Question

divide.
3 ÷ 3\frac{3}{7} = \square

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( 3\frac{3}{7} \) 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 \( 3\frac{3}{7} \), we have \( a = 3 \), \( b = 3 \), \( c = 7 \). Then \( 3\times7 + 3 = 21 + 3 = 24 \), so \( 3\frac{3}{7}=\frac{24}{7} \).

Step2: Rewrite division as multiplication

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So \( 3\div\frac{24}{7} = 3\times\frac{7}{24} \).

Step3: Simplify the multiplication

Now, multiply \( 3 \) and \( \frac{7}{24} \). \( 3\times\frac{7}{24}=\frac{3\times7}{24}=\frac{21}{24} \). Then simplify the fraction \( \frac{21}{24} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \( \frac{21\div3}{24\div3}=\frac{7}{8} \).

Answer:

\(\frac{7}{8}\)