Question

It takes 1/3 cups of powered punch mix to make 2/3 gallons of punch. If the recipe is for 1 gallon of punch, how much punch is need to make 1/4 the recipe ?

Answer 1

1/8

Explanation:

To find the unit rate: multiply the numerator by the reciprocal of the denominator.

unit rate = 1/3/2/3 =
`(1)/(3)` ×
`(3)/(2)` =
`(3)/(6)` =
`(1)/(2)` cups of punch mix per gallon

Therefore, 1/4 the recipe: 1/2 × 1/4 = 1/8 cups of punch mix

Answer 2

`(1)/(8)`

Explanation:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of powered punch mix cups required to make
`(2)/(3)` gallons of punch is
`(1)/(3)`

Number of powered punch mix cups required to make
`(2)/(3)` gallons of punch is
`(3)/(2)*`
`(1)/(3)`=
`(1)/(2)`

Since the recipe is for
`1` gallon,

`(1)/(2)` powered punch mix cups are required to make the complete recipe.

`(1)/(4) * (1)/(2)` powered punch mix cups are required to make
`(1)/(4)` recipe.

So,
`(1)/(8)` cups of powered punch mix cups are required to make
`(1)/(4)` recipe.