Understanding the Calculation: What is One Half of One Quarter of One Tenth of 400?
The question may seem confusing initially, but breaking it down step by step can help clarify the process. What is one half of one quarter of one tenth of 400? This post will guide you through the steps to reach the final answer while also explaining various methods and the reasoning behind each of them.
Step-by-Step Calculation
To find the solution, we will follow a step-by-step process as outlined in the examples provided:
Find one tenth of 400:
400 ÷ 10 40
Find one quarter of 40:
40 ÷ 4 10
Find one half of 10:
10 ÷ 2 5
Therefore, the final answer is 5.
Alternative Methods of Calculation
Let's explore an alternative method that uses fractional multiplication:
Express the problem as a fraction: [frac{1}{2} times frac{1}{4} times frac{1}{10} times 400]
Simplify the expression: [frac{1}{2} times frac{1}{4} times frac{1}{10} times 400 frac{1}{2} times frac{1}{4} times 40 frac{1}{2} times 10 5]
The answer remains 5, confirming our previous calculations.
Using the J Programming Language
Another interesting approach is to use the J programming language, which provides a straightforward way to compute the value:
1r2 * 1r4 * 1r10 * 4005
The result is again 5, showing the consistency of the calculation across different methods.
Common Misinterpretations
It's important to note that the original question could be interpreted in different ways. For instance:
Option 1: Separate values: [frac{1}{2} times 400 200] [frac{1}{4} times 400 100] [frac{1}{10} times 400 40]
Option 2: Sum of values: [200 100 40 340]
While these interpretations change the final answer, the original question specifically asks for one half of one quarter of one tenth of 400, which is correctly answered as 5.
Conclusion
In summary, the calculation of one half of one quarter of one tenth of 400 leads to the answer 5. This can be achieved through multiple methods, including step-by-step division, fractional multiplication, or using specialized programming languages. Understanding these methods is crucial for tackling similar problems accurately and efficiently.