randRange( 1, 5 ) randRange( 1, 5 ) randRange( 1, 5 ) A + B + LEFT

person( 1 ) ate plural( A, "slice" ) of pizza( 1 ), and person( 2 ) ate plural( B, "slice" ).

If there were initially TOTAL slices, what fraction of the pizza( 1 ) was eaten?

(A + B) / TOTAL

\text{fraction of pizza( 1 ) eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}

They ate \color{#6495ED}{A + B} out of TOTAL slices.

init({ range: [ [-2, 2], [-2, 2] ], scale: 25 }); var eaten = A + B; piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );

They ate \dfrac{A + B}{TOTAL} of the pizza( 1 ).

person( 1 ) ate plural( A, "slice" ) of pizza( 1 ), and person( 2 ) ate plural( B, "slice" ).

If there were plural(LEFT, "slice") remaining, what fraction of the pizza( 1 ) was eaten?

(A + B) / TOTAL

\text{fraction of pizza( 1 ) eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}

Since they ate A + B slices of pizza( 1 ) with plural( LEFT, "slice" ) remaining, they must have begun with TOTAL slices.

They ate \color{#6495ED}{A + B} out of TOTAL slices.

init({ range: [ [-2, 2], [-2, 2] ], scale: 25 }); var eaten = A + B; piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );

They ate \dfrac{A + B}{TOTAL} of the pizza( 1 ).

person( 1 ) ate plural( A, "slice" ) of pizza( 1 ), and person( 2 ) ate plural( B, "slice" ).

If person( 1 ) ate \dfrac{A}{TOTAL} of the pizza( 1 ), what fraction of the pizza( 1 ) was eaten?

(A + B) / TOTAL

If plural( A, "slice") representA > 1 ? "" : "s" \dfrac{A}{TOTAL} of the pizza( 1 ), there must have been a total of TOTAL slices.

\text{fraction of pizza( 1 ) eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}

They ate \color{#6495ED}{A + B} out of TOTAL slices.

init({ range: [ [-2, 2], [-2, 2] ], scale: 25 }); var eaten = A + B; piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );

They ate \dfrac{A + B}{TOTAL} of the pizza( 1 ).

person( 1 ) ate plural( A, "slice" ) of pizza( 1 ), and person( 2 ) ate plural( B, "slice" ).

If there were initially TOTAL slices, what fraction of the pizza( 1 ) is remaining?

LEFT / TOTAL

\text{fraction of pizza( 1 ) remaining} = \dfrac{\text{number of slices remaining}}{\text{number slices total}}

Together they ate A + B slices, which leaves LEFT out of TOTAL slices remaining.

init({ range: [ [-2, 2], [-2, 2] ], scale: 25 }); var remaining = TOTAL - A - B; piechart( [ remaining, TOTAL - remaining ], [ "#FFA500", "#6495ED" ], 2 );

There is \dfrac{LEFT}{TOTAL} of the pizza( 1 ) remaining.

person( 1 ) ate plural( A, "slice" ) of pizza( 1 ), and person( 2 ) ate plural( B, "slice" ).

If person( 1 ) ate \dfrac{A}{TOTAL} of the pizza( 1 ), what fraction of the pizza( 1 ) is remaining?

LEFT / TOTAL

If plural( A, "slice" ) representA > 1 ? "" : "s" \dfrac{A}{TOTAL} of the pizza( 1 ), there must have been a total of TOTAL slices.

\text{fraction of pizza( 1 ) remaining} = \dfrac{\text{number of slices remaining}}{\text{number slices total}}

Together they ate A + B slices, which leaves LEFT out of TOTAL slices remaining.

init({ range: [ [-2, 2], [-2, 2] ], scale: 25 }); var remaining = TOTAL - A - B; piechart( [ remaining, TOTAL - remaining ], [ "#FFA500", "#6495ED" ], 2 );

There is \dfrac{LEFT}{TOTAL} of the pizza( 1 ) remaining.

randRange( 10, 20 ) randFromArray([ 6, 8 ]) randRange( 1, D - 1 ) N / D * INVITEES

person( 1 ) invited INVITEES friends to his( 1 ) birthday party. Some people had other plans and could not attend, but N/D of the people person( 1 ) invited were able to attend.

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

SOLUTION

We can multiply \dfrac{N}{D} by INVITEES to find out how many people attended the party.

