what is 20 of 135

Natashya

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25-12-2024

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What is 20 of 135? Understanding Percentages and Fractions

The question "What is 20 of 135?" can be interpreted in a couple of ways, most commonly as a fraction or a percentage. Let's explore both:

1. 20 as a Fraction of 135

To express 20 out of 135 as a fraction, we simply write 20 as the numerator (the top number) and 135 as the denominator (the bottom number):

20/135

This fraction can be simplified by finding the greatest common divisor (GCD) of 20 and 135. The GCD of 20 and 135 is 5. Dividing both the numerator and the denominator by 5, we get:

4/27

Therefore, 20 out of 135 is equivalent to the simplified fraction 4/27.

2. 20 as a Percentage of 135

To find the percentage, we need to determine what proportion 20 represents of 135. We can do this using the following formula:

(Part / Whole) * 100%

In this case:

(20 / 135) * 100% ≈ 14.81%

Therefore, 20 is approximately 14.81% of 135.

Calculating Percentages and Fractions: A Step-by-Step Guide

Here's a more general approach to calculating fractions and percentages:

1. Identify the Part and the Whole: Determine which number represents the "part" and which represents the "whole." In our example, 20 is the part, and 135 is the whole.

2. Form the Fraction: Write the part as the numerator and the whole as the denominator. This gives you 20/135.

3. Simplify the Fraction (optional): Find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD to simplify the fraction. Online calculators or manual methods can help find the GCD.

4. Convert to Percentage (optional): Divide the numerator by the denominator, and then multiply the result by 100% to express the fraction as a percentage.

Example using different numbers:

Let's say we want to find what 30 is out of 200.

1. Part: 30; Whole: 200
2. Fraction: 30/200
3. Simplified Fraction: 3/20 (after dividing both by 10)
4. Percentage: (30/200) * 100% = 15%

Conclusion

Understanding how to express a part of a whole as a fraction or percentage is a fundamental skill with applications in many areas, from everyday calculations to more complex mathematical problems. Whether you need to calculate discounts, determine proportions, or solve problems in finance or other fields, mastering these techniques will prove invaluable. Remember that the key is to accurately identify the "part" and the "whole" before applying the appropriate formula.