Question

a baker used $3\frac{1}{2}$ cups of flour to make 3 small loaves of challah bread. how many cups of flour are needed for 1 loaf?

Explanation:

Step1: Convert mixed number to improper fraction

The total flour used is \( 3\frac{1}{2} \) cups. Convert this to an improper fraction: \( 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2} \) cups.

Step2: Divide by number of loaves

We need to find the flour per loaf, so divide the total flour by the number of loaves (3). So we calculate \( \frac{7}{2}\div3 \). Dividing by a number is the same as multiplying by its reciprocal, so \( \frac{7}{2}\times\frac{1}{3}=\frac{7}{6} \).

Step3: Convert improper fraction to mixed number

Convert \( \frac{7}{6} \) to a mixed number: \( \frac{7}{6}=1\frac{1}{6} \)? Wait, no, wait. Wait, \( 3\frac{1}{2} \) is \( \frac{7}{2} \), divided by 3 is \( \frac{7}{2}\times\frac{1}{3}=\frac{7}{6} \)? Wait, no, maybe I made a mistake. Wait, \( 3\frac{1}{2} \) cups for 3 loaves. So per loaf is \( 3\frac{1}{2}\div3 \). Let's do it as mixed number division. \( 3\frac{1}{2}\div3=(3 + \frac{1}{2})\div3 = 3\div3+\frac{1}{2}\div3 = 1+\frac{1}{6}=1\frac{1}{6} \)? Wait, but looking at the options, maybe I miscalculated. Wait, wait, \( 3\frac{1}{2} \) is \( \frac{7}{2} \), divided by 3 is \( \frac{7}{2}\times\frac{1}{3}=\frac{7}{6}=1\frac{1}{6} \)? But the options have \( 1\frac{1}{6} \)? Wait, the options: first is \( \frac{1}{2} \), second is \( 1\frac{1}{6} \), third is \( 1\frac{1}{2} \), fourth is \( \frac{8}{7} \). Wait, maybe I messed up the initial conversion. Wait, \( 3\frac{1}{2} \) is \( \frac{7}{2} \), divided by 3: \( \frac{7}{2}\div3=\frac{7}{6}=1\frac{1}{6} \), which is the second option.

Wait, no, wait, maybe the question is \( 3\frac{1}{2} \) cups for 3 loaves, so per loaf is \( 3\frac{1}{2}\div3 \). Let's compute again:

\( 3\frac{1}{2}=\frac{7}{2} \)

\( \frac{7}{2}\div3=\frac{7}{2}\times\frac{1}{3}=\frac{7}{6}=1\frac{1}{6} \). So the answer should be \( 1\frac{1}{6} \), which is the second option.

Answer:

\( 1\frac{1}{6} \) (corresponding to the option labeled \( 1\frac{1}{6} \))