To simplify the fraction 13/250, we need to find the greatest common divisor (GCD) of the numerator (13) and the denominator (250). The GCD is the largest number that divides both 13 and 250 without leaving a remainder.
Step-by-Step Simplification Process
First, let’s list the factors of 13 and 250 to identify any common factors. The factors of 13 are 1 and 13, since 13 is a prime number. The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
Identifying the Greatest Common Divisor
By comparing the factors of 13 and 250, we find that the only common factor is 1. This means that the GCD of 13 and 250 is 1. When the GCD is 1, it indicates that the fraction is already in its simplest form because there is no common factor other than 1 to divide both the numerator and the denominator.
| Numerator | Denominator | GCD | Simplified Fraction |
|---|---|---|---|
| 13 | 250 | 1 | 13/250 |
Conclusion on Simplification
In conclusion, the fraction 13⁄250 is already simplified because its numerator and denominator have no common divisors other than 1. This is a key property of fractions in their simplest form, making them essential for precise calculations and expressions in mathematics.
What if the GCD is greater than 1?
+If the GCD of the numerator and the denominator is greater than 1, you can simplify the fraction by dividing both the numerator and the denominator by the GCD. This process reduces the fraction to its simplest form.
How does simplifying fractions help in calculations?
+Simplifying fractions makes calculations easier and more efficient. It reduces the numbers involved, making it simpler to perform operations like addition, subtraction, multiplication, and division, especially when dealing with complex fractions.
