Solve Mixed Number Division: 1¼ ÷ ⅓

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number $1\frac{1}{4}$ to an improper fraction.
• Step 2: Calculate the reciprocal of $\frac{1}{3}$.
• Step 3: Multiply the improper fraction by the reciprocal.
• Step 4: Simplify the resulting fraction, if necessary, to achieve the final result.

Now, let’s work through each step:

Step 1: Convert $1\frac{1}{4}$ to an improper fraction.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction part, and then add the numerator. Keep the same denominator:

$1\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}$.

Step 2: Calculate the reciprocal of $\frac{1}{3}$.

The reciprocal of $\frac{1}{3}$ is $3$ or $\frac{3}{1}$.

Step 3: Multiply $\frac{5}{4}$ by $\frac{3}{1}$:

$\frac{5}{4} \times \frac{3}{1} = \frac{5 \times 3}{4 \times 1} = \frac{15}{4}$.

Step 4: Simplify and convert $\frac{15}{4}$ back to a mixed number:

Divide the numerator by the denominator: $15 \div 4 = 3$ with a remainder of $3$.

The mixed number is $3\frac{3}{4}$.

Therefore, the solution to the problem is $3\frac{3}{4}$.