Question

what is the product of 6 and $2\frac{3}{5}$?\
a. $3\frac{3}{5}$\
b. $12\frac{3}{5}$\
c. $15\frac{3}{5}$\
d. $8\frac{3}{5}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(2\frac{3}{5}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{3}{5}\), we have \(a = 2\), \(b = 3\), \(c = 5\). Then \(2\frac{3}{5}=\frac{2\times5 + 3}{5}=\frac{10 + 3}{5}=\frac{13}{5}\).

Step2: Multiply by 6

Now, find the product of 6 and \(\frac{13}{5}\). We know that \(6\times\frac{13}{5}=\frac{6\times13}{5}=\frac{78}{5}\).

Step3: Convert back to mixed number

Convert \(\frac{78}{5}\) back to a mixed number. Divide 78 by 5: \(5\times15 = 75\), so \(78-75 = 3\). Thus, \(\frac{78}{5}=15\frac{3}{5}\).

Answer:

C. \(15\frac{3}{5}\)