Question

multiply: (-1\frac{1}{6} \times 7\frac{1}{2} =)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(-1\frac{1}{6}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). For \(-1\frac{1}{6}\), \(a=-1\), \(b = 1\), \(c = 6\), so we have \(\frac{-1\times6 + 1}{6}=\frac{-6 + 1}{6}=\frac{-5}{6}\).

Next, convert \(7\frac{1}{2}\) to an improper fraction. Using the same formula, \(a = 7\), \(b=1\), \(c = 2\), so \(\frac{7\times2+1}{2}=\frac{14 + 1}{2}=\frac{15}{2}\).

Step2: Multiply the two improper fractions

Now, multiply \(\frac{-5}{6}\) and \(\frac{15}{2}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(\frac{-5\times15}{6\times2}=\frac{-75}{12}\).

Step3: Simplify the resulting fraction

Simplify \(\frac{-75}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \(\frac{-75\div3}{12\div3}=\frac{-25}{4}\). We can also convert this back to a mixed number: \(-6\frac{1}{4}\) (since \(-25\div4=-6\) with a remainder of \(-1\), but more accurately, \(\frac{-25}{4}=-6\frac{1}{4}\)).

Answer:

\(-\frac{25}{4}\) (or \(-6\frac{1}{4}\))