Question

divide, write the answer in simplest form.
$3\frac{2}{3} \div \frac{1}{3} = \square$

Explanation:

Step1: Convert mixed number to improper fraction

To convert \( 3\frac{2}{3} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{9 + 2}{3}=\frac{11}{3} \).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{11}{3}\div\frac{1}{3}=\frac{11}{3}\times\frac{3}{1} \).

Step3: Simplify the multiplication

When we multiply \( \frac{11}{3}\times\frac{3}{1} \), the 3 in the numerator and the 3 in the denominator cancel out, leaving us with \( 11\times1 = 11 \).

Answer:

11