Problem 42 - Fundamentals of Mathematics

Question

For the following 4 problems, perform the indica ted operations When a particular machine is operating properly, its meter will read \(34 .\) If a broken bearing in the machine causes the meter reading to drop by 45 units, what is the meter reading?

Step-by-Step Solution

Answer

The meter reading is -11.

Step 1: Understanding the Problem

We are given that the machine's meter reads 34 when operating correctly. If a broken bearing causes the reading to drop by 45 units, we need to find the new meter reading.

Step 2: Setting Up the Equation

To determine the new meter reading, we start with the original reading of 34. Since the bearing malfunction causes this reading to decrease by 45 units, we will subtract 45 from 34.

Step 3: Performing the Calculation

Calculate the new reading by subtracting 45 from 34. This is done as follows: \[ 34 - 45 = -11 \]

Step 4: Interpreting the Result

The result of the calculation shows that the meter reading is -11, indicating that the meter reading is negative due to the significant drop caused by the broken bearing.

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation that represents the process of taking one quantity away from another. It is often phrased as "finding the difference" between numbers. To perform subtraction, start with the number from which you want to subtract, called the "minuend," and the number being subtracted, known as the "subtrahend." In our example, the original meter reading is the minuend at 34, and the value dropped, 45, is the subtrahend.

The subtraction is set up as:

• Original meter reading: 34
• Minus the drop caused by the broken bearing: 45

The task is to compute \(34 - 45\). In straightforward cases, the minuend is larger than the subtrahend, resulting in a positive number. However, as we can see here, subtraction does not always lead to positive results, leading us to the next topic - understanding negative numbers.

Negative Numbers

Negative numbers are numbers less than zero, and they are denoted with a minus sign (-). They often represent a decrease or deficit, like in our exercise where the machine's meter reading dropped significantly.

When performing subtraction that results in a negative result, think of it as the amount needed to reach zero, and then continue into negative territory to reach the total difference. So, when we calculated \(34 - 45\), the result \(-11\) means there is a deficit equivalent to 11 units lower than zero.

• Negative numbers are crucial in representing values below a certain standard reference, such as temperatures below freezing or below a baseline functioning rate.
• They add a significant layer of understanding in real-world numerical applications.

Recognition of negative results is important in problem interpretations, ensuring the conditions meet the real-world scenario described.

Problem Solving

Problem-solving involves both understanding the problem and applying the appropriate operations to find the solution. First, break down the problem into understandable parts: recognize what's known and what's the desired outcome.

In the exercise, you start with identifying the machine's correct reading and understanding the effect of the broken bearing drop.

• Translate the problem into an equation: Here, it was \(34 - 45\).
• Perform the necessary mathematical operations: In the form of subtraction.
• Interpret the result: Understanding that a negative result indicates a substantial drop beyond zero.

Apply these structured steps of problem-solving to systematically tackle similar arithmetic problems, ensuring clarity in both process and results.