Question

$$ 3 \frac{2}{3} \cdot 3 $$

Short answer

The result of the multiplication \(3 \frac{2}{3} \cdot 3\) is 33.

Step-by-step solution

Convert mixed number to improper fraction

Firstly, convert the mixed number \(3 \frac{2}{3}\) to an improper fraction. To do this, multiply the whole number by the denominator of the fraction and add the numerator. This will give the numerator of the improper fraction. The denominator remains as is. In this case, the result is: \(3 \cdot 3 + 2 = 11\), so the mixed number converts to \(\frac{11}{3}\).

Multiplication with integer

Now, multiply this improper fraction \(\frac{11}{3}\) with the integer 3. This can be done as follows: \(\frac{11}{3} \cdot 3 = \frac{11 \cdot 3}{3}\). Because the same number (3) appears in the numerator and denominator, they cancel out given term as result.

Simplify product

Finally, simplify the expression \(\frac{11 \cdot 3}{3}\) to get the final answer. Multiplication in the numerator leads to 33. As mentioned before, the 3 from the numerator and the 3 from the denominator cancel out, leading to a final result of 33.