Introduction

Understanding how to convert numbers into fractions, particularly percentages, is a crucial skill in mathematics. In this post, we'll explore how to convert 120 into its simplest fractional form. This involves taking the percentage 120, expressing it as a fraction over 100, and then simplifying it to its simplest form. We'll cover various methods and provide a clear explanation along with examples for easy understanding.

Expressing 120 as a Fraction

To start, let's express 120 as a fraction. When we say 120%, we can write it as:

120 frac{120}{100}

This is the simplest way to represent 120 as a fraction, where the numerator is 120 and the denominator is 100.

Simplifying the Fraction

Next, we need to simplify the fraction frac{120}{100}. To do this, we look for the greatest common divisor (GCD) of 120 and 100. The GCD of 120 and 100 is 20. We can simplify the fraction by dividing both the numerator and the denominator by their GCD:

frac{120 div 20}{100 div 20} frac{6}{5}

Thus, the simplest form of the fraction representing 120 is frac{6}{5}.

Alternative Methods

There are several other methods to simplify and express 120 as a fraction. Here, we'll look at a few different approaches:

Method 1: Starting with frac{120}{100} and canceling common zeros:

frac{120 div 10}{100 div 10} frac{12}{10}

Since both 12 and 10 are even numbers, we can further simplify by canceling the common factor of 2:

frac{12 div 2}{10 div 2} frac{6}{5}

Method 2: Directly using the fact that 120 is equivalent to 6/5:

120 frac{120}{100} frac{6}{5}

Method 3: Expressing 120 as a mixed number:

120 can also be expressed as 1 whole and a fraction part:

120 1 frac{1}{5}

This is equivalent to expressing 120 as a mixed fraction 1 frac{1}{5}, which can be converted to an improper fraction:

1 frac{1}{5} frac{5}{5} frac{1}{5} frac{6}{5}

Conclusion

In conclusion, converting 120 to a fraction in its simplest form involves expressing it as frac{120}{100} and then simplifying it to frac{6}{5}. This process can be achieved through various methods, from canceling common factors to converting to mixed numbers. Whether you use frac{6}{5}, 1 frac{1}{5}, or 1.2, the essence remains the same—understanding the relationship between percentages and fractions is key.