\color{#e00}{\dfrac{N}{D}} \cdot INVITEES

\color{#e00}{\dfrac{N}{D}} \cdot INVITEES

init({ range: [ [ 0, 1 ], [ 0, INVITEES + 1 ] ],scale: [ 250, 25 ] }); for ( var y = 1; y <= INVITEES; y++ ) { rectchart( [ N, D - N ], ["#e00", "#999" ], y ); }

\color{#e00}{\dfrac{N * INVITEES}{D}} = SOLUTION

SOLUTION people attended person( 1 )’s party.
randRange( 20, 40 ) randFromArray([ 3, 4 ]) randRange( 1, D - 1 ) roundTo( 2, N / D * AMOUNT )

After saving up for a while, person( 1 ) had $AMOUNT in his( 1 ) piggy bank, and he( 1 ) spent N/D of that money on books at the bookstore.

How much money did person( 1 ) spend?

Round to the nearest cent, or hundredth of a dollar.

SOLUTION

We, we can multiply AMOUNT by \dfrac{N}{D} to find out how much money person( 1 ) spent.

\color{#e00}{\dfrac{N}{D}} \cdot AMOUNT

init({ range: [ [ 0, 1 ], [ 0, AMOUNT + 1 ] ],scale: [ 250, 25 ] }); for ( var y = 1; y <= AMOUNT; y++ ) { rectchart( [ N, D - N ], ["#e00", "#999" ], y ); }

\color{#e00}{\dfrac{N * AMOUNT}{D}} = SOLUTION

person( 1 ) spent $SOLUTION on books.

randRange( 15, 40 ) randFromArray([ 8, 6 ]) randRange( 1, D - 1 ) roundTo( 2, N / D * AMOUNT )

Every day person( 1 ) put the extra change from his( 1 ) pockets into a glass jar. After randRange( 10, 30 ) weeks, person( 1 ) had saved up $AMOUNT. person( 1 ) decided to use N/D of the money from the jar to buy canned food for a homeless shelter.

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

Round to the nearest cent, or hundredth of a dollar.

SOLUTION

We can multiply AMOUNT by \dfrac{N}{D} to find out how much money person( 1 ) spent on canned food.

\color{#e00}{\dfrac{N}{D}} \cdot AMOUNT

init({ range: [ [ 0, 1 ], [ 0, AMOUNT + 1 ] ],scale: [ 250, 25 ] }); for ( var y = 1; y <= AMOUNT; y++ ) { rectchart( [ N, D - N ], ["#e00", "#999" ], y ); }

\color{#e00}{\dfrac{N * AMOUNT}{D}} = SOLUTION

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

randRange( 10, 20 ) randFromArray([ 8, 6, 10 ]) randRange( 1, D - 1 ) N / D * GALLONS

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 N/D full.

How many gallons of gas were left in the tank?

SOLUTION

Since a fraction of the gas in his( 1 ) tank was left, we can multiply GALLONS by \dfrac{N}{D} to find out how much gas was left in the tank.

\color{#e00}{\dfrac{N}{D}} \cdot GALLONS

init({ range: [ [ 0, 1 ], [ 0, GALLONS + 1 ] ],scale: [ 250, 25 ] }); for ( var y = 1; y <= GALLONS; y++ ) { rectchart( [ N, D - N ], ["#e00", "#999" ], y ); }

\color{#e00}{\dfrac{N * GALLONS}{D}} = SOLUTION

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

randRange( 15, 40 ) randFromArray([ 8, 6, 10 ]) randRange( 1, D - 1 ) N / D * ATTENDEES

ATTENDEES people had a picnic in the park. N/D of the people at the picnic were adults.

How many adults were at the picnic?

SOLUTION

We can multiply ATTENDEES by \dfrac{N}{D} to find out how many people at the picnic were adults.

\color{#e00}{\dfrac{N}{D}} \cdot ATTENDEES

init({ range: [ [ 0, 1 ], [ 0, ATTENDEES + 1 ] ],scale: [ 250, 25 ] }); for ( var y = 1; y <= ATTENDEES; y++ ) { rectchart( [ N, D - N ], ["#e00", "#999" ], y ); }

\color{#e00}{\dfrac{N * ATTENDEES}{D}} = SOLUTION

SOLUTION people at the picnic were adults.