35/48 in simplest form

Daniel Parker

2 min read

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28-02-2025

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Fractions represent parts of a whole. Sometimes, we need to express a fraction in its simplest form, also known as its lowest terms. This means reducing the fraction to its smallest equivalent fraction where the numerator and denominator have no common factors other than 1. Let's find the simplest form of the fraction 35/48.

Finding the Greatest Common Divisor (GCD)

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (35) and the denominator (48). The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.

One way to find the GCD is to list the factors of each number:

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

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

Alternatively, we can use the Euclidean algorithm, a more efficient method for larger numbers. However, in this case, the factors are easily identifiable.

Simplifying 35/48

Since the greatest common divisor of 35 and 48 is 1, we can't simplify the fraction further. This means 35/48 is already in its simplest form.

Therefore, the answer is: 35/48

Understanding Irreducible Fractions

A fraction that cannot be simplified further is called an irreducible fraction. These fractions are expressed in their lowest terms. In this case, 35/48 is an irreducible fraction because the numerator (35) and the denominator (48) share no common factors other than 1.

Practice Makes Perfect

Simplifying fractions is a fundamental skill in mathematics. Practice with various examples to build confidence and speed. Start with simpler fractions and gradually progress to more complex ones. Remember to always look for the greatest common divisor to ensure the fraction is in its simplest form. Using prime factorization can also be helpful in finding the GCD, especially for larger numbers.

Further Exploration: Working with Fractions

Understanding how to simplify fractions is crucial for various mathematical operations. It's essential when:

• Adding and Subtracting Fractions: You often need to find a common denominator before performing these operations. Simplifying the resulting fraction after calculation is important.
• Comparing Fractions: Simplifying allows for easier comparison of fractions.
• Solving Equations: Fractions often appear in equations, and simplification makes the solution process clearer and more efficient.
• Real-World Applications: Fractions are used in many everyday situations, from cooking and construction to finance. Knowing how to simplify them is essential for accuracy.

This article has shown you how to simplify the fraction 35/48. Remember, practice makes perfect when it comes to mastering fraction simplification!