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

A mixed number \( 3\frac{2}{3} \) can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator. 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. The reciprocal of \( \frac{1}{3} \) is \( \frac{3}{1} \). So, \( \frac{11}{3}\div\frac{1}{3}=\frac{11}{3}\times\frac{3}{1} \).

Step3: Multiply the fractions

When multiplying fractions, we multiply the numerators together and the denominators together. So, \( \frac{11}{3}\times\frac{3}{1}=\frac{11\times3}{3\times1} \). The 3 in the numerator and the 3 in the denominator cancel out, leaving \( \frac{11\times1}{1\times1}=11 \).

Answer:

\( 11 \)