randFromArray([5, 8]) randRange(3, D - 1)
randRange(2, 5) * N PIECES * D / N $._("candy bars") $._("bar per person") $._("total people") $._("people per bar") $._("people")

{Many|All|Several} of person(1)'s friends wanted to try the candy bars he brought back from his trip, but there were only `PIECES` candy bars. person(1) decided to cut the candy bars into pieces so that each person could have `\frac{N}{D}` of a candy bar.

{Many|All|Several} of person(1)'s friends wanted to try the candy bars she brought back from her trip, but there were only `PIECES` candy bars. person(1) decided to cut the candy bars into pieces so that each person could have `\frac{N}{D}` of a candy bar.

After cutting up the candy bars, to how many friends could person(1) give his candy, assuming he didn't eat any?

After cutting up the candy bars, to how many friends could person(1) give her candy, assuming she didn't eat any?

SOLUTION

We can divide the number of candy bars (`PIECES`) by the amount person(1) gave to each person (`\frac{N}{D}` of a bar) to find out how many people he could give a piece to.

We can divide the number of candy bars (`PIECES`) by the amount person(1) gave to each person (`\frac{N}{D}` of a bar) to find out how many people she could give a piece to.

`\dfrac{\red{PIECES \text{ CANDY_BARS}}} {\blue{\dfrac{N}{D} \text{ BAR_PER_PERSON}}} = \green{\text{ TOTAL_PEOPLE}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\dfrac{N}{D} \text{ BAR_PER_PERSON}` is `\green{\dfrac{D}{N} \text{ PEOPLE_PER_BAR}}`.

`\red{PIECES\text{ CANDY_BARS}} \times \green{\dfrac{D}{N} \text{ PEOPLE_PER_BAR}} = \green{\text{TOTAL_PEOPLE}}`

`\green{\dfrac{D * PIECES}{N}\text{ PEOPLE}} = SOLUTION\text{ PEOPLE}`

By cutting up the candy bars, person(1) could give his candy to `SOLUTION` of his friends.

By cutting up the candy bars, person(1) could give her candy to `SOLUTION` of her friends.

randFromArray([ 3, 5 ]) randRange( 2, D - 1 )
randRange( 3, 6 ) * N YARN * D / N $._("balls of yarn") $._("ball per scarf") $._("number of scarves") $._("scarves per ball") $._("scarves")

person(1) just found beautiful yarn {for `randFromArray([5,20]) \%` off }at his favorite yarn store. He can make one scarf from `\frac{N}{D}` of a ball of yarn.

person(1) just found beautiful yarn {for `randFromArray([5,20]) \%` off }at her favorite yarn store. She can make one scarf from `\frac{N}{D}` of a ball of yarn.

If person(1) buys `YARN` balls of yarn, how many scarves can he make?

If person(1) buys `YARN` balls of yarn, how many scarves can she make?

SOLUTION

We can divide the balls of yarn (`YARN`) by the yarn needed per scarf (`\frac{N}{D}` of a ball) to find out how many scarves person(1) can make.

`\dfrac{\red{YARN \text{ BALLS_OF_YARN}}} {\blue{\dfrac{N}{D} \text{ BALL_PER_SCARF}}} = \green{\text{ NUMBER_OF_SCARVES}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\blue{\dfrac{N}{D} \text{ BALL_PER_SCARF}}` is `\green{\dfrac{D}{N} \text{ SCARVES_PER_BALL}}`.

`\red{YARN\text{ BALLS_OF_YARN}} \times \green{\dfrac{D}{N} \text{ SCARVES_PER_BALL}} = \green{\text{ NUMBER_OF_SCARVES}}`

`\green{\dfrac{D * YARN}{N}\text{ SCARVES}} = SOLUTION\text{ SCARVES}`

person(1) can make `SOLUTION` scarves.

randFromArray([2, 5]) randRange(2, D - 1)
randRange(1, 3) * N PAINT * D / N randRange(1, 20) + SOLUTION $._("cans of paint") $._("can per room") $._("rooms") $._("can per room") $._("rooms per can")

person(1) decided to paint some of the rooms at his `ROOM`-room inn, person(1)'s Place. He discovered he needed `\frac{N}{D}` of a can of paint per room.

person(1) decided to paint some of the rooms at her `ROOM`-room inn, person(1)'s Place. She discovered she needed `\frac{N}{D}` of a can of paint per room.

If person(1) had `PAINT` cans of paint, how many rooms could he paint?

If person(1) had `PAINT` cans of paint, how many rooms could she paint?

SOLUTION

We can divide the cans of paint (`PAINT`) by the paint needed per room (`\frac{N}{D}` of a can) to find out how many rooms person(1) could paint.

