what is 40 of 180

Natashya

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27-12-2024

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So, you want to know what 40 out of 180 is? This question involves understanding fractions and how to express them in simpler terms, as well as converting them to percentages. Let's break it down step-by-step.

Understanding the Fraction 40/180

The phrase "40 of 180" can be written as the fraction 40/180. This means 40 out of a total of 180 parts. To understand its value, we need to simplify this fraction.

Simplifying the Fraction

Simplifying a fraction means reducing it to its lowest terms. We do this by finding the greatest common divisor (GCD) of both the numerator (40) and the denominator (180). The GCD is the largest number that divides both numbers evenly.

In this case, the GCD of 40 and 180 is 20. We divide both the numerator and the denominator by 20:

40 ÷ 20 = 2

180 ÷ 20 = 9

Therefore, the simplified fraction is 2/9. This means that 40 out of 180 is equivalent to 2 out of 9.

Converting to a Percentage

To express 40/180 (or its simplified equivalent, 2/9) as a percentage, we perform the following calculation:

(Numerator / Denominator) * 100%

Using the simplified fraction:

(2/9) * 100% ≈ 22.22%

Therefore, 40 out of 180 is approximately 22.22%.

Real-World Applications

Understanding fractions and percentages is crucial in many real-world scenarios. For example:

• Calculating test scores: If you answered 40 questions correctly out of a total of 180, your score would be approximately 22.22%.
• Determining proportions: If you have 40 apples out of a total of 180 fruits, apples make up about 22.22% of the total fruit.
• Analyzing data: In various fields, such as statistics and finance, working with fractions and percentages is essential for analyzing data and making informed decisions.

Conclusion

In conclusion, 40 out of 180 is equivalent to the fraction 2/9 and represents approximately 22.22%. Understanding how to simplify fractions and convert them to percentages is a valuable skill with wide-ranging applications. Remember that the simplified fraction 2/9 is often easier to understand and use in calculations than the original fraction 40/180.