Simplifying Fractions: A Step-by-Step Guide
When working with fractions, simplification is a crucial concept in mathematics. It allows us to express fractions in their lowest terms, making them easier to understand and work with. In this article, we will explore the process of simplifying fractions, with a specific focus on simplifying the fraction 15/60.
Simplifying 15/60: Step-by-Step Guide
To simplify the fraction 15/60, we need to find the Greatest Common Factor (GCF), which is the largest number that divides evenly into both the numerator and denominator.
Step 1: Find the GCF
To find the GCF of 15 and 60, we can use different methods such as listing the factors, prime factorization, or using a calculator. In this example, let’s use the listing method:
The factors of 15 are: 1, 3, 5, 15
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
By comparing the factors, we can see that the largest number that divides evenly into both 15 and 60 is 15. Therefore, the GCF of 15 and 60 is 15.
Step 2: Divide by the GCF
Once we have found the GCF of 15 and 60, we can proceed to the next step, which is dividing both the numerator and denominator by the GCF. This division will simplify the fraction by reducing it to its lowest terms:
15 ÷ 15 = 1
60 ÷ 15 = 4
After dividing both the numerator and denominator by the GCF, we get the simplified fraction:
15/60 = 1/4
In conclusion, we have successfully simplified the fraction 15/60 to its simplest form, which is 1/4. By using the steps of finding the GCF and dividing by the GCF, we can simplify any fraction to its lowest terms. Simplifying fractions not only helps us understand and compare them easily but also makes mathematical calculations and problem-solving more manageable.
Remember, when simplifying fractions, it’s essential to find the GCF and divide both the numerator and denominator by it. Practice simplifying fractions with different numerators and denominators to strengthen your skills in fraction simplification.