Question

a soup recipe calls for $1\frac{1}{4}$ cups of broth. how many batches of soup could you make with 10 cups of broth?

Explanation:

Step1: Convert mixed number to improper fraction

The amount of broth per batch is \(1\frac{1}{4}\) cups. Convert \(1\frac{1}{4}\) to an improper fraction: \(1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4}\) cups.

Step2: Set up division for number of batches

We have 10 cups of broth and each batch needs \(\frac{5}{4}\) cups. So the number of batches \(n\) is \(10\div\frac{5}{4}\).

Step3: Perform the division

Dividing by a fraction is multiplying by its reciprocal: \(10\div\frac{5}{4}=10\times\frac{4}{5}\).
Simplify: \(10\times\frac{4}{5}=\frac{10\times4}{5}=\frac{40}{5} = 8\).

Answer:

8