What is PART_PERCENT\% of WHOLE?
PART_PERCENT * MULTIPLE
Having PART_PERCENT\% of something means that you get
PART_PERCENT out of every 100.
We can set up a proportion to find out what number is
PART_PERCENT\% of WHOLE:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{\text{PART}}}{\green{\text{WHOLE_TEXT}}}
Which things do we know, and what are we trying to find?
We know the \blue{\text{PERCENT}} is PART_PERCENT.
Is WHOLE the \pink{\text{PART}}
or the \green{\text{WHOLE_TEXT}}?
The WHOLE is the \green{\text{WHOLE_TEXT}}.
We are trying to find the \pink{\text{PART}}
that makes up PART_PERCENT\% of it:
\qquad \dfrac{\blue{PART_PERCENT}}{100} = \dfrac{\pink{\text{PART}}}{\green{WHOLE}}
If we multiply the denominator of the fraction on the left by MULTIPLE,
it will be the same denominator of the fraction on the right.
To keep things equal, let's also multiply the numerator on the left by MULTIPLE:
\qquad \dfrac{\blue{PART_PERCENT} \times MULTIPLE}{100 \times MULTIPLE} =
\dfrac{\pink{\text{PART}}}{\green{WHOLE}}
\qquad \dfrac{\blue{PART_PERCENT * MULTIPLE}}{WHOLE} =
\dfrac{\pink{\text{PART}}}{\green{WHOLE}}
\qquad \blue{PART_PERCENT * MULTIPLE} = \pink{\text{PART}}
So PART_PERCENT * MULTIPLE is PART_PERCENT\% of WHOLE.
What is PART_PERCENT\% of WHOLE?
PART_PERCENT / FACTOR
Having PART_PERCENT\% of something means that you get
PART_PERCENT out of every 100.
We can set up a proportion to find out what number is
PART_PERCENT\% of WHOLE:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{\text{PART}}}{\green{\text{WHOLE_TEXT}}}
Which things do we know, and what are we trying to find?
We know the \blue{\text{PERCENT}} is PART_PERCENT.
Is WHOLE the \pink{\text{PART}}
or the \green{\text{WHOLE_TEXT}}
?
The WHOLE is the \green{\text{WHOLE_TEXT}}.
We are trying to find the \pink{\text{PART}}
that makes up PART_PERCENT\% of it:
\qquad \dfrac{\blue{PART_PERCENT}}{100} =
\dfrac{\pink{\text{PART}}}{\green{WHOLE}}
If we divide the denominator of the fraction on the left by FACTOR, it will be the same denominator of the fraction on the right. To keep things equal, let's also divide the numerator on the left by FACTOR:
\qquad \dfrac{\color{BLUE}{PART_PERCENT} \div FACTOR}{100 \div FACTOR} = \dfrac{\color{PINK}{\text{PART}}}{\color{GREEN}{WHOLE}}
\qquad \dfrac{\color{BLUE}{PART_PERCENT / FACTOR}}{WHOLE} = \dfrac{\color{PINK}{\text{PART}}}{\color{GREEN}{WHOLE}}
\qquad \color{BLUE}{PART_PERCENT / FACTOR} = \color{PINK}{\text{PART}}
So PART_PERCENT / FACTOR is PART_PERCENT\% of WHOLE.
PART_PERCENT * MULTIPLE is what percent of WHOLE?
\%
Having a percent of something means that you get that percent out of every 100.
We can set up a proportion to find out what percent of WHOLE
we need to take to get PART_PERCENT * MULTIPLE:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{\text{PART}}}{\green{\text{WHOLE_TEXT}}}
Which things do we know, and what are we trying to find?
We are trying to find the \blue{\text{PERCENT}}.
Is WHOLE the \pink{\text{PART}}
or the \green{\text{WHOLE_TEXT}}?
The WHOLE is the \green{\text{WHOLE_TEXT}}.
This means the \pink{\text{PART}} is PART_PERCENT * MULTIPLE:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT * MULTIPLE}}{\green{WHOLE}}
If we divide the denominator of the fraction on the right by MULTIPLE,
it will be the same denominator of the fraction on the left.
To keep things equal, let's also divide the numerator on the right by MULTIPLE:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT * MULTIPLE \div MULTIPLE}}{\green{WHOLE \div MULTIPLE}}
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT}}{\green{WHOLE / MULTIPLE}}
\qquad \blue{\text{PERCENT}} = \pink{PART_PERCENT}
So PART_PERCENT * MULTIPLE is PART_PERCENT\% of WHOLE.
PART_PERCENT / FACTOR is what percent of WHOLE?
\%
Having a percent of something means that you get that percent out of every 100.
We can set up a proportion to find out what percent of WHOLE
we need to take to get PART_PERCENT / FACTOR:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{\text{PART}}}{\green{\text{WHOLE_TEXT}}}
Which things do we know, and what are we trying to find?
We are trying to find the \blue{\text{PERCENT}}.
Is WHOLE the \pink{\text{PART}}
or the \green{\text{WHOLE_TEXT}}?
The WHOLE is the \green{\text{WHOLE_TEXT}}.
This means the \pink{\text{PART}} is PART_PERCENT / FACTOR:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT / FACTOR}}{\green{WHOLE}}
If we multiply the denominator of the fraction on the right by FACTOR,
it will be the same denominator of the fraction on the left.
To keep things equal, let's also multiply the numerator on the right by FACTOR:
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT / FACTOR \times FACTOR}}{\green{WHOLE \times FACTOR}}
\qquad \dfrac{\blue{\text{PERCENT}}}{100} =
\dfrac{\pink{PART_PERCENT}}{\green{WHOLE * FACTOR}}
\qquad \blue{\text{PERCENT}} = \pink{PART_PERCENT}
So PART_PERCENT / FACTOR is PART_PERCENT\% of WHOLE.