SOLUTION: Hello, Not sure how to find the solution to this: The number 297 is 24 3/4% of which number? The answer is 1,200. I just have no idea how it was solved! Can someone please

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Question 893352: Hello,
Not sure how to find the solution to this: The number 297 is 24 3/4% of which number? The answer is 1,200. I just have no idea how it was solved! Can someone please tell me how to solve a problem like this step by step?
Thanks
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
%2824.75%2F100%29%2Aq=297, the percent used as a fraction for part per onehundred.
q=297%28100%2F24.75%29 and you could try to reduce or simplify the fraction.
q=297%28100%2F24.75%29%284%2F4%29
297%28400%2F99%29
%2833%2A9%2A400%29%2F%283%2A3%2A11%29
%2833%2A9%2A400%29%2F%289%2A11%29
%2833%2A400%29%2F11
3%2A400
1200=q

Some confusion still reported.
Turn the description around some: 24%263%2F4 percent of the number q is 297. What is q?
%28%2824%263%2F4%29%2F100%29%2Aq=297, translation into an equation, using meaning of PERCENT. This is an equation.
We can begin simplifying the equation using the RECIPROCAL of the %2824%263%2F4%29%2F%28100%29.
A number multiplied by its reciprocal is 1; and 1 multiplied by a number is still the number being multiplied.

%28%2824%263%2F4%29%2F100%29%2Aq%28100%2F%2824%263%2F4%29%29=297%28100%2F%2824%263%2F4%29%29, still an equality because multiplied BOTH sides by same number.

%28%2824%263%2F4%29%2F100%29%28100%2F%2824%263%2F4%29%29q=297%28100%2F%2824%263%2F4%29%29, factors in a product can be moved to other positions.

1%2Aq=297%28100%2F%2824%263%2F4%29%29, fraction multiplied by its reciprocal equals 1.

q=297%28100%2F%2824%263%2F4%29%29, 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%2F4. This will not change the meaning. It will only allow
simplification of the fraction.

q=297%28100%2F%2824%2B3%2F4%29%29%284%2F4%29, 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%28%28100%2A4%29%2F%284%2824%2B3%2F4%29%29%29

q=297%28%28400%29%2F%284%2A24%2B4%2A3%2F4%29%29

q=297%28400%2F%2896%2B3%29%29

highlight_green%28q=297%28400%2F99%29%29
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:
%2833%2A9%2A400%29%2F%289%2A11%29
%283%2A11%2A3%2A3%2A400%29%2F%283%2A3%2A11%29
%283%2Across%2811%2A3%2A3%29%2A400%29%2F%28cross%283%2A3%2A11%29%29
highlight_green%283%2A400=highlight%281200%29%29


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