Question

suppose a brownie recipe calls for $2\frac{1}{5}$ cups of sugar. each brownie requires $\frac{1}{2}$ cups of sugar. how many brownies does the recipe make? enter the answer as a mixed number or fraction. show your work here

Explanation:

Step1: Convert mixed number to improper fraction

The total sugar is \(2\frac{1}{5}\) cups. To convert to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}\) cups.

Step2: Divide total sugar by sugar per brownie

We need to find how many times \(\frac{1}{2}\) fits into \(\frac{11}{5}\). This is done by dividing \(\frac{11}{5}\) by \(\frac{1}{2}\), which is the same as multiplying \(\frac{11}{5}\) by the reciprocal of \(\frac{1}{2}\), so \(\frac{11}{5}\div\frac{1}{2}=\frac{11}{5}\times2=\frac{22}{5}\).

Step3: Convert improper fraction to mixed number (optional, but as per instruction)

\(\frac{22}{5}\) as a mixed number is \(4\frac{2}{5}\) (since \(22\div5 = 4\) with a remainder of \(2\)).

Answer:

\(\frac{22}{5}\) (or \(4\frac{2}{5}\))