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

$\dfrac{1}{8}$

Step-by-step 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 $\frac{2}{3}$ gallons of punch is $\frac{1}{3}$

Number of powered punch mix cups required to make $\frac{2}{3}$ gallons of punch is $\frac{3}{2}\times$$\frac{1}{3}$=$\frac{1}{2}$

Since the recipe is for $1$ gallon,

$\frac{1}{2}$ powered punch mix cups are required to make the complete recipe.

$\frac{1}{4} \times \frac{1}{2}$ powered punch mix cups are required to make $\frac{1}{4}$ recipe.

So,$\frac{1}{8}$ cups of powered punch mix cups are required to make $\frac{1}{4}$ recipe.

Answer 2

Answer:

1/8

Step-by-step explanation:

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

unit rate = 1/3/2/3 = $\frac{1}{3}$ × $\frac{3}{2}$ = $\frac{3}{6}$ = $\frac{1}{2}$ cups of punch mix per gallon

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