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35/48 in simplest form

35/48 in simplest form

less than a minute read 05-02-2025
35/48 in simplest form

Fractions can seem intimidating, but simplifying them is a straightforward process. Let's break down how to simplify the fraction 35/48 to its simplest form. Understanding this process will help you tackle other fraction simplification problems with ease.

What Does "Simplest Form" Mean?

A fraction is in its simplest form when the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number) is 1. In other words, no number other than 1 can divide both the numerator and the denominator evenly.

Finding the Greatest Common Divisor (GCD)

The key to simplifying fractions lies in finding the GCD. There are a couple of ways to do this:

Method 1: Listing Factors

  1. List the factors of the numerator (35): 1, 5, 7, 35
  2. List the factors of the denominator (48): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  3. Identify the greatest common factor: The largest number that appears in both lists is 1.

Method 2: Prime Factorization

This method is particularly useful for larger numbers.

  1. Find the prime factorization of 35: 5 x 7
  2. Find the prime factorization of 48: 2 x 2 x 2 x 2 x 3 = 24 x 3
  3. Identify common factors: There are no common prime factors between 35 and 48.

Simplifying 35/48

Since the GCD of 35 and 48 is 1, the fraction 35/48 is already in its simplest form. There's no further simplification possible.

Why is Simplifying Fractions Important?

Simplifying fractions makes them easier to understand and work with. A simplified fraction provides a clearer representation of the value. It's essential for accurate calculations and problem-solving in various mathematical contexts.

Practicing Fraction Simplification

Try simplifying these fractions using the methods outlined above:

  • 12/18
  • 24/36
  • 15/25

By understanding the concepts of GCD and prime factorization, you can confidently simplify any fraction. Remember, the goal is to find the largest number that divides both the numerator and denominator evenly, reducing the fraction to its simplest form.

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