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Simplify this fractional expression

$$\frac{4b}{3y} \frac{-4y}{12b^2} $$

This is the format in which the question is written and I do not understand what to do in order to solve for.

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  • $\begingroup$ What does the question actually say? A question is comprised of more than just an expression. $\endgroup$ – Dan Rust Aug 14 '13 at 13:43
  • $\begingroup$ @DanielRust++; in particular, many books will have a set of instructions in a common place above a series of problems, where the intent is that you apply the instructions to all the problems below until a new set of instructions is given. What is the subject matter? $\endgroup$ – abiessu Aug 14 '13 at 13:44
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    $\begingroup$ The missing words are "Simplify as much as you can" with probability about 99%... $\endgroup$ – fedja Aug 14 '13 at 13:48
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$$\frac{\frac{4b}{3y}}{\frac{-4y}{12b^2}}=\frac{\color{red}4b}{\color{green}3y}\cdot\left(-\frac{\color{green}{12}b^2}{\color{red}4y}\right)$$

Pay attention to the colors for the cancellations that will happen...

If you meant

$$\frac{4b}{3y}\cdot\frac{-4y}{12b^2}=-\frac{16by}{36b^2y}$$

and now just cancel, for example

$$\frac{16}{36}=\frac8{18}=\frac49$$

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  • $\begingroup$ +1 Nice work, @DonAntonio. Just a note, you created a new word: "cancellate" (i.e., I think cancel works just fine!) ;-) $\endgroup$ – Namaste Aug 14 '13 at 14:39
  • $\begingroup$ And that's only one out of many, @amWhy . I think some day I'm going to publish all my contributions to enrich and color up the english language $\endgroup$ – DonAntonio Aug 14 '13 at 14:41
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Assuming that you are dealing with fractions and learning to cancel terms, here is a hint:

Always break complicated multiplications into the smallest pieces possible, then line up the pieces vertically:

$${4b \over 3y} * {-4y \over 12b^2} = {-2*2*2*2*b*y \over 2*2*3*3*b*b*y}$$

It should be straightforward to consider which terms are appropriate to cancel.

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Break it up into number and variable pieces:

  • (4/3)*(-4/12)
  • (b/y)*(y/b^2)

Simplify each piece:

  • (4/3)*(-4/12) -> -16/36 -> -4/9
  • (b*y)/(y*b^2) -> (1/b) (the y's cancel, as well as one b, one remains on the bottom)

Group the two pieces:

  • -4/9 * 1/b -> -4/9b
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  • $\begingroup$ The last line's rightmost expression is lacking a $\,9\,$ in the denominator...and perhaps writing with LaTeX will make your answers/posts more appealling (do :edit: in any nicely written question answer to read how to type mathematical expressions) $\endgroup$ – DonAntonio Aug 14 '13 at 14:35

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