Solve Mixed Number Division: 3½ ÷ 1¼ Step-by-Step

To solve the problem $3\frac{1}{2} : 1\frac{1}{4}$, we will follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Divide the improper fractions by multiplying by the reciprocal of the second fraction.
• Step 3: Simplify the resulting fraction if possible.
• Step 4: Convert the simplified improper fraction back to a mixed number if needed.

Let's work through each step:

Step 1: Convert $3\frac{1}{2}$ to an improper fraction.

$3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$

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

$1\frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}$

Step 2: Divide $\frac{7}{2}$ by $\frac{5}{4}$.

The division of fractions is done by multiplying by the reciprocal: $\frac{7}{2} \times \frac{4}{5}$.

Step 3: Perform the multiplication.

$\frac{7 \times 4}{2 \times 5} = \frac{28}{10}$

Step 4: Simplify $\frac{28}{10}$.

Divide both the numerator and the denominator by 2: $\frac{28 \div 2}{10 \div 2} = \frac{14}{5}$.

Convert $\frac{14}{5}$ back to a mixed number.

$\frac{14}{5} = 2\frac{4}{5}$ because 14 divided by 5 is 2 with a remainder of 4.

Therefore, the solution to the problem $3\frac{1}{2} : 1\frac{1}{4}$ is $2\frac{4}{5}$.