The problem is to evaluate the division of two numbers: a fraction $\frac{3}{10}$ divided by a mixed number $1\frac{1}{4}$.

1. Problem Description

The problem is to evaluate the division of two numbers: a fraction $\frac{3}{10}$ divided by a mixed number $1\frac{1}{4}$.

2. Solution Steps

First, we convert the mixed number $1\frac{1}{4}$ to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator. The result becomes the new numerator, and we keep the same denominator.

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

Now, we can rewrite the original problem as:

$\frac{3}{10} \div \frac{5}{4}$

To divide fractions, we multiply by the reciprocal of the second fraction:

$\frac{3}{10} \div \frac{5}{4} = \frac{3}{10} \times \frac{4}{5}$

Now we multiply the numerators together and the denominators together:

$\frac{3}{10} \times \frac{4}{5} = \frac{3 \times 4}{10 \times 5} = \frac{12}{50}$

Next, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 50 is

2. $\frac{12}{50} = \frac{12 \div 2}{50 \div 2} = \frac{6}{25}$

3. Final Answer

The final answer is $\frac{6}{25}$.