Solve Mixed Number Division: 10⅓ ÷ 4 1/14 Step-by-Step

To solve the problem, follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Divide by multiplying by the reciprocal of the second fraction.
• Step 3: Simplify the result, and if required, convert back to a mixed number.

Let's proceed with each step:
Step 1: Convert $10\frac{3}{7}$ and $4\frac{1}{14}$ to improper fractions.
The first mixed number $10\frac{3}{7}$ becomes: $\frac{10 \times 7 + 3}{7} = \frac{73}{7}$.
The second mixed number $4\frac{1}{14}$ becomes: $\frac{4 \times 14 + 1}{14} = \frac{57}{14}$.

Step 2: Divide by multiplying by the reciprocal.
$\frac{73}{7} \div \frac{57}{14} = \frac{73}{7} \times \frac{14}{57}$.

Step 3: Perform the multiplication and simplify.
The multiplication of fractions gives: $\frac{73 \times 14}{7 \times 57} = \frac{1022}{399}$.

Step 4: Convert to a mixed number, if necessary.
$1022 \div 399$ gives a quotient of 2 and a remainder of 224: $1022 = 2 \times 399 + 224$.
Thus, the mixed number is $2\frac{224}{399}$.

The solution to the problem is $2\frac{224}{399}$, which corresponds to choice 4.