randRange(1, 10) MULTIPLE*100 randRange(2,100) $._("part") $._("whole") $._("percent")

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`.

randFromArray([2, 4, 5, 10, 20, 25]) 100 / FACTOR randRange(1, WHOLE - 1) * FACTOR $._("part") $._("whole") $._("percent")

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`.

randRange(1, 10) MULTIPLE * 100 randRange(1,99) $._("part") $._("whole") $._("percent")

`PART_PERCENT * MULTIPLE` is what percent of `WHOLE`?

PART_PERCENT `\%`

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`.

randFromArray([2, 4, 5, 10, 20, 25]) 100 / FACTOR randRange(1, WHOLE - 1) * FACTOR $._("part") $._("whole") $._("percent")

`PART_PERCENT / FACTOR` is what percent of `WHOLE`?

PART_PERCENT `\%`

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`.