`person( 1 )` invited `INVITEES` friends to `his( 1 )` birthday party. Some people
had other plans and could not attend, but `\frac{`

of the people `N`}{`D`}`person( 1 )`
invited were able to attend.

How many people went to `person( 1 )`'s birthday party?

We need to figure out what `\dfrac{`

of `N`}{`D`}

is to find out
how many people attended the party.
`INVITEES`

We can find `\dfrac{`

of `N`}{`D`}

by multiplying
`INVITEES``\dfrac{`

and `N`}{`D`}

.
`INVITEES`

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`INVITEES`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`INVITEES`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`INVITEES`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`INVITEES`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * INVITEES`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

We can also visually see that `\dfrac{`

of
`N`}{`D`}

is `INVITEES`

:
`SOLUTION`

init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] });
rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 );
rectchart( [ INVITEES, 0 ], [ ORANGE, "#999" ], 1 );
rectchart( [ SOLUTION, INVITEES - SOLUTION ], [ GREEN, BACKGROUND ], 0 );
style({ color: BLUE }, function() {
label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" );
});
style({ color: ORANGE }, function() {
label([ 0, 1.5 ], INVITEES, "left" );
});
style({ color: GREEN }, function() {
label([ 0, 0.5 ], SOLUTION, "left" );
});

`SOLUTION` people attended `person( 1 )`'s party.

After saving up for a while, `person( 1 )` had $`AMOUNT`.00 in
`his( 1 )` piggy bank, and `he( 1 )` spent
`\frac{`

of that money on books at the bookstore.
`N`}{`D`}

How much money did `person( 1 )` spend?

We need to figure out what `\dfrac{`

of `N`}{`D`}`$`

is to find out
how much `AMOUNT`.00`person(1)` spent.

We can find `\dfrac{`

of `N`}{`D`}`$`

by multiplying
`AMOUNT`.00`\dfrac{`

and `N`}{`D`}

.
`AMOUNT`

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`AMOUNT`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`AMOUNT`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`AMOUNT`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`AMOUNT`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * AMOUNT`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

We can also visually see that `\dfrac{`

of
`N`}{`D`}

is `AMOUNT`

:
`SOLUTION`

init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] });
rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 );
rectchart( [ AMOUNT, 0 ], [ ORANGE, "#999" ], 1 );
rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, BACKGROUND ], 0 );
style({ color: BLUE }, function() {
label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" );
});
style({ color: ORANGE }, function() {
label([ 0, 1.5 ], AMOUNT, "left" );
});
style({ color: GREEN }, function() {
label([ 0, 0.5 ], SOLUTION, "left" );
});

`person( 1 )` spent $`SOLUTION`.00 on books.

Every day `person( 1 )` put the extra change from `his( 1 )` pockets into a glass jar. After
`randRange( 10, 30 )` weeks, `he( 1 )` had saved up $`AMOUNT`.00. `person( 1 )`
decided to use `\frac{`

of the money from the jar to buy canned food for a homeless shelter.
`N`}{`D`}

How much money did `person( 1 )` spend on canned food?

We need to figure out what `\dfrac{`

of `N`}{`D`}`$`

is to find out
how much `AMOUNT`.00`person(1)` spent.

We can find `\dfrac{`

of `N`}{`D`}`$`

by multiplying
`AMOUNT`.00`\dfrac{`

and `N`}{`D`}

.
`AMOUNT`

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`AMOUNT`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`AMOUNT`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`AMOUNT`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`AMOUNT`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * AMOUNT`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

We can also visually see that `\dfrac{`

of
`N`}{`D`}

is `AMOUNT`

:
`SOLUTION`

init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] });
rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 );
rectchart( [ AMOUNT, 0 ], [ ORANGE, "#999" ], 1 );
rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, BACKGROUND ], 0 );
style({ color: BLUE }, function() {
label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" );
});
style({ color: ORANGE }, function() {
label([ 0, 1.5 ], AMOUNT, "left" );
});
style({ color: GREEN }, function() {
label([ 0, 0.5 ], SOLUTION, "left" );
});

`person( 1 )` spent $`SOLUTION`.00 on canned food for the homeless shelter.

