Solve Mixed Number Division: 2 2/7 ÷ 3/4 Step by Step

To solve the division problem $2\frac{2}{7}:\frac{3}{4}$, follow these steps:

• Convert the mixed number to an improper fraction:

$2\frac{2}{7}$ can be rewritten as $\frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}$.

• Rewrite the division as multiplication by the reciprocal:

Instead of dividing by $\frac{3}{4}$, multiply by its reciprocal: $\frac{16}{7} \times \frac{4}{3}$.

• Perform the multiplication:

Calculate: $\frac{16 \times 4}{7 \times 3} = \frac{64}{21}$.

• Convert the improper fraction to a mixed number.

Divide 64 by 21: the quotient is 3 and the remainder is 1, giving us the mixed number:

• $64 \div 21 = 3$ remainder $1$.
• The mixed number is $3\frac{1}{21}$.

Therefore, the result of $2\frac{2}{7} \div \frac{3}{4}$ is $\boxed{3\frac{1}{21}}$.