35 48 simplified

2 min read 01-03-2025

The fraction 35/48 represents a part of a whole. Simplifying, or reducing, a fraction means finding an equivalent fraction where the numerator (top number) and denominator (bottom number) are smaller. This makes the fraction easier to understand and work with. Let's learn how to simplify 35/48.

Finding the Greatest Common Divisor (GCD)

The key to simplifying fractions is 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 all the factors (numbers that divide evenly) of 35 and 48:

Factors of 35: 1, 5, 7, 35
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest number that appears in both lists is 1.

2. Prime Factorization

This method is more efficient for larger numbers. Break down each number into its prime factors (numbers divisible only by 1 and themselves):

35 = 5 x 7
48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

Since there are no common prime factors between 35 and 48, their GCD is 1.

Simplifying the Fraction

Because the GCD of 35 and 48 is 1, the fraction 35/48 is already in its simplest form. We cannot reduce it further. Dividing both the numerator and denominator by the GCD (which is 1) doesn't change the fraction's value.

Therefore, the simplified form of 35/48 is 35/48.

Understanding Irreducible Fractions

A fraction that cannot be simplified further is called an irreducible fraction. 35/48 is an example of an irreducible fraction because its numerator and denominator share no common factors other than 1.

Practical Applications

Simplifying fractions is a fundamental skill in mathematics with many real-world applications:

Baking: Recipes often use fractions. Simplifying fractions can make measurements easier to understand and work with.
Construction: Precise measurements are crucial in construction. Simplifying fractions helps ensure accuracy.
Finance: Working with budgets and financial statements often involves fractions. Simplifying makes these calculations clearer.

This comprehensive guide explains how to simplify fractions, emphasizing the importance of finding the greatest common divisor. While 35/48 is already in its simplest form, understanding the process is crucial for simplifying other fractions. Remember to always look for common factors to reduce the fraction to its lowest terms.