^2} = \dfrac{2}{t^2}\)

Here is a LaTeX tip on using \dfrac.
[TEX]\dfrac{6s^2}{5t^3} * \dfrac{10st}{6s^3} = \dfrac{60s^3t}{30s^3t^3} = \dfrac{2 * 30}{30t^2} = \dfrac{2}{t^2}[/TEX]

gives
\(\displaystyle \dfrac{6s^2}{5t^3} * \dfrac{10st}{6s^3} = \dfrac{60s^3t}{30s^3t^3} = \dfrac{2 * 30}{30t^2} = \dfrac{2}{t^2}\)

 

[lookagain]

About the same as my math and pedagogic skills.

Please stop posting this kind of comment. It's akin to false humility.
If it were true, you would have had me riding your comments in
most of your posts by now. Your strong mathematical talents
are present in abundance in different threads.

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One example: (6s^2/5t^3)*(10st/6s^3)

So I just multiply it so it looks like (6s^2)(10st)/(6s^3)(5t^3) right?

lydiamay19,

you would want to use Latex as a preference. However, if you
type it out horizontally, you must use grouping symbols. Certain
ones must be used, but others may be optional and used
for consistency in style:


[(6s^2)/(5t^3)][(10st)/(6s^3)]

[(6s^2)(10st)]/[(6s^3)(5t^3)]

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[lookagain]

Supposedly, the equivalent to one of the other methods is shown here:


\(\displaystyle \dfrac{6s^2}{5t^3} \cdot \dfrac{10st}{6s^3} = \)


\(\displaystyle \dfrac{60s^3t}{30s^3t^3} = \)


\(\displaystyle \dfrac{2 * 30}{30t^2} = \)


\(\displaystyle \dfrac{2}{t^2}\)


Cancelling of common factors of coefficients should be done
(should be taken advantage of) from any numerator to any
denominator in a string of multiplications first. Otherwise,
you're having to multiply numbers (coefficients) together
to get larger numbers (products), and then have to reduce
those results at the end.


\(\displaystyle Instead, \ as \ a \ recommendation, try:\)


\(\displaystyle \dfrac{6s^2}{5t^3} \cdot \dfrac{10st}{6s^3} = \)


\(\displaystyle \dfrac{s^2}{t^3} \cdot \dfrac{2st}{s^3} = \)


\(\displaystyle \dfrac{2s^3t}{t^3s^3} =\)


\(\displaystyle \dfrac{2}{t^2}\)

 

[lydiamay19]

Thanks everyone! New problem:

How do I multiply/divide/simplify a fraction that has addition and subtraction in it?

EX: (3y+9)/(14y)*(y^3)/(y^2-9)

 

[Deleted member 4993]

Thanks everyone! New problem:

How do I multiply/divide/simplify a fraction that has addition and subtraction in it?

EX: (3y+9)/(14y)*(y^3)/(y^2-9)

Please start a new thread witha new problem.

Hint for the EX above:

Factorize y² - 9, using,

a² - b² = (a+b)(a-b)

Notice that the term (3y + 9) can be factorized too.