Multiplying Fractions with variables....

[sportywarbz]

Hi here's the problem.

((v^2)-(w^2))/((2v^2)(w) * ((4v^2)(w^5))/((2v+2w))

Here's what I have so far...

((v+w)(v-w))/((2v^2)(w) * ((4v^2)(w^5))/((2v+2w))
((v-w)/(2)) * ((2w^4)/(v+w))

I always get confused on whether you can cross multiply these or not... I also am HORRIBLE with exponents... Help me pleaseeee Thanks.

 

[mmm4444bot]

((v^2)-(w^2))/((2v^2)(w) * ((4v^2)(w^5))/((2v+2w))

You typed 11 open parentheses and 10 close parentheses. Hence, we need to first confirm what you're trying to type.

Is the above supposed to mean this?

\(\displaystyle \frac{v^2 - w^2}{2v^2w} \cdot \frac{4v^2w^5}{2v + 2w}\)


If so, then here is how we text it:

(v^2 - w^2)/(2v^2w) * 4v^2w^5/(2v + 2w)

Please take note that three sets of grouping symbols are sufficient; most of your parentheses are unnecessary.

:idea: Inserting a lot of unneeded grouping symbols makes expressions more difficult to decipher.


If my guess above is not correct, then please edit your post.

 

[JeffM]

Hi here's the problem.

((v^2)-(w^2))/((2v^2)(w) * ((4v^2)(w^5))/((2v+2w)) As mmm said, this is not correctly expressed. Personally I am not afraid to use a few extra sets of grouping symbols, but I like to use square braces, [ and ], and even curly braces, { and }, in addition to parentheses. I also prefer using the "sup" button for exponents rather than the ^.So I would show this as
[(v[sup:3se1k7q9]2[/sup:3se1k7q9] - w[sup:3se1k7q9]2[/sup:3se1k7q9])/(2v[sup:3se1k7q9]2[/sup:3se1k7q9]w)] * [4v[sup:3se1k7q9]2[/sup:3se1k7q9]w[sup:3se1k7q9]5[/sup:3se1k7q9]/(2v + 2w)] which relies less on the conventions for order of operations and avoids the ^. Provided you avoid errors, you can group in the way that seems most helpful to you.
Here's what I have so far...

((v+w)(v-w))/((2v^2)(w) * ((4v^2)(w^5))/((2v+2w)) Good so far ignoring grouping symbols
((v-w)/(2)) * ((2w^4)/(v+w)) Good so far. What next?

I always get confused on whether you can cross multiply these or not... I also am HORRIBLE with exponents... Help me pleaseeee Thanks.

You simply have to MEMORIZE the RULE for multiplying fractions (which has NOTHING to do with cross-multiplying): (a/b) * (c/d) = (ac)/(bd). Once you have the rule memorized, multiplying fractions involves no conceptual issues, just the mechanical ones of calculating products and cancelling like terms in numerator and denominator.

You also have to MEMORIZE the laws of exponents. Once they are memorized, conceptual problems go away and only mechnical ones remain.

Editted before going to the corner

 

[sportywarbz]

Yes to the first response. That is the equation I was trying to write out...

To the second response....
If I continue on this is what I think it would be.
(v-w)(v+w)=4w^4
(v^2)-(w^2)=4w^4
v^2=(4w^4)-(w^2)
v^2=4w^2

The directions for this problem were to carry out the indicated operation. Thank you for your help!

 

[mmm4444bot]

Yes to the first response. That is the equation I was trying to write

But it's not an equation. :?

An equation always contains an equals sign. Always.

There is no equals sign in your exercise, so there is no equation.

I can't figure out what you are thinking by posting these four equations:

(v-w)(v+w)=4w^4
(v^2)-(w^2)=4w^4
v^2=(4w^4)-(w^2)
v^2=4w^2


After factoring and multiplying the given expression, the next step is to cancel all of the common factors in the numerators and denominators.

\(\displaystyle \frac{(v - w)(v + w)(2)(2)(v^2)(w)(w^4)}{(2)(v^2)(w)(2)(v + w)}\)

Are you able to recognize the identical factors on top and bottom?

PS: I factored 4 as (2)(2) and I factored w^5 as (w)(w^4) to help you "see" the common factors.

 

[mmm4444bot]

(a/b) * ((c/d) = (ab)/(cd)

Whoops. I'm sure that Jeff meant to type:

a/b * c/d = (ac)/(bd)

In other words, the product of two fractions is [numerator times numerator] written over [denominator times denominator].

 

[sportywarbz]

So would it be (v-w)(w^4) ?

 

[mmm4444bot]

would it be (v-w)(w^4) ?

This is a correct answer (written in factored form).

I think that you should now practice by doing about 15-20 additional exercises similar to this one.

 

[JeffM]

Re:

(a/b) * ((c/d) = (ab)/(cd)

Whoops. I'm sure that Jeff meant to type:

a/b * c/d = (ac)/(bd) Off to the corner after I edit my typo

In other words, the product of two fractions is [numerator times numerator] written over [denominator times denominator].