Question 893352
{{{(24.75/100)*q=297}}}, the percent used as a fraction for part per onehundred.
{{{q=297(100/24.75)}}} and you could try to reduce or simplify the fraction.
{{{q=297(100/24.75)(4/4)}}}
{{{297(400/99)}}}
{{{(33*9*400)/(3*3*11)}}}
{{{(33*9*400)/(9*11)}}}
{{{(33*400)/11}}}
{{{3*400}}}
{{{1200=q}}}


<b>Some confusion still reported.</b>
Turn the description around some:  {{{24&3/4}}} percent of the number q is 297.  What is q?

{{{((24&3/4)/100)*q=297}}}, translation into an equation, using meaning of PERCENT.  This is an equation.
We can begin simplifying the equation using the RECIPROCAL of the {{{(24&3/4)/(100)}}}.
A number multiplied by its reciprocal is 1; and 1 multiplied by a number is still the number being multiplied.


 {{{((24&3/4)/100)*q(100/(24&3/4))=297(100/(24&3/4))}}}, still an equality because multiplied BOTH sides by same number.


{{{((24&3/4)/100)(100/(24&3/4))q=297(100/(24&3/4))}}}, factors in a product can be moved to other positions.


{{{1*q=297(100/(24&3/4))}}}, fraction multiplied by its reciprocal equals 1.


{{{q=297(100/(24&3/4))}}}, same thing; multiplication by 1.
This is where you became stuck.
Simplify that complex fraction factor.
Note the denominator within the denominator, is 4.  AGAIN perform a multiplication by 1 on the
right side, in the form of {{{4/4}}}.  This will not change the meaning.  It will only allow
simplification of the fraction.


{{{q=297(100/(24+3/4))(4/4)}}}, which might still not be the best form for you, since you maybe are not
yet familiar with the distributive property; but I continue this way...


{{{q=297((100*4)/(4(24+3/4)))}}}


{{{q=297((400)/(4*24+4*3/4))}}}


{{{q=297(400/(96+3))}}}


{{{highlight_green(q=297(400/99))}}}
What comes next is just simplification; looking for factors common to both numerator and denominator
and eliminating those which form factors of 1.  Use you standard elementary divisibility rules.
You will find that 297 is a product of 9.  99 is also a product of 9.


ALMOST Complete Prime Factorization of the expression for q:
{{{(33*9*400)/(9*11)}}}
{{{(3*11*3*3*400)/(3*3*11)}}}
{{{(3*cross(11*3*3)*400)/(cross(3*3*11))}}}
{{{highlight_green(3*400=highlight(1200))}}}



(I did this WITHOUT a calculator except for factorizing the 297).