Why do we multiply by 100 for finding percentage?

Question

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 ?.

Answer 1

In response to suggested edits...

Read "50 boys in a school and the total number of students is 200"

as 50 boys out of 200 students

which is represented by the fraction $\dfrac{50}{200}$

Converting to percents means converting to a fraction with a denominator of 100.

Which is to say

$$\dfrac{50}{200} = \dfrac{x}{100}$$

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

Answer 2

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.

Answer 3

I saw Steven 's answer and it is describing the case correctly.

We can prove it in general also:-

Let $\frac{a}{b}$ be fraction then to find percentage which is out of hundred we have to find the equivalent numerator of the percentage. n would be our numerator in this case:-

$$\frac{a}{b} = \frac{n}{100}$$

Then,

$$\frac{a}{b} • 100 = n $$

And we got why would we multiply by hundred to get percentage.