Problem 21 - Technical Mathematics with Calculus

Question

A stretch of roadway \(1858.54 \mathrm{m}\) long is to be divided into 5 equal sections. Find the length of each section.

Step-by-Step Solution

Answer

Each section of the roadway is 371.708 meters long.

Step 1: Understand the Problem

We need to divide a stretch of roadway that is 1858.54 meters long into 5 equal sections. This requires us to divide the total length by the number of sections.

Step 2: Divide the Total Length by Number of Sections

Perform the division of the total length of the roadway (1858.54 meters) by the number of sections (5) to find the length of each section. The calculation is: \( 1858.54 \div 5 = 371.708 \) meters.

Step 3: Conclusion

The length of each of the 5 equal sections of the roadway is 371.708 meters.

Key Concepts

Mathematical Problem-Solving

Understanding mathematical problem-solving is essential not just in academics, but in daily life as well. This process typically starts with identifying and comprehending the problem. For instance, in our exercise, we needed to determine how to split a given roadway into five equal parts. With any problem, it's crucial to break it down into manageable steps that guide us to the solution.

After understanding the problem, we devised a strategy by recognizing that we needed to divide the total length by the number of equal sections desired. Checking our work is a final—and significant—step often overlooked. In our case, multiplying the length of one section by the number of sections should bring us back to our original roadway length if done correctly. This systematic approach is what underpins successful mathematical problem-solving.

Division of Quantities

The division of quantities is a fundamental concept of arithmetic that involves splitting a single quantity into multiple equal parts. In our roadway example, we divided the total length by the number of sections to find each section's length. Understanding how division works is central to many practical applications, from slicing a pizza equally among friends to allocating resources in a project.

One of the tips for effective division is to ensure the quantity being divided is accurately measured or counted. Small errors can lead to incorrect results when divided. Also, considering the context is essential—sometimes, the results don't need to be exact, and estimations can suffice, especially when dealing with natural measurements, like the length of a road.

Mathematical Operations

Mathematical operations, including addition, subtraction, multiplication, and division, are the building blocks of more complex mathematical problem-solving. Each operation has a specific purpose and set of rules. Division, for example, can be thought of as the process of determining how many times one number is contained within another, or dividing something into equal parts, as we see in our road-dividing problem.

The correct application of mathematical operations is critical. In real-life scenarios, mistakes in these operations can lead to significant issues, such as construction faults, financial discrepancies, and more. Therefore, it's imperative to have a solid grasp of these operations and practice regularly to minimize errors and enhance problem-solving efficiency.