Before leaving on a road trip, `person( 1 )` filled up `his( 1 )` gas tank, which holds
`GALLONS` gallons of gas. After `0.5 * randRange( 3 / 0.5, 10 / 0.5 )` hours, `person( 1 )`
noticed that the gas tank was `\frac{`

full.
`N`}{`D`}

How many gallons of gas were left in the tank?

Since a fraction of the gas in `his( 1 )` tank was left, we just need to figure out what
`\dfrac{`

of `N`}{`D`}

gallons is to find out
how much gas was left in the tank.
`GALLONS`

We can find `\dfrac{`

of `N`}{`D`}

gallons by multiplying
`GALLONS``\dfrac{`

and `N`}{`D`}

.
`GALLONS`

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`GALLONS`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`GALLONS`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`GALLONS`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`GALLONS`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * GALLONS`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

We can also visually see that `\dfrac{`

of
`N`}{`D`}

is `GALLONS`

:
`SOLUTION`

init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] });
rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 );
rectchart( [ GALLONS, 0 ], [ ORANGE, "#999" ], 1 );
rectchart( [ SOLUTION, GALLONS - SOLUTION ], [ GREEN, BACKGROUND ], 0 );
style({ color: BLUE }, function() {
label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" );
});
style({ color: ORANGE }, function() {
label([ 0, 1.5 ], GALLONS, "left" );
});
style({ color: GREEN }, function() {
label([ 0, 0.5 ], SOLUTION, "left" );
});

`person( 1 )` had `SOLUTION` gallons of gas left in `his( 1 )` tank when `he( 1 )` checked.

`ATTENDEES` people had a picnic in the park.
`\frac{`

of the people at the picnic were adults.
`N`}{`D`}

How many adults were at the picnic?

We need to figure out what `\dfrac{`

of `N`}{`D`}

is to find out
how many people at the picnic were adults.
`ATTENDEES`

We can find `\dfrac{`

of `N`}{`D`}

by multiplying
`ATTENDEES``\dfrac{`

and `N`}{`D`}

.
`ATTENDEES`

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`ATTENDEES`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`ATTENDEES`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`ATTENDEES`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`ATTENDEES`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * ATTENDEES`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

We can also visually see that `\dfrac{`

of
`N`}{`D`}

is `ATTENDEES`

:
`SOLUTION`

init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] });
rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 );
rectchart( [ ATTENDEES, 0 ], [ ORANGE, "#999" ], 1 );
rectchart( [ SOLUTION, ATTENDEES - SOLUTION ], [ GREEN, BACKGROUND ], 0 );
style({ color: BLUE }, function() {
label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" );
});
style({ color: ORANGE }, function() {
label([ 0, 1.5 ], ATTENDEES, "left" );
});
style({ color: GREEN }, function() {
label([ 0, 0.5 ], SOLUTION, "left" );
});

`SOLUTION` people at the picnic were adults.

`person(1)` decided to bake cookies for the school bake sale. `He(1)` found a recipe
that called for `\frac{`

of a cup of chocolate chips.
`N`}{`D`}

To have enough cookies for the bake sale, `person(1)` needed to make `BATCHES` batches of cookies.

How many cups of chocolate chips did `person(1)` need in total?

We can multiply `\dfrac{`

cup by `N`}{`D`}

batches to find out how many cups of chocolate chips `BATCHES``person(1)` needed.

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{`BATCHES`} =
\color{`GREEN`}{\text{?}}

```
\color{
```

`BLUE`}{\dfrac{`N`}{`D`}} \times \color{`ORANGE`}{\dfrac{`BATCHES`}{1}} =
\dfrac{\color{`BLUE`}{`N`} \cdot \color{`ORANGE`}{`BATCHES`}}
{\color{`BLUE`}{`D`} \cdot \color{`ORANGE`}{1}} = \color{`GREEN`}{\text{?}}

```
\dfrac{\color{
```

`BLUE`}{`N`} \cdot \color{`ORANGE`}{`BATCHES`}}
{\color{`BLUE`}{`D`}} = \color{`GREEN`}{\dfrac{`N * BATCHES`}{`D`}} =
\color{`GREEN`}{`SOLUTION`}

`person(1)` needed `plural(SOLUTION, "cup")` of chocolate chips to make enough cookies for the bake sale.