Question

perform the indicated operation. if possible, reduce the answer to its lowest terms.
\left(-1\frac{1}{5}\
ight)\left(12\frac{1}{2}\
ight)
\left(-1\frac{1}{5}\
ight)\left(12\frac{1}{2}\
ight)=\square
simplify your answer. type an integer, fraction, or mixed number.

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(-1\frac{1}{5}\) 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 \(-1\frac{1}{5}\), we have \(a=-1\), \(b = 1\), \(c = 5\). Then \(-1\frac{1}{5}=-\frac{1\times5 + 1}{5}=-\frac{6}{5}\).

Next, convert \(12\frac{1}{2}\) to an improper fraction. Here, \(a = 12\), \(b=1\), \(c = 2\). So \(12\frac{1}{2}=\frac{12\times2+1}{2}=\frac{25}{2}\).

Step2: Multiply the two improper fractions

Now, multiply \(-\frac{6}{5}\) and \(\frac{25}{2}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(-\frac{6}{5}\times\frac{25}{2}=-\frac{6\times25}{5\times2}\).

Simplify the numerator and denominator: \(6\times25 = 150\) and \(5\times2=10\), so we have \(-\frac{150}{10}\).

Step3: Simplify the fraction

Simplify \(-\frac{150}{10}\) by dividing the numerator by the denominator: \(-\frac{150}{10}=- 15\).

Answer:

\(-15\)