To simplify the fraction 13/250, we can follow these steps:
Step 1: Find the Greatest Common Divisor (GCD)
The GCD of two numbers is the largest number that can divide both of them without leaving a remainder. In this case, we need to find the GCD of 13 and 250.
One way to find the GCD is by listing the factors of each number and identifying the common factors. Here are the factors of 13 and 250:
- Factors of 13: 1, 13
- Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
The common factors between 13 and 250 are 1 and 13. Therefore, the GCD is 13.
Step 2: Divide Both Numerator and Denominator by the GCD
Now that we have found the GCD, we can simplify the fraction by dividing both the numerator and denominator by the GCD, which is 13.
13 ÷ 13 = 1
250 ÷ 13 ≈ 19.23 (rounded to two decimal places)So, the simplified fraction is 1/19.23 or 1/19 (rounded to the nearest whole number)
Conclusion
By following these steps, we have simplified the fraction 13/250 to its simplest form, which is 1/19. Remember, simplifying fractions helps reduce them to their lowest terms, making them easier to work with in various mathematical calculations.
What is a fraction, and why do we simplify it?
+A fraction represents a part of a whole or a ratio between two numbers. Simplifying a fraction is important because it reduces the fraction to its simplest form, making it easier to understand and work with in calculations.
Can all fractions be simplified?
+Yes, all fractions can be simplified. The process of simplifying a fraction involves finding the greatest common divisor (GCD) of the numerator and denominator and then dividing both by this GCD. This step ensures that the fraction is reduced to its simplest form.
What if the GCD is 1? Does it mean the fraction is already in its simplest form?
+Yes, if the GCD is 1, it indicates that the fraction is already in its simplest form. In such cases, no further simplification is needed.
