Solve: Division of Mixed Numbers 5 4/5 ÷ 2 1/10

To solve the problem $5\frac{4}{5} \div 2\frac{1}{10}$, we follow these steps:

• Step 1: Convert mixed numbers to improper fractions.
  $5\frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{25 + 4}{5} = \frac{29}{5}$
• $2\frac{1}{10} = \frac{2 \times 10 + 1}{10} = \frac{20 + 1}{10} = \frac{21}{10}$
• Step 2: Divide $\frac{29}{5}$ by $\frac{21}{10}$ by multiplying by the reciprocal.
  $\frac{29}{5} \div \frac{21}{10} = \frac{29}{5} \times \frac{10}{21}$
• Step 3: Multiply the fractions and simplify.
  $\frac{29}{5} \times \frac{10}{21} = \frac{29 \times 10}{5 \times 21} = \frac{290}{105}$
• Step 4: Simplify $\frac{290}{105}$.
  Find the greatest common divisor (GCD) of 290 and 105. The GCD is 5.
  $\frac{290 \div 5}{105 \div 5} = \frac{58}{21}$
• Step 5: Convert the improper fraction $\frac{58}{21}$ into a mixed number.
  $58 \div 21 = 2$ remainder $16$, so $\frac{58}{21} = 2\frac{16}{21}$

Therefore, the solution is $2\frac{16}{21}$.