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Question about simplifying fractions

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Question about simplifying fractions  [#permalink]

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New post 08 Mar 2019, 23:16
I recently started studying for the GMAT and my quant skills are lacking. I am struggling to understand why I cannot simply this answer further. This was the final solution to a problem:

\(\frac{zp+q}{x(zp+q)+yp}\)

Why does the zp+q in the numerator and denominator not cancel out? I see it as \(\frac{1}{x+yp}\)

I appreciate any feedback.
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New post 08 Mar 2019, 23:31
If yp is multiply with x(zp+q) we can cancel. but in here x(zp+q) +yp is addition form .
that's why we can't cancel (zp+q)
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Re: Question about simplifying fractions  [#permalink]

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New post 09 Mar 2019, 10:50
Not to sound rude, I would recommend that you revisit your math concepts. If you are stuck at such a basic concept, then chances are that you would need work on average to tough areas.

No to answer your query, please remember that ONLY common items cancel out in numerator and denominator.
Let's consider zp+q = A, now the expression becomes \(\frac{A}{xA+yp}\). Do you notice that the term "yp" do not have the so-called common recent A. Hence, A is not actually the common element in the numerator and denominator. Therefore, we cannot cancel out A, i.e zp+q. I hope this explanation helps.

All the best.

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Re: Question about simplifying fractions  [#permalink]

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New post 12 Mar 2019, 08:39
Hi Zixzix

your question is so basic and fundamental. You have a revise the basic rules of arithmetic.
This thread would help you learn every thing needed for GMAT. Start with the arithmatics, number properties and fractions.
https://gmatclub.com/forum/ultimate-gmat-quantitative-megathread-244512.html
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Re: Question about simplifying fractions  [#permalink]

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New post 12 Mar 2019, 09:10
Hi ,

this is a fundamental question.

I would try to explain

we can only cancel in scenario where we have experssion in the form or multiplication

example

x*(x+y)*(y+z)

here these all are in multiply and each one in ()

is considered as a single unit

but if you put + or - then

we have ,

(x+x+y) *(y+z) then these two in () become two units

now x+x+y will be treated as a single unit for division operation

hope it helps

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Re: Question about simplifying fractions  [#permalink]

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New post 14 Mar 2019, 07:22
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A lot of people have questions like this, and when people start reviewing math again for the GMAT, it's in these kinds of situations where mistakes are most common. When you are canceling in a fraction, anything you cancel must be a factor of the entire numerator and of the entire denominator. So if you want to cancel something, you must be able to rewrite the numerator and denominator as products, where the thing you're canceling is part of each product. So in the basic case, with numbers:

8/36

We can rewrite the numerator and denominator as products, both containing the number '4':

(4)(2) / (4)(9)

and now we cancel the '4' to get 2/9.

The algebraic case is similar. I'll give one example where we can factor and cancel (using quadratic factoring) :

\(\frac{x^2 - 7x + 12}{x^2 - 5x + 6} = \frac{(x-3)(x-4)}{(x-3)(x-2)} = \frac{x-4}{x-2}\)

Notice we can cancel the "x-3" because it is part of a product in both the numerator and denominator. Or in this case you can cancel:

\(\frac{ab + ac}{ab - ac} = \frac{(a)(b+c)}{(a)(b-c)} = \frac{b+c}{b-c}\)

because "a" is a factor of both the numerator and denominator. But in cases like this, say:

\(\frac{xz + y}{xz - y}\)

no cancellation is possible, because there is no identical factor we can create in both the numerator and denominator (in fact there's no factorization we can even do here). So even though the numerator and denominator appear quite similar here, that is no guarantee that any cancellation will be possible - you need to see what factoring you can do.

Factoring is one of the most useful techniques in all of algebra, so if it's something you're not completely comfortable with yet, I'd suggest practicing it a lot, because it's a crucial skill for GMAT math.
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Re: Question about simplifying fractions  [#permalink]

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New post 18 Mar 2019, 04:36
IanStewart wrote:
A lot of people have questions like this, and when people start reviewing math again for the GMAT, it's in these kinds of situations where mistakes are most common. When you are canceling in a fraction, anything you cancel must be a factor of the entire numerator and of the entire denominator. So if you want to cancel something, you must be able to rewrite the numerator and denominator as products, where the thing you're canceling is part of each product. So in the basic case, with numbers:

8/36

We can rewrite the numerator and denominator as products, both containing the number '4':

(4)(2) / (4)(9)

and now we cancel the '4' to get 2/9.

The algebraic case is similar. I'll give one example where we can factor and cancel (using quadratic factoring) :

Such a great and helpful answer.

\(\frac{x^2 - 7x + 12}{x^2 - 5x + 6} = \frac{(x-3)(x-4)}{(x-3)(x-2)} = \frac{x-4}{x-2}\)

Notice we can cancel the "x-3" because it is part of a product in both the numerator and denominator. Or in this case you can cancel:

\(\frac{ab + ac}{ab - ac} = \frac{(a)(b+c)}{(a)(b-c)} = \frac{b+c}{b-c}\)

because "a" is a factor of both the numerator and denominator. But in cases like this, say:

\(\frac{xz + y}{xz - y}\)

no cancellation is possible, because there is no identical factor we can create in both the numerator and denominator (in fact there's no factorization we can even do here). So even though the numerator and denominator appear quite similar here, that is no guarantee that any cancellation will be possible - you need to see what factoring you can do.

Factoring is one of the most useful techniques in all of algebra, so if it's something you're not completely comfortable with yet, I'd suggest practicing it a lot, because it's a crucial skill for GMAT math.


Such a great and helpful answer.
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Re: Question about simplifying fractions   [#permalink] 18 Mar 2019, 04:36
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