To calculate \(0.4 \times 3 \frac{1}{3}\), first convert the mixed number into an improper fraction.
The mixed number \(3 \frac{1}{3}\) can be converted as follows:
\[ 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \times 3}{3} + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \]
Now, we can multiply:
\[ 0.4 \times \frac{10}{3} \]
First, convert \(0.4\) into a fraction:
\[ 0.4 = \frac{4}{10} = \frac{2}{5} \]
Now perform the multiplication:
\[ \frac{2}{5} \times \frac{10}{3} = \frac{2 \times 10}{5 \times 3} = \frac{20}{15} \]
Now simplify:
\[ \frac{20}{15} = \frac{4}{3} \]
So, \(0.4 \times 3 \frac{1}{3} = \frac{4}{3}\), which can also be expressed as \(1 \frac{1}{3}\) if you convert it back to a mixed number.