16/60 simplified

2 min read 05-02-2025

Simplifying Fractions: A Step-by-Step Guide to 16/60

Title Tag: Simplify 16/60: Easy Fraction Reduction Guide

Meta Description: Learn how to simplify the fraction 16/60 step-by-step. This guide provides a clear explanation and practical examples to master fraction reduction. Improve your math skills with our easy-to-understand tutorial!

Understanding Fraction Simplification

Simplifying a fraction, also known as reducing a fraction to its lowest terms, means finding an equivalent fraction where the numerator (top number) and denominator (bottom number) have no common factors other than 1. This makes the fraction easier to understand and work with. Our goal is to simplify 16/60.

Finding the Greatest Common Factor (GCF)

The key to simplifying fractions is finding the greatest common factor (GCF) of the numerator and denominator. The GCF is the largest number that divides both numbers evenly. Let's find the GCF of 16 and 60.

One way to find the GCF is by listing the factors of each number:

Factors of 16: 1, 2, 4, 8, 16
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The largest number that appears in both lists is 4. Therefore, the GCF of 16 and 60 is 4.

Simplifying 16/60

Now that we know the GCF is 4, we can simplify the fraction:

Divide both the numerator and the denominator by the GCF:

16 ÷ 4 = 4 60 ÷ 4 = 15
The simplified fraction is: 4/15

Therefore, 16/60 simplified is 4/15.

Another Method: Prime Factorization

Another method to find the GCF is using prime factorization. This involves breaking down each number into its prime factors (numbers only divisible by 1 and themselves).

Prime factorization of 16: 2 x 2 x 2 x 2 (or 2⁴)
Prime factorization of 60: 2 x 2 x 3 x 5 (or 2² x 3 x 5)

The common prime factors are two 2s (2²). Multiplying these together gives us the GCF of 4. We then divide the numerator and denominator by 4, as shown above, to arrive at 4/15.

Checking Your Work

It's always a good idea to double-check your work. Make sure the numerator and denominator of your simplified fraction (4/15) have no common factors other than 1. In this case, they don't, so we know our simplification is correct.

Conclusion

Simplifying fractions is a fundamental skill in mathematics. By understanding the concept of the greatest common factor and applying the steps outlined above, you can easily simplify any fraction, including 16/60, which simplifies to 4/15. Remember to practice regularly to build your confidence and proficiency. Now you can tackle more complex fractions with ease!