Question

multiply.
$-2\frac{1}{3} \times -3\frac{3}{10} = $
submit

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(-2\frac{1}{3}\) 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 \(-2\frac{1}{3}\), we have \(a = -2\), \(b = 1\), \(c = 3\). Then \(-2\frac{1}{3}=-\frac{2\times3 + 1}{3}=-\frac{7}{3}\).

Next, convert \(-3\frac{3}{10}\) to an improper fraction. Using the same formula, with \(a = -3\), \(b = 3\), \(c = 10\), we get \(-3\frac{3}{10}=-\frac{3\times10 + 3}{10}=-\frac{33}{10}\).

Step2: Multiply the two improper fractions

When multiplying two fractions \(\frac{m}{n}\times\frac{p}{q}=\frac{m\times p}{n\times q}\), and also remember that the product of two negative numbers is positive. So we have \(-\frac{7}{3}\times(-\frac{33}{10})=\frac{7\times33}{3\times10}\).

Simplify the numerator and denominator. We can cancel out the common factor of 3 in the numerator and denominator. \(33\div3 = 11\), so the expression becomes \(\frac{7\times11}{1\times10}=\frac{77}{10}\).

Step3: Convert back to a mixed number (optional, but let's check)

\(\frac{77}{10}=7\frac{7}{10}\) since \(7\times10 + 7 = 77\).

Answer:

\(7\frac{7}{10}\) (or \(\frac{77}{10}\))