what is 20 of 195

2 min read 28-02-2025

What is 20/195? Simplifying Fractions and Understanding Percentages

The question "What is 20/195?" asks us to determine the value of the fraction 20/195. This can be expressed as a simplified fraction, a decimal, or a percentage. Let's explore how to solve this and understand the different ways to represent the answer.

Simplifying the Fraction

The first step in understanding 20/195 is to simplify the fraction to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (20) and the denominator (195) and dividing both by it.

The GCD of 20 and 195 is 5. Dividing both the numerator and denominator by 5, we get:

20 ÷ 5 = 4 195 ÷ 5 = 39

Therefore, the simplified fraction is 4/39.

Converting to a Decimal

To convert the fraction 4/39 to a decimal, we simply divide the numerator (4) by the denominator (39):

4 ÷ 39 ≈ 0.10256

Rounding to three decimal places, we get approximately 0.103.

Expressing as a Percentage

To express the fraction as a percentage, we multiply the decimal value by 100:

0.10256 x 100 ≈ 10.256%

Rounding to one decimal place, we get approximately 10.3%.

Understanding the Result

So, 20 out of 195 represents:

A simplified fraction: 4/39
A decimal: Approximately 0.103
A percentage: Approximately 10.3%

This means that 20 is approximately 10.3% of 195. Understanding these different representations allows for a more comprehensive understanding of the relationship between the numbers. The simplified fraction provides the most concise mathematical representation, while the decimal and percentage offer more easily understandable interpretations in various contexts.

Practical Applications

This type of calculation is useful in many real-world scenarios. For example:

Calculating percentages in sales: If a store sold 20 items out of a total of 195, they could calculate their sales percentage.
Determining proportions in recipes: If a recipe calls for 195 grams of flour and you only want to use 20 grams, you can calculate the proportion.
Analyzing statistical data: In many fields, understanding proportions and percentages is crucial for analyzing data and drawing conclusions.

By understanding how to simplify fractions, convert to decimals and percentages, we can easily interpret the meaning of 20 out of 195 in any given situation.