Question

ms. clemente made 3\\(\frac{1}{2}\\) pounds of fruit salad for a picnic. at the picnic, \\(\frac{3}{4}\\) of the fruit salad was eaten. how many pounds of fruit salad were eaten at the picnic?\
\\(\bigcirc\\) a. 2\\(\frac{1}{4}\\) pounds\
\\(\bigcirc\\) b. 2\\(\frac{5}{8}\\) pounds\
\\(\bigcirc\\) c. 3\\(\frac{3}{8}\\) pounds\
\\(\bigcirc\\) d. 4\\(\frac{1}{4}\\) pounds

Explanation:

Step1: Convert mixed number to improper fraction

The total fruit salad is \( 3\frac{1}{2} \) pounds. Convert \( 3\frac{1}{2} \) to an improper fraction: \( 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2} \) pounds.

Step2: Multiply by the fraction eaten

We know \( \frac{3}{4} \) of the fruit salad was eaten. So we calculate \( \frac{7}{2}\times\frac{3}{4} \). Multiply the numerators: \( 7\times3 = 21 \), and the denominators: \( 2\times4 = 8 \). So we get \( \frac{21}{8} \).

Step3: Convert back to mixed number

Convert \( \frac{21}{8} \) to a mixed number: \( 21\div8 = 2 \) with a remainder of \( 5 \), so \( \frac{21}{8}=2\frac{5}{8} \) pounds.

Answer:

B. \( 2\frac{5}{8} \) pounds