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  1. For example, if there are 50 boys in a school and the total number of students is $200$ then, for finding percentage of boys why do we do like this, $\left(\, 50/200\, \right)100\ \% = 25\ \%$ ?.
  2. Why does the fraction '$50/200$' represent ?. I know 'percentage' means out of $100$ but $50/200$ is not representing $50$ out of hundred ?.
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  • $\begingroup$ $25$% or $25$ for each $100$. For example if we have $50$ seniors and $200$ high school students, then we have $25$ seniors for each $100$ high school students, and that is $25$% seniors. $\endgroup$ – Ahmed S. Attaalla Sep 4 '16 at 3:24
  • $\begingroup$ Multiplying by $100\%$ equals to multiplying by $ 100 × 1/100$, that is $1$, and that is doing nothing. Instead, try to "factor out" a $1/100$ term just as you can swap "1 mile" and "1.609 km" in any physics equation. So: $50/200=25/100 = 25 × 1/100 = 25\%$. $\endgroup$ – JnxF Sep 4 '16 at 3:31
  • $\begingroup$ Per cent means for every 100. So we multiply by 100 to see how much we get for one group of 100. $\endgroup$ – Tac-Tics Sep 4 '16 at 3:59
  • $\begingroup$ Because "percent" means $\frac{1}{100}$. $\endgroup$ – barak manos Sep 4 '16 at 4:52
  • $\begingroup$ 50/200 is not representing 50 out of 100 because 50/200 is not 50%. It is 25 % and it absolutely does indeed represent 25 out of 100. $\endgroup$ – fleablood Sep 4 '16 at 5:38
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What you are solving is $$\dfrac{50}{200} = \dfrac{x}{100}$$

Which becomes $$x= 100\times \dfrac{50}{200}$$

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When you take a portion and divide it by the whole, you create a value that must always be less than or equal to 1.

Let $w$ represent the whole.

Let $p$ represent the portion such that $p \underline{<} w$.

Therefore, $\frac{p}{w} \underline{<} 1$.

When $\frac{p}{w}$ is multiplied by 100, you're just scaling the decimal to I guess what you might consider a more user-friendly, comprehensive value. The ratio is still the same, of course.

The word percent actually comes from the Latin per centum, which means per one hundred. So instead of visualizing data in terms of values greater than $100$, such as in your case, ratios can be scaled to a denominator of $100$, simplifying all data to a more comprehensible manner.

$50$%, $75$%, and $90$% are easier to compare than $\frac{2234}{4468}$, $\frac{2935929}{3914572}$, and $\frac{37901171181738.6}{42112412424154}$. By multipling these fractions by $100$, they are set standardized and thus much easier to compare and contrast with other standardized values.

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