Negative fractions

What is the product of negative 2 1 half and negative 3 1 third? Enter your answer as an improper fraction or mixed number in the simplest form.

Correct answer:

x =  8 ¹⁄₃ = 25/3

Step-by-step explanation:

$$\begin{gathered} a=-2\frac{1}{2}=-(2+\frac{1}{2})=-\frac{2\cdot 2+1}{2}=-\frac{4+1}{2}=-\frac{5}{2}=-2.5 \\ b=-3\frac{1}{3}=-(3+\frac{1}{3})=-\frac{3\cdot 3+1}{3}=-\frac{9+1}{3}=-\frac{10}{3}\doteq -3.3333 \\ x=a\cdot b=\frac{-5}{2}\cdot \frac{-10}{3}=\frac{-5\cdot -10}{2\cdot 3}=\frac{50}{6}=\frac{25}{3}=8\frac{1}{3}=8.3333 \end{gathered}$$

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