Decoding the Quarter of One Tenth of 120: A Comprehensive Guide

In this article, we will explore the mathematical concept of finding the quarter of one tenth of 120. This simple yet intriguing problem involves both division and fractions. We will break down the steps and provide various methods to ensure a clear understanding for all readers.

Understanding the Problem

The problem asks us to find the quarter (1/4) of one tenth (1/10) of 120. Let's start by breaking down the problem into simpler parts.

Step-by-Step Solution

Method 1: Direct Division

First, let's find one tenth of 120:

Calculate one tenth of 120:

120 / 10  12

Next, find one quarter of 12:

12 / 4  3

The answer is 3. This method follows a straightforward and intuitive approach.

Method 2: Simplified Fraction Calculation

We can also approach this problem by directly calculating the fraction:

Find one tenth of 120:

1/10 x 120  12

Find one quarter of 12:

1/4 x 12  3

Alternatively, if we are dealing with base 3, the problem can be reinterpreted:

Convert 120 in base 3 to base 10:

120 base 3  3^2   2*3^1   0  9   6   0  15

Find one tenth of 15:

1/10 x 15  15 / 10  1.5

Find one quarter of 1.5:

1/4 x 1.5  0.375

However, the typical interpretation of the problem stays with base 10, yielding 3.

Revisiting the Problem with Different Interpretations

Interpretation via Algebraic Formulation

Let's express the problem algebraically:

Define the equation:

y  1/4 x 1/10 x 120

Calculate the expression step-by-step:

1/10 x 120  12

Find one quarter of 12:

1/4 x 12  3

Thus, the quarter of one tenth of 120 is 3.

Interpretation via Unitary Method

Another method to solve the problem is using the unitary method:

Calculate one tenth of 120:

120 / 10  12

Find one quarter of 12:

12 / 4  3

This method ensures that each step is clearly understood and easy to follow.

Conclusion

The quarter of one tenth of 120 is 3. This problem demonstrates the importance of breaking down complex calculations into simpler, manageable parts. Whether you are using direct division, fraction multiplication, or algebraic formulation, the final answer remains consistent.