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I am studying for GRE and One of the practice questions is a division. After converting my Mixed numeral I get $\frac{90}{72}$ now I just have to simplify.

What I understood is that you divide by Least common multiplier so I

$1.)$ Divide $\frac{90}{72}$ by $2$: And I got $\frac{45}{36}$

$2.)$ Divide $\frac{45}{36}$ by $3$: And I got $\frac{9}{12}$

$3.)$ and so on until I got to 3/4 which is the wrong answer

If in step $1$, I would have divide by $3$

$1.)$ Divide $\frac{90}{72}$ by $3$ and I got $\frac{10}{8}$ $2.)$ Divide $\frac{10}{8}$ by $2$ and I got \frac{5}{4} which is the right answer

What is the rule to simplify fractions?

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    $\begingroup$ You divided 45 by 3 and got 9? $\endgroup$ – user296602 Apr 27 '16 at 4:46
  • $\begingroup$ 45 divided by 3 is 15 not 9, that's why this question is even here :) $\endgroup$ – KKZiomek Apr 27 '16 at 4:49
  • $\begingroup$ Not divided by LCM. But by HCF. $\endgroup$ – N.S.JOHN Apr 27 '16 at 16:37
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You have $\frac{90}{72}$.Now,$\gcd(90,72)=18$.

So,dividing numerator and denominator by $18$ we get $\frac{5}{4}.$

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  • $\begingroup$ OP's method is to divide by the LCD (which he or she refers to as Least common multiplier for some reason), not by the GCD. So you essentially haven't answered the question. $\endgroup$ – barak manos Apr 27 '16 at 5:02
  • $\begingroup$ @barakmanos His method is by the least divisor which is essentially the common prime factors of the two terms...multiplying the common LCDs will always give you the GCD.... $\endgroup$ – tatan Apr 27 '16 at 5:21
  • $\begingroup$ Of course, but that's not the problem that he or she is facing. $\endgroup$ – barak manos Apr 27 '16 at 5:43

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