`\dfrac{\red{PAINT \text{ CANS_OF_PAINT}}} {\blue{\dfrac{N}{D} \text{ CAN_PER_ROOM}}} = \blue{\text{ ROOMS}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\blue{\dfrac{N}{D} \text{ CAN_PER_ROOM}}` is `\green{\dfrac{D}{N} \text{ ROOMS_PER_CAN}}`.

`\red{PAINT\text{ CANS_OF_PAINT}} \times \green{\dfrac{D}{N} \text{ ROOMS_PER_CAN}} = \blue{\text{ ROOMS}}`

`\blue{\dfrac{D * PAINT}{N}\text{ ROOMS}} = SOLUTION\text{ ROOMS}`

person(1) could paint `SOLUTION` rooms.

randRange(8, 15) randRange(2, D - 1)
randRange(3, 7) randRange(2, B - 1)
((A * D) / (B * N))
getGCD(N, A) A / GCD1 N / GCD1 getGCD(D, B) B / GCD2 D / GCD2 $._("mile") $._("mile per swimmer") $._("number of swimmers") $._("swimmers per mile")

As the swim coach at school(1), person(1) selects which athletes will participate in the state-wide swim relay.

The relay team swims `\frac{A}{B}` of a mile in total, with each team member responsible for swimming `\frac{N}{D}` of a mile. The team must complete the swim in `\frac{3}{randRange(4,5)}` of an hour.

How many swimmers does person(1) need on the relay team?

SOLUTION

To find out how many swimmers person(1) needs on the team, divide the total distance (`\frac{A}{B}` of a mile) by the distance each team member will swim (`\frac{N}{D}` of a mile).

`\dfrac{\red{\dfrac{A}{B} \text{ MILE}}} {\blue{\dfrac{N}{D} \text{ MILE_PER_SWIMMER}}} = \blue{\text{ NUMBER_OF_SWIMMERS}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\blue{\dfrac{N}{D} \text{ MILE_PER_SWIMMER}}` is `\green{\dfrac{D}{N} \text{ SWIMMERS_PER_MILE}}`.

`\red{\dfrac{A}{B}\text{ MILE}} \times \green{\dfrac{D}{N} \text{ SWIMMERS_PER_MILE}} = \blue{\text{ NUMBER_OF_SWIMMERS}}`

`\dfrac{\red{A} \cdot \green{D}} {\red{B} \cdot \green{N}} = \blue{\text{ NUMBER_OF_SWIMMERS}}`

Reduce terms with common factors by dividing the `A` in the numerator and the `N` in the denominator by `GCD1`:

`\dfrac{\red{\cancel{A}^{SIMP_A}} \cdot \green{D}} {\red{B} \cdot \green{\cancel{N}^{SIMP_N}}} = \blue{\text{ NUMBER_OF_SWIMMERS}}`

Reduce terms with common factors by dividing the `D` in the numerator and the `B` in the denominator by `GCD2`:

`\dfrac{\red{SIMP_A} \cdot \green{\cancel{D}^{SIMP_D}}} {\red{\cancel{B}^{SIMP_B}} \cdot \green{SIMP_N}} = \blue{\text{ NUMBER_OF_SWIMMERS}}`

Simplify:

`\dfrac{\red{SIMP_A} \cdot \green{SIMP_D}} {\red{SIMP_B} \cdot \green{SIMP_N}} = \blue{SOLUTION}`

person(1) needs `SOLUTION` swimmers on his team.

person(1) needs `SOLUTION` swimmers on her team.

randRange(6, 30) randRange(2, D - 1)
randRange(3, 5) randRange(2, B - 1)
((A * D) / (B * N))
getGCD(N, A) A / GCD1 N / GCD1 getGCD(D, B) B / GCD2 D / GCD2 $._("pound of chocolate") $._("pound per bag") $._("number of bags") $._("pound") $._("bags per pound")

person(1) thought it would be nice to include `\frac{N}{D}` of a pound of chocolate in each of the holiday gift bags he made for his friends and family.

person(1) thought it would be nice to include `\frac{N}{D}` of a pound of chocolate in each of the holiday gift bags she made for her friends and family.

How many holiday gift bags could person(1) make with `\frac{A}{B}` of a pound of chocolate?

SOLUTION

To find out how many gift bags person(1) could create, divide the total chocolate (`\frac{A}{B}` of a pound) by the amount he wanted to include in each gift bag (`\frac{N}{D}` of a pound).

To find out how many gift bags person(1) could create, divide the total chocolate (`\frac{A}{B}` of a pound) by the amount she wanted to include in each gift bag (`\frac{N}{D}` of a pound).

