28 45 simplified

less than a minute read 11-03-2025

The fraction 28/45 represents a part of a whole. Sometimes, it's helpful to express this fraction in its simplest form. This means finding an equivalent fraction where the numerator (top number) and denominator (bottom number) have no common factors other than 1. Let's learn how to simplify 28/45.

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 without leaving a remainder. There are several ways to find the GCD:

1. Listing Factors

List the factors of 28: 1, 2, 4, 7, 14, 28
List the factors of 45: 1, 3, 5, 9, 15, 45

Comparing the lists, we see that the largest common factor is 1.

2. Prime Factorization

This method is especially useful for larger numbers.

Prime factorization of 28: 2 x 2 x 7 (2² x 7)
Prime factorization of 45: 3 x 3 x 5 (3² x 5)

Since there are no common prime factors between 28 and 45, their GCD is 1.

Simplifying the Fraction

Since the GCD of 28 and 45 is 1, the fraction 28/45 is already in its simplest form. We cannot simplify it further.

Therefore, the simplified form of 28/45 is 28/45.

Understanding Irreducible Fractions

A fraction that cannot be simplified further is called an irreducible fraction. This means the numerator and denominator share no common factors other than 1. 28/45 is an example of an irreducible fraction.

Practical Applications

Simplifying fractions is a fundamental skill in mathematics. It's used in various fields, including:

Baking and Cooking: Scaling recipes often requires simplifying fractions.
Engineering: Precise measurements frequently involve fractional calculations.
Construction: Accurate estimations rely on simplified fractions.

This detailed explanation should help you understand why 28/45 is already in its simplest form. Remember, the process involves finding the greatest common divisor and then dividing both the numerator and denominator by that GCD. In this case, the GCD is 1, meaning no simplification is possible.