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Sorry if this is very basic! But I can't seem to do something like

$\frac{10000}{0.08}$, without a calculator. How would one go about solving this without a calculator?

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  • $\begingroup$ Multiply both the numerator and denominator by $100$ to get $1000000/8$, then divide. $\endgroup$ – N. F. Taussig Apr 21 at 10:11
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    $\begingroup$ Observe that $0.08 = \frac {8} {100}.$ So we have $$\frac {10000} {0.08} = \frac {10000 \times 100} {8}.$$ Can you proceed now? $\endgroup$ – Dbchatto67 Apr 21 at 10:12
  • $\begingroup$ So, now how many 8's go int 1 million? I don't know how to even do that without a calculator $\endgroup$ – natalie99 Apr 21 at 10:18
  • $\begingroup$ Firstly: Dividing by $8$ is three times dividing by $2$. Consequently, $1000:2=500$, $1000:4=(1000:2):2)=500:2=250$ and $$1000:8=((1000:2):2):2=(500:2):2=250:2=125.$$ Secondly, learn these quotients by heart: every humanistically educated human being should know how much a half, a quarter and an eighth of $1000$ is. As well as that a day has $86400$ seconds ... $\endgroup$ – Michael Hoppe Apr 21 at 11:32
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Just make some transformations:

$0.08=\frac8{100}$. Therefore the term becomes $\frac{10000}{\frac8{100}}$

Then:

Dividing a term by a fraction is the same as multiplying the term by the reciprocal of the fraction.

That means $10000\cdot \frac{100}8=\frac{10000}{8}\cdot 100=1250\cdot 100=125,000$.

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  • $\begingroup$ Thank you, but how comes it's 1000 and not 10000, now? $\endgroup$ – natalie99 Apr 21 at 10:22
  • $\begingroup$ I´ve omitted the one 0. I´ve corrected it. $\endgroup$ – callculus Apr 21 at 10:24
  • $\begingroup$ Thanks, I really like your explanation, it makes it so easy! $\endgroup$ – natalie99 Apr 21 at 10:26
  • $\begingroup$ @natalie99 Nice to hear. You are welcome. $\endgroup$ – callculus Apr 21 at 10:26
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We know that $0.08=\frac{8}{100}$, so $\frac{1}{0.08} = \frac{100}{8}$ we can do this as one divided by a fraction can be just flipped to remove the divided "bit".

So $$\frac{10000}{0.08}=\frac{100 * 10000}{8}$$

Then $8$ goes into $10000$, $1250$ times so $\frac{10000}{0.08}=1250*100= 125000$

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You can write $$\frac{10000\cdot 100}{8}$$

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You could turn 0.08 to a fraction, take recipricol, then multiply that by 10000 which is a lot easier imo. If you don't want to do the weird decimal movement thing.

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$$\frac{10000}{\frac8{100}}=\frac{1000000}{8}=\frac{(50*2)(50*2)(50*2)}{2*2*2}=??$$

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