Question

6 what is the value of $3\frac{1}{3} \div \frac{2}{3}$? show your work on the scratchpad.

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \( 3\frac{1}{3} \) can be converted to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 3\frac{1}{3} \), we have \( a = 3 \), \( b = 1 \), \( c = 3 \). Then \( 3\times3 + 1 = 10 \), so \( 3\frac{1}{3}=\frac{10}{3} \).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction \( \frac{2}{3} \) is the same as multiplying by its reciprocal. The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \). So we have \( \frac{10}{3}\div\frac{2}{3}=\frac{10}{3}\times\frac{3}{2} \).

Step3: Simplify the multiplication

When we multiply \( \frac{10}{3}\times\frac{3}{2} \), the 3 in the numerator and the 3 in the denominator cancel out. Then we have \( \frac{10}{2} = 5 \).

Answer:

\( 5 \)