Problem 33 - Beginning and Intermediate Algebra

Question

Use a signed number to express each number in boldface italics. On Friday, November \(10,2017,\) the Dow Jones Industrial Average (DJIA) closed at 23,422.21 . On the previous day it had closed at \(23,461.94 .\) Thus, on Friday, it closed down 39.73 points. (Data from The Wall Street Journal.)

Step-by-Step Solution

Answer

-39.73

Step 1: Identify the Change in DJIA

The DJIA changed from 23,461.94 to 23,422.21. Calculate the difference: Difference = Previous Day's Close - Friday's Close 23,461.94 - 23,422.21 = 39.73 points.

Step 2: Determine the Sign of the Change

Since the DJIA closed down, the change in points is negative. Thus, the difference of -39.73 points.

Step 3: Express the Change as a Signed Number

The signed number expressing the change in DJIA on Friday, November 10, 2017, is -39.73.

Key Concepts

Calculating Differences

Calculating differences is a fundamental concept in algebra.
It's crucial for understanding how quantities change over time.
The difference is simply the result of subtracting one value from another.

In our example, we need to find out how much the DJIA changed from one day to the next.
To do this, subtract the closing value on Friday from the closing value on the previous day:
Difference = 23,461.94 - 23,422.21

This gives us 39.73 points.
Since we need to know the direction of the change (up or down), it's important to track whether the result is positive or negative. This will be discussed more in the next section.

Negative Numbers

Negative numbers are essential when dealing with changes in values, especially in algebra.
They indicate a decrease or a loss in quantity.
In our exercise, the DJIA closed down, meaning it decreased.

After calculating the difference of 39.73 points, we observe that the DJIA went down.
In algebra, a decrease is represented by a negative number.
Thus, the change in points is expressed as -39.73.

This negative sign is very important as it provides clear information that the difference was a decrease, not an increase. Without the negative sign, the difference of 39.73 could be misleading.

Real-World Applications of Algebra

Algebra is not just for solving abstract problems; it has numerous real-world applications.
One common application is in financial markets.
For instance, tracking the changes in the DJIA helps investors understand market trends.

Using signed numbers to express these changes is vital.
It provides a clear indication of whether the values are increasing or decreasing.
This kind of data is crucial for making informed financial decisions.

Algebraic calculations like these are used every day by analysts to predict future market movements.
Understanding this real-world application emphasizes the importance of mastering fundamental algebra concepts.