What is 11304/19.625 ?

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=62510000.625 = \frac{625}{1000}0.625=1000625​

To simplify 6251000\frac{625}{1000}1000625​, we find the greatest common divisor (GCD) of 625 and 1000.

$\text{GCD of 625 and 1000}=125$

625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}1000÷125625÷125​=85​

So,

19.625=19+58=19×8+58=152+58=157819.625 = 19 + \frac{5}{8} = \frac{19 \times 8 + 5}{8} = \frac{152 + 5}{8} = \frac{157}{8}19.625=19+85​=819×8+5​=8152+5​=8157​

Step 2: Form the Original Fraction

Now that we have 19.625 as a fraction, 11304/19.625  1578\frac{157}{8}8157​, we can form the original fraction:

1130419.625=113041578\frac{11304}{19.625} = \frac{11304}{\frac{157}{8}}19.62511304​=8157​11304​

Step 3: Perform the Division

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

113041578=11304×8157\frac{11304}{\frac{157}{8}} = 11304 \times \frac{8}{157}8157​11304​=11304×1578​

Now, perform the multiplication:

11304×8157=90432157\frac{11304 \times 8}{157} = \frac{90432}{157}15711304×8​=15790432​

Step 4: Simplify the Fraction

Next, we simplify 90432157\frac{90432}{157}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:

90432157=576\frac{90432}{157} = 57615790432​=576

Conclusion

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

$576$