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I had some exercises and I came upon something that got me confused.

$$\frac{6*10^{w}}{7}$$ Turns out to be $$\frac{6}{7}*\frac{10^{w}}{7}$$ $$\frac{6*10^{w}}{49}$$ On the other hand, for example:$$\frac{12*10^{w}}{14}$$ does NOT equal: $$\frac{2*6}{2*7}*\frac{10^{w}}{7}$$ $$\frac{6}{7}*\frac{10^{w}}{7}$$ $$\frac{6*10^{w}}{49}$$ Why is that? I'm a bit confused so if I could get cleared up on some rules I've missed, I would appreciate it. Thanks.

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closed as off-topic by TheGeekGreek, Strants, Brian Borchers, Andrew Li, José Carlos Santos Apr 8 '18 at 21:40

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    $\begingroup$ I downvoted purely for the abuse in your last comment. To answer your question: Your first statement is wrong. You cannot rewrite $(6 \cdot 10^w) / 7$ as $6/7 \cdot 10^w/7$. $\endgroup$ – user296602 Jan 31 '18 at 3:04
  • $\begingroup$ Your operations are not correct. You can say $\frac {6\cdot 10}{7} =\frac {6}{7} \cdot 10 = 6\cdot \frac {10}{7}.$ But you should never have a situation where $\frac {6\cdot 10}{7} = \frac {6\cdot 10}{49}$ $\endgroup$ – Doug M Jan 31 '18 at 3:04
  • $\begingroup$ You get downvotes because it simply does not show research efforts as a general policy of the forum. However, I myself am ok with all questions. $\endgroup$ – Mehrdad Zandigohar Jan 31 '18 at 3:05
  • $\begingroup$ You're misunderstanding something. There is no way that $\frac{6 \cdot 10^w}{7} = \frac{6 \cdot 10^w}{49}$ That would mean $7 = 49$. $\endgroup$ – saulspatz Jan 31 '18 at 3:06
  • $\begingroup$ Saul, I simply checked on mathway and that was their result. See here: gyazo.com/65ae64f00f15c749421ee13038a3d5e6 $\endgroup$ – oijioj Jan 31 '18 at 3:10
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$\frac{6*10^{w}}{7}$ is not equal to $\frac{6}{7}*\frac{10^{w}}{7}$, it is equal to $\frac{6}{1}*\frac{10^{w}}{7}$ or $\frac{6}{7}*\frac{10^{w}}{1}$ though.

It is not like a summation.

Generally, we have:

$\frac{a+b}{c}=\frac ac + \frac bc$

and

$\frac{ab}{c}=\frac a1 * \frac bc=\frac ac * \frac b1$

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  • $\begingroup$ Hey, thanks a lot for the effort. I did use mathway to check and it gave me 49 in the denominator tho.. any idea? Pic: gyazo.com/65ae64f00f15c749421ee13038a3d5e6 $\endgroup$ – oijioj Jan 31 '18 at 3:07
  • $\begingroup$ @oijioj You are welcome! If you use divide command, it again divides for the second time. You can enter divide command again and see it gives you another division in addition to the divisions earlier. $\endgroup$ – Mehrdad Zandigohar Jan 31 '18 at 3:10
  • $\begingroup$ Are you certain that that they're not dividing $\frac{6 \cdot 10^w}{7}$ by $7?$ That would give $\frac{6 \cdot 10^w}{49}$ I tried to do to that link, but I couldn't get it to do anything when I clicked on the button, so I'm not saying that's what it means. I just saw the word "divide," and thought that might be it. That would explain the steps. $\endgroup$ – saulspatz Jan 31 '18 at 3:12
  • $\begingroup$ Apparently they did, which I don't really understand why they would do so. Thanks you two. $\endgroup$ – oijioj Jan 31 '18 at 3:13
  • $\begingroup$ @saulspatz The link provided was a screenshot of the environment and not the environment itself. Second, as you also said it did divide $\frac{6 \cdot 10^w}{7}$ by another 7 again. I'm saying if you enter the divide command in the environment you will see it divides the answer again by 7. It works like a calculator. $\endgroup$ – Mehrdad Zandigohar Jan 31 '18 at 3:18
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Note that $$\frac{6*10^{w}}{7} \ne \frac{6}{7}*\frac{10^{w}}{7}$$

Because you have only one $7$ on the left side but two $7$ on the right side.

cross out the extra $7$ and you will not be confused any more.

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