Percent Of This vs. Percent Of That

$\color{#3D99F6}{x\%} \times y = \dfrac{\color{#3D99F6}{x}y}{\color{#3D99F6}{100}} = \dfrac{x\color{#D61F06}{y}}{\color{#D61F06}{100}} = \boxed{x} \times \color{#D61F06}{y\%}$

Simple example $x=100 \ , \ y=1$ :

$100\% \ of \ 1 \ = 1 = \ 1\% \ of \ 100$

$\frac{x}{100} \times y=\frac{xy}{100}$ .
Let the reqd. Answer be $a$ A.T.Q $\frac{y}{100}\times a=\frac{xy}{100}\\ a=\frac{xy}{100} \times \frac{100}{y}=x$

Ans. $x$

(X/100) Y=(XY/100)=(Y/100) X

5% of 100 is 5 and 100% of 5 is 5

x% y = y% a => x y% = a y% => x=a

$x \text{\% of } y = \frac{x}{100} \cdot y$

$\frac{xy}{100}$

$\frac{y}{100} \cdot x$

$y \text{\% of } x$

$\large \boxed{x \text{\% of } y = y \text{\% of } x}$

x% of y =xy/100=yx/100= y% of x

x% expressed as a fraction is x/100. Therefore x% of y is x times y all divided by 100. In similar fashion, y% = y/100. Ergo, the factor to make equivalency is multiplying y/100 by x.

X% of y= (X/100)(y)=(y/100)(X)=Y% of X

$x\% of y = \frac{xy}{100} \;and\; y\% \;of\; x = \frac{xy}{100}$

{ $x\%$ of $y$ = $y\%$ of, say something $a$ } so covert all percentages into fractions then $\frac{x}{100}$ * $y$ = $y$ * $a$ Now we will convert all fractions into"unit fraction" so $\frac{1}{100}$ * $x$ * $y$ = $\frac{1}{100}$ * $y$ * $a$ now we will do $\frac{y}{100}$ in both equations so equation will be looking like this $\frac{y}{100}$ * $x$ = $\frac{y}{100}$ * $a$ so both balance scales are equal and in both balance scales there is one thing equal that is $\frac{y}{100}$ so $x$ must be $=$ $a$ so finally equation will be looking like this $x\%$ of $y$ = $y\%$ * $x$ .😊