Question

multiply.
$-2 \times 4 \frac{3}{4} = \square$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(4\frac{3}{4}\) 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 \(4\frac{3}{4}\), we have \(a = 4\), \(b = 3\), \(c = 4\). Then \(4\times4+3 = 19\), so \(4\frac{3}{4}=\frac{19}{4}\).

Step2: Multiply the integers and fractions

Now we multiply \(-2\) by \(\frac{19}{4}\). We can write \(-2\) as \(\frac{-2}{1}\). Then the multiplication of fractions is \(\frac{-2}{1}\times\frac{19}{4}\). Multiply the numerators: \(-2\times19=-38\), and multiply the denominators: \(1\times4 = 4\). So we get \(\frac{-38}{4}\).

Step3: Simplify the fraction

Simplify \(\frac{-38}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \(\frac{-38\div2}{4\div2}=\frac{-19}{2}\), and \(\frac{-19}{2}\) can also be written as \(-9\frac{1}{2}\) (since \(19\div2 = 9\) with a remainder of 1).

Answer:

\(-\frac{19}{2}\) (or \(-9\frac{1}{2}\))