Question

You own 18 shares of stock in a computer company. The total value of the shares changes by \(-\$ 3.06 .\) By how much does the value of each share of stock change?

Short answer

The value of each share decreases by approximately -\$0.17.

Step-by-step solution

Identify the Total Change in Value

The total value of the shares changes by -\$3.06. This means that the total value decreases by \$3.06.

Identify the Number of Shares

There are 18 shares of stock in total. These shares were equally affected by the change in total value.

Calculate the Change in Value per Share

To find out the change in value of each share we divide the total change in value by the number of shares: \[-\$3.06 / 18\].

Key concepts

Algebraic Problem Solving

Understanding algebraic problem-solving is crucial for students to tackle a range of mathematical challenges. In the exercise given, we were asked to find out how much the value of each share of stock changed when the total value of 18 shares decreased by $3.06. The process of solving such algebraic problems typically involves breaking down the problem into smaller, manageable steps and applying arithmetic operations logically.

Firstly, decipher what is being asked. In this case, it's the change in value per share. Next, identify what you are given, which is the total change in value and the number of shares. From this, you can establish a relationship between these quantities, creating an equation to solve for the desired variable. This approach not only solves the immediate problem but also strengthens analytical skills and the ability to apply mathematical concepts in various real-world scenarios. When facing algebraic problems, always remember to slow down, break them into parts, and solve each piece methodically.

Division in Algebra

Division in algebra is a fundamental operation used when we need to split a quantity into equal parts. In our stock value change calculation, we used division to determine the change in value for each individual share from the total change. The total change, represented by \( -\$3.06 \), was divided by the number of shares, which is 18, as follows: \[ -\$3.06 / 18 \].

When we perform division in algebra, it's essential to comprehend two things: the dividend (the number to be divided) and the divisor (the number by which we divide). The result is known as the quotient. Moreover, keeping track of signs is crucial; a negative dividend and a positive divisor result in a negative quotient, which makes sense in financial contexts—the decrease in stock value in this case. Division is powerful in algebra; it simplifies expressions and solves for unknowns by distributing a collective amount into individual components.

Negative Numbers in Finance

In finance, negative numbers play a significant role in representing debts, losses, or decreases in value. The exercise presented involves a negative change in the total value of the shares, depicted by \( -\$3.06 \). This indicates that there is a decrease in the stock's overall worth.

Negative numbers can often seem intimidating, but in the context of finance, they provide clarity by distinctly showing the direction of a transaction or value change—positive for gains or additions, and negative for losses or subtractions. Having a firm grasp of how negative numbers are used in financial calculations is imperative for understanding market trends and the performance of investments. When dealing with such numbers, especially in division, remember that the sign of the quotient is determined by the rules of dividing positive and negative numbers. It also helps to associate negative figures with drawing funds out of an account, paying off debts, or, as in our example, a decrease in the value of stock investments.