Solve Mixed Number Division: 7½ ÷ 2¼ Step by Step

To solve this problem, follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Divide by multiplying by the reciprocal.
• Step 3: Simplify the result.

Now, let's work through the steps:

Step 1: Convert the mixed numbers to improper fractions.
For $7\frac{1}{2}$, convert it as follows: $7\frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{15}{2}$.
For $2\frac{1}{4}$, convert it as follows: $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$.

Step 2: To divide $\frac{15}{2}$ by $\frac{9}{4}$, multiply $\frac{15}{2}$ by the reciprocal of $\frac{9}{4}$:
$\frac{15}{2} \times \frac{4}{9}$.

Step 3: Multiply and simplify the fractions:
$\frac{15 \times 4}{2 \times 9} = \frac{60}{18}$.

Now simplify $\frac{60}{18}$ by dividing both the numerator and denominator by their greatest common divisor, which is 6:
$\frac{60 \div 6}{18 \div 6} = \frac{10}{3}$.

Convert $\frac{10}{3}$ back to a mixed number:

The whole number part is $10 \div 3 = 3$ with a remainder of 1. Thus, the mixed number is $3\frac{1}{3}$.

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