Reduce 48 80 To Lowest Terms

Reducing 48/80 to Lowest Terms: A Step-by-Step Guide

This article will guide you through the process of simplifying the fraction 48/80 to its lowest terms. Understanding how to reduce fractions is a fundamental skill in mathematics, crucial for various applications from basic arithmetic to advanced calculus. We'll explore different methods, ensuring you grasp the concept thoroughly. This is also a great example of simplifying ratios and proportions.

What does it mean to reduce a fraction to its lowest terms?

Reducing a fraction to its lowest terms, also known as simplifying a fraction, means finding an equivalent fraction where the numerator and denominator have no common factors other than 1. In simpler terms, you're finding the smallest possible version of that fraction.

Method 1: Finding the Greatest Common Factor (GCF)

This is the most efficient method for reducing larger fractions. The GCF is the largest number that divides evenly into both the numerator and the denominator.

1. Find the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

2. Find the factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

3. Identify the greatest common factor: Comparing the lists, we see that the largest number that appears in both lists is 16.

4. Divide both the numerator and the denominator by the GCF:

   48 ÷ 16 = 3 80 ÷ 16 = 5

Therefore, 48/80 reduced to its lowest terms is 3/5.

Method 2: Prime Factorization

This method is particularly useful for larger numbers where finding the GCF directly might be challenging.

1. Find the prime factorization of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

2. Find the prime factorization of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5

3. Identify common prime factors: Both 48 and 80 share four factors of 2 (2⁴).

4. Cancel out the common factors: We can cancel out 2⁴ from both the numerator and the denominator.

   (2⁴ x 3) / (2⁴ x 5) = 3/5

Again, we arrive at the simplified fraction of 3/5.

Method 3: Stepwise Simplification

This method involves repeatedly dividing the numerator and denominator by common factors until no common factors remain. It's less efficient than the GCF method but can be helpful for visualizing the simplification process.

1. Divide both by 2: 48/80 = 24/40
2. Divide both by 2 again: 24/40 = 12/20
3. Divide both by 2 again: 12/20 = 6/10
4. Divide both by 2 again: 6/10 = 3/5

This method also leads to the simplified fraction of 3/5.

Conclusion:

Regardless of the method used, reducing 48/80 to its lowest terms results in the simplified fraction 3/5. Choosing the most efficient method depends on your comfort level and the complexity of the fraction. Mastering fraction simplification is a valuable skill that will enhance your mathematical abilities. Remember to always look for common factors and simplify until you reach the lowest terms!