Solve Mixed Number Division: 7½ ÷ 2½ Step-by-Step

To solve the problem of dividing the mixed numbers $7\frac{1}{2}$ by $2\frac{1}{2}$, follow these steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Divide the fractions by multiplying by the reciprocal.
• Step 3: Simplify the resulting fraction to find the answer.

Now, let’s break it down step-by-step:

Step 1: Convert $7\frac{1}{2}$ to an improper fraction. To do this, multiply the whole number 7 by the denominator 2 and add the numerator 1:
$7 \times 2 + 1 = 14 + 1 = 15$.

This makes the improper fraction $\frac{15}{2}$.

Convert $2\frac{1}{2}$ in a similar manner:
$2 \times 2 + 1 = 4 + 1 = 5$, giving $\frac{5}{2}$.

Step 2: Divide $\frac{15}{2}$ by $\frac{5}{2}$ by multiplying $\frac{15}{2}$ by the reciprocal of $\frac{5}{2}$, which is $\frac{2}{5}$:
$\frac{15}{2} \times \frac{2}{5} = \frac{15 \times 2}{2 \times 5} = \frac{30}{10}$.

Step 3: Simplify $\frac{30}{10}$: divide the numerator and the denominator by their greatest common divisor, 10,
$\frac{30}{10} = \frac{30 \div 10}{10 \div 10} = \frac{3}{1} = 3$.

Therefore, the solution to $7\frac{1}{2} \div 2\frac{1}{2}$ is $3$, which corresponds to choice 3.