what is 15 of 84

2 min read 26-12-2024

Finding the simplified form of a fraction like 15/84 might seem daunting, but it's a straightforward process involving finding the greatest common divisor (GCD). Let's break it down step-by-step.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the biggest number that divides evenly into both the numerator (top number) and the denominator (bottom number). This number is called the greatest common divisor (GCD) or greatest common factor (GCF). Once we find the GCD, we divide both the numerator and the denominator by it.

Finding the GCD of 15 and 84

To find the greatest common divisor of 15 and 84, we can use a few different methods. The most common are:

1. Listing Factors

List all the factors (numbers that divide evenly) of 15 and 84:

Factors of 15: 1, 3, 5, 15
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The largest number that appears in both lists is 3. Therefore, the GCD of 15 and 84 is 3.

2. Prime Factorization

This method involves breaking down each number into its prime factors (numbers divisible only by 1 and themselves):

Prime factorization of 15: 3 x 5
Prime factorization of 84: 2 x 2 x 3 x 7 (or 2² x 3 x 7)

The common prime factor is 3. Therefore, the GCD is 3.

Simplifying 15/84

Now that we know the GCD is 3, we divide both the numerator and the denominator by 3:

15 ÷ 3 = 5 84 ÷ 3 = 28

Therefore, the simplified form of 15/84 is 5/28.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and work with. It provides a more concise and manageable representation of the same value. For example, 5/28 is much easier to visualize and use in calculations than 15/84.

Other Examples of Fraction Simplification

Let's look at a couple of additional examples:

Example 1: Simplify 12/18. The GCD of 12 and 18 is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3. Therefore, 12/18 simplifies to 2/3.
Example 2: Simplify 20/25. The GCD of 20 and 25 is 5. 20 ÷ 5 = 4 and 25 ÷ 5 = 5. Therefore, 20/25 simplifies to 4/5.

By following these steps, you can confidently simplify any fraction. Remember to always find the greatest common divisor for the most reduced form. Practice makes perfect!