`\dfrac{\red{\dfrac{A}{B} \text{ POUND_OF_CHOCOLATE}}} {\blue{\dfrac{N}{D} \text{ POUND_PER_BAG}}} = \blue{\text{ NUMBER_OF_BAGS}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\blue{\dfrac{N}{D} \text{ POUND_PER_BAG}}` is `\green{\dfrac{D}{N} \text{ BAGS_PER_POUND}}`.

`\red{\dfrac{A}{B}\text{ POUND}} \times \green{\dfrac{D}{N} \text{ BAGS_PER_POUND}} = \blue{\text{ NUMBER_OF_BAGS}}`

`\dfrac{\red{A} \cdot \green{D}} {\red{B} \cdot \green{N}} = \blue{\text{ NUMBER_OF_BAGS}}`

Reduce terms with common factors by dividing the `A` in the numerator and the `N` in the denominator by `GCD1`:

`\dfrac{\red{\cancel{A}^{SIMP_A}} \cdot \green{D}} {\red{B} \cdot \green{\cancel{N}^{SIMP_N}}} = \blue{\text{ NUMBER_OF_BAGS}}`

Reduce terms with common factors by dividing the `D` in the numerator and the `B` in the denominator by `GCD2`:

`\dfrac{\red{SIMP_A} \cdot \green{\cancel{D}^{SIMP_D}}} {\red{\cancel{B}^{SIMP_B}} \cdot \green{SIMP_N}} = \blue{\text{ NUMBER_OF_BAGS}}`

Simplify:

`\dfrac{\red{SIMP_A} \cdot \green{SIMP_D}} {\red{SIMP_B} \cdot \green{SIMP_N}} = \blue{SOLUTION}`

person(1) could create `SOLUTION` gift bags.

randRange(7, 20) randRange(2, D - 1)
randRange(3, 6) randRange(2, B - 1)
((A * D) / (B * N))
getGCD(N, A) A / GCD1 N / GCD1 getGCD(D, B) B / GCD2 D / GCD2 $._("hour") $._("hour per exercise") $._("number of exercises") $._("exercises per hour")

person(1) works out for `\frac{A}{B}` of an hour every day. To keep his exercise routines interesting, he includes different types of exercises, such as plural_form(exercise(1)) and plural_form(exercise(2)), in each workout.

person(1) works out for `\frac{A}{B}` of an hour every day. To keep her exercise routines interesting, she includes different types of exercises, such as plural_form(exercise(1)) and plural_form(exercise(2)), in each workout.

If each type of exercise takes `\frac{N}{D}` of an hour, how many different types of exercise can person(1) do in each workout?

SOLUTION

To find out how many types of exercise person(1) could do in each workout, divide the total amount of exercise time (`\frac{A}{B}` of an hour) by the amount of time each exercise type takes (`\frac{N}{D}` of an hour).

`\dfrac{\red{\dfrac{A}{B} \text{ HOUR}}} {\blue{\dfrac{N}{D} \text{ HOUR_PER_EXERCISE}}} = \blue{\text{ NUMBER_OF_EXERCISES}}`

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of `\blue{\dfrac{N}{D} \text{ HOUR_PER_EXERCISE}}` is `\green{\dfrac{D}{N} \text{ EXERCISES_PER_HOUR}}`.

`\red{\dfrac{A}{B}\text{ HOUR}} \times \green{\dfrac{D}{N} \text{ EXERCISES_PER_HOUR}} = \blue{\text{ NUMBER_OF_EXERCISES}}`

`\dfrac{\red{A} \cdot \green{D}} {\red{B} \cdot \green{N}} = \blue{\text{ NUMBER_OF_EXERCISES}}`

Reduce terms with common factors by dividing the `A` in the numerator and the `N` in the denominator by `GCD1`:

`\dfrac{\red{\cancel{A}^{SIMP_A}} \cdot \green{D}} {\red{B} \cdot \green{\cancel{N}^{SIMP_N}}} = \blue{\text{ NUMBER_OF_EXERCISES}}`

Reduce terms with common factors by dividing the `D` in the numerator and the `B` in the denominator by `GCD2`:

`\dfrac{\red{SIMP_A} \cdot \green{\cancel{D}^{SIMP_D}}} {\red{\cancel{B}^{SIMP_B}} \cdot \green{SIMP_N}} = \blue{\text{ NUMBER_OF_EXERCISES}}`

Simplify:

`\dfrac{\red{SIMP_A} \cdot \green{SIMP_D}} {\red{SIMP_B} \cdot \green{SIMP_N}} = \blue{SOLUTION}`

person(1) can do `SOLUTION` different types of exercise per workout.