Solve Fraction Division: 1/4 ÷ 1 1/5 Step by Step

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

• Step 1: Convert the mixed number $1\frac{1}{5}$ into an improper fraction.
• Step 2: Divide $\frac{1}{4}$ by the improper fraction using the reciprocal.
• Step 3: Simplify the resulting fraction.

Now, let's work through each step:

Step 1: Convert the mixed number $1\frac{1}{5}$ into an improper fraction. The integer part is 1 and the fraction part is $\frac{1}{5}$. The improper fraction becomes:

$\frac{5 \times 1 + 1}{5} = \frac{6}{5}$

Step 2: Divide $\frac{1}{4}$ by the improper fraction $\frac{6}{5}$. This is equivalent to multiplying $\frac{1}{4}$ by the reciprocal of $\frac{6}{5}$:

$\frac{1}{4} \div \frac{6}{5} = \frac{1}{4} \times \frac{5}{6}$

Perform the multiplication:

$\frac{1 \times 5}{4 \times 6} = \frac{5}{24}$

Step 3: The resulting fraction $\frac{5}{24}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{5}{24}$. The correct choice is option 4.