45 63 simplified

2 min read 26-02-2025

The fraction 45/63 might look daunting at first, but simplifying it is easier than you think! Simplifying a fraction, also known as reducing it to its lowest terms, means finding an equivalent fraction where the numerator (top number) and denominator (bottom number) have no common factors other than 1. This guide will walk you through the process of simplifying 45/63 step-by-step.

Finding the Greatest Common Divisor (GCD)

The key to simplifying fractions lies in finding the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers evenly. There are a couple of ways to find the GCD:

Method 1: Listing Factors

List the factors of 45: 1, 3, 5, 9, 15, 45
List the factors of 63: 1, 3, 7, 9, 21, 63
Identify the common factors: 1, 3, 9
The greatest common factor is 9.

Method 2: Prime Factorization

This method is particularly useful for larger numbers.

Find the prime factorization of 45: 3 x 3 x 5 (3²) x 5
Find the prime factorization of 63: 3 x 3 x 7 (3²) x 7
Identify the common prime factors: 3 x 3 = 9
The greatest common factor is 9.

Simplifying the Fraction

Now that we've found the GCD (which is 9), we can simplify the fraction:

Divide both the numerator and the denominator by the GCD: 45 ÷ 9 = 5 and 63 ÷ 9 = 7
The simplified fraction is 5/7.

Therefore, 45/63 simplified is 5/7.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and work with. A simplified fraction represents the same value as the original fraction, but in a more concise and manageable form. This is crucial for further calculations and comparisons.

Practice Makes Perfect!

Try simplifying other fractions using these methods. The more you practice, the easier it will become to identify the GCD quickly and efficiently. Remember, the goal is always to find the largest number that divides both the numerator and the denominator without leaving a remainder.

Other Examples of Fraction Simplification

Here are a few more examples to help you grasp the concept:

12/18: The GCD of 12 and 18 is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3. Simplified fraction: 2/3
20/25: The GCD of 20 and 25 is 5. 20 ÷ 5 = 4 and 25 ÷ 5 = 5. Simplified fraction: 4/5
16/24: The GCD of 16 and 24 is 8. 16 ÷ 8 = 2 and 24 ÷ 8 = 3. Simplified fraction: 2/3

Mastering fraction simplification is a fundamental skill in mathematics. By understanding the concepts of GCD and prime factorization, you can confidently simplify any fraction. Remember to always divide both the numerator and denominator by their greatest common divisor to arrive at the simplest form of the fraction.