what is 20 of 144

2 min read 22-12-2024

Finding a fraction's simplest form is a fundamental math skill. This article will guide you through simplifying the fraction 20/144. We'll break down the process step-by-step, making it easy to understand and apply to other fractions. Understanding how to simplify fractions is crucial for various applications, from basic arithmetic to more advanced mathematical concepts.

Understanding Fraction Simplification

Before we dive into simplifying 20/144, let's quickly review the concept. Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number) and dividing both by it. The result is an equivalent fraction that's easier to work with.

Finding the Greatest Common Divisor (GCD) of 20 and 144

The first step to simplifying 20/144 is to find the greatest common divisor (GCD) of 20 and 144. The GCD is the largest number that divides both 20 and 144 without leaving a remainder. There are several methods to find the GCD; we'll use the prime factorization method.

Prime Factorization Method

Prime Factorization of 20: We break down 20 into its prime factors: 2 x 2 x 5 (or 2² x 5).
Prime Factorization of 144: We break down 144 into its prime factors: 2 x 2 x 2 x 2 x 3 x 3 (or 2⁴ x 3²).
Identifying Common Factors: Comparing the prime factorizations, we see that both 20 and 144 share two factors of 2.
Calculating the GCD: The GCD is the product of the common prime factors, which is 2 x 2 = 4.

Simplifying 20/144

Now that we've found the GCD (4), we can simplify the fraction:

Divide both the numerator (20) and the denominator (144) by the GCD (4):

20 ÷ 4 = 5 144 ÷ 4 = 36
Therefore, the simplified fraction is 5/36.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and work with. A simplified fraction provides a clearer representation of the value, making calculations and comparisons more straightforward. It's also essential for consistency in mathematical operations and problem-solving.

Practice Makes Perfect

Try simplifying other fractions using the same method. Start with smaller numbers, then gradually increase the difficulty. The more you practice, the faster and more confident you'll become in simplifying fractions. Remember, mastering fraction simplification is a valuable skill with wide-ranging applications in mathematics and beyond.

Conclusion

Simplifying 20/144 to its simplest form, 5/36, involves finding the greatest common divisor of the numerator and denominator and then dividing both by that number. This process is fundamental to working effectively with fractions in various mathematical contexts. Remember to practice regularly to build your skills and confidence.