Question

find the product.
$3\frac{1}{3} \times \frac{2}{3} = ? \frac{}{}$
give your answer as a mixed number in simplest form.
enter the whole number.
(there are some cartoon characters and a start flag in the image, but they are not relevant to the math problem itself.)

Explanation:

Step1: Convert mixed number to improper fraction

A mixed number \(3\frac{1}{3}\) can be converted to an improper fraction by multiplying the whole number (3) by the denominator (3) and adding the numerator (1). So, \(3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3}\).

Step2: Multiply the two fractions

Now, we multiply \(\frac{10}{3}\) by \(\frac{2}{3}\). When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{10}{3}\times\frac{2}{3}=\frac{10\times2}{3\times3}=\frac{20}{9}\).

Step3: Convert improper fraction to mixed number

To convert \(\frac{20}{9}\) to a mixed number, we divide 20 by 9. 9 times 2 is 18, and the remainder is 20 - 18 = 2. So, \(\frac{20}{9}=2\frac{2}{9}\). The whole number part is 2.

Answer:

2