Solve Mixed Number Division: 2⅔ ÷ ¾ Step-by-Step

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

• Step 1: Convert the mixed number $2\frac{2}{7}$ to an improper fraction.

The whole number is 2 and the fraction is $\frac{2}{7}$. Convert this by using the formula: $2\frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}$

• Step 2: Invert the divisor $\frac{3}{4}$ to its reciprocal and multiply.

The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. Thus, the division changes to multiplication: $\frac{16}{7} \times \frac{4}{3}$

• Step 3: Multiply the fractions.

Multiply the numerators and the denominators: $\frac{16 \times 4}{7 \times 3} = \frac{64}{21}$

• Step 4: Convert the improper fraction back to a mixed number.

Divide the numerator by the denominator: $\text{21 goes into 64 three times (since } 21 \times 3 = 63\text{). The remainder is } 64 - 63 = 1.$ Thus, the improper fraction can be written as the mixed number: $3\frac{1}{21}$

Therefore, the solution to the problem is $3\frac{1}{21}$.