what is 66/20 simplified

2 min read 02-02-2025

The fraction 66/20 might look daunting at first, but simplifying it is easier than you think! This article will guide you through the process, showing you how to reduce this fraction to its simplest form. We'll cover the key concepts and provide a step-by-step solution. By the end, you'll understand not just the answer, but the method behind it, allowing you to simplify other fractions with confidence.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator (the top number) and the denominator (the bottom number), and then dividing both by that GCD. The result is an equivalent fraction that's easier to work with.

Finding the Greatest Common Divisor (GCD) of 66 and 20

The first step in simplifying 66/20 is to find the greatest common divisor (GCD) of 66 and 20. There are several ways to do this:

Method 1: Listing Factors

List all the factors of 66 and 20:

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 20: 1, 2, 4, 5, 10, 20

The largest number that appears in both lists is 2. Therefore, the GCD of 66 and 20 is 2.

Method 2: Prime Factorization

This method is particularly useful for larger numbers. We break down each number into its prime factors:

66 = 2 x 3 x 11
20 = 2 x 2 x 5

The only common prime factor is 2. Therefore, the GCD is 2.

Simplifying the Fraction

Now that we know the GCD is 2, we can simplify the fraction:

66/20 = (66 ÷ 2) / (20 ÷ 2) = 33/10

Therefore, the simplified form of 66/20 is 33/10.

Expressing the Answer as a Mixed Number

While 33/10 is perfectly acceptable, we can also express it as a mixed number. To do this, we perform the division:

33 ÷ 10 = 3 with a remainder of 3.

So, 33/10 can be written as 3 3/10.

Conclusion: 66/20 Simplified

We've successfully simplified the fraction 66/20. Through finding the greatest common divisor (GCD) and dividing both the numerator and denominator by it, we arrived at the simplified fraction 33/10, which can also be expressed as the mixed number 3 3/10. Remember, understanding the process of finding the GCD is key to simplifying any fraction effectively. Practice makes perfect, so try simplifying other fractions using these methods!