To simplify the fraction $11304/19.625$, we need to convert the decimal into a fraction first and then perform the division. Here’s the step-by-step process:

## Step 1: Convert the Decimal to a Fraction

The number **19.625** can be converted into a fraction.

$19.625=19+0.625$

We know that:

$0.625=1000625 $

To simplify $1000625 $, we find the greatest common divisor (GCD) of 625 and 1000.

$GCD of 625 and 1000=125$

$÷÷ =85 $

So,

$19.625=19+85 =8×+ =8+ =8157 $

## Step 2: Form the Original Fraction

Now that we have 19.625 as a fraction, 11304/19.625 $8157 $, we can form the original fraction:

$19.62511304 =8157 11304 $

## Step 3: Perform the Division

Dividing by a fraction is the same as multiplying by its reciprocal.

$8157 11304 =11304×1578 $

Now, perform the multiplication:

$157× =15790432 $

## Step 4: Simplify the Fraction

Next, we simplify $15790432 $. To do this, we need to see if the numerator and the denominator share any common factors.

First, let’s check if 157 is a** prime number**. It is, as it has no divisors other than 1 and itself.

Next, we need to see if 157 divides 90432.

$90432÷157=576$

Since 157 divides 90432 evenly, 11304/19.625 we can simplify the fraction to:

$15790432 =576$

## Conclusion

The simplified result of the fraction $11304/19.625$ is:

$576$