To simplify the fraction 19.625/1130419.625/11304, we need to follow a few steps involving conversion 19.625/11304Â and reduction. Let’s break down the process step by step.
Step 1: Convert the Decimal to a Fraction
The number 19.625 is a decimal, and we need to convert it to a fraction first.
19.625=19+0.62519.625 = 19 + 0.625
We know that:
0.625=62510000.625 = \frac{625}{1000}
To simplify 6251000\frac{625}{1000}, we find the greatest common divisor (GCD) of 625 and 1000.
GCD of 625 and 1000=125\text{GCD of 625 and 1000} = 125
625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
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}
Step 2: Form the Original Fraction
Now that we have 19.625 as a fraction, 1578\frac{157}{8}, we can form the original fraction:
157/811304\frac{157/8}{11304}
This can be rewritten as:
1578×11304=15790432\frac{157}{8 \times 11304} = \frac{157}{90432}
Step 3: Simplify the Fraction
Next, we simplify 15790432\frac{157}{90432}. We need to find the GCD of 157 and 90432 to reduce the 19.625/11304Â fraction to its simplest form.
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.
Since 157 does not divide 90432 evenly, the fraction 15790432\frac{157}{90432} is already in its simplest form.
Conclusion
The simplified form of the fraction 19.625/1130419.625/11304 is:
15790432\frac{157}{90432}