Question

1. simplify if necessary.

$3\frac{1}{5} \times \frac{1}{2}$
type a response

Explanation:

Step1: Convert mixed number to improper fraction

To convert \(3\frac{1}{5}\) to an improper fraction, we use the formula: \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(3\frac{1}{5}\), we have \(a = 3\), \(b=1\), \(c = 5\). Then \(3\frac{1}{5}=\frac{3\times5 + 1}{5}=\frac{15 + 1}{5}=\frac{16}{5}\).

Step2: Multiply the two fractions

Now we multiply \(\frac{16}{5}\) by \(\frac{1}{2}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(\frac{16}{5}\times\frac{1}{2}=\frac{16\times1}{5\times2}=\frac{16}{10}\).

Step3: Simplify the fraction

Simplify \(\frac{16}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{16\div2}{10\div2}=\frac{8}{5}\). We can also write this as a mixed number: \(\frac{8}{5}=1\frac{3}{5}\).

Answer:

\(1\frac{3}{5}\) (or \(\frac{8}{5}\))