Problem 116 - Elementary Algebra

Question

The price of a share of one stock fell from \(\$ 8.75\) to \(\$ 8.54 .\) Find the percent decrease.

Step-by-Step Solution

Answer

The percent decrease is approximately 2.4%.

Step 1: Calculate the Difference in Price

Subtract the final price from the initial price to find the amount of decrease.\( \text{Decrease} = 8.75 - 8.54 = 0.21 \text{ dollars} \)

Step 2: Find the Decrease as a Fraction of the Initial Price

Divide the decrease by the initial price.\( \frac{0.21}{8.75} \)

Step 3: Convert the Fraction to a Percentage

Multiply the fraction by 100 to convert it to a percentage.\( \left( \frac{0.21}{8.75} \right) \times 100 \approx 2.4\% \)

Key Concepts

headline of the respective core concept

Percent decrease is a useful concept for understanding how much a value has gone down in comparison to its original value. To calculate the percent decrease, you first need to determine the difference between the initial and final values. Then, convert this difference into a fraction of the initial value. Finally, multiply by 100 to express it as a percentage. Percent decrease shows you the relative reduction—how much one quantity has become smaller compared to its starting point. This is particularly handy when analyzing prices, as it gives a clear picture of how much a stock, or any other item, has depreciated over time.

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Solving math problems step-by-step ensures you understand each part of the solution. Begin by identifying the different steps needed to solve the problem. In our stock price example, we first calculated the decrease in price by subtracting the new price from the original price. Next, we converted this decrease into a fraction of the initial price. Lastly, we converted that fraction into a percentage. Breaking down problems into smaller, manageable steps helps you understand the process and makes complicated problems much easier to tackle.
Follow these steps:

• Step 1: Calculate the Difference in Price.
• Step 2: Find the Decrease as a Fraction of the Initial Price.
• Step 3: Convert the Fraction to a Percentage.

headline of the respective core concept

Understanding stock price calculations can significantly improve your financial literacy. In our example, the price of a stock fell from \(\$8.75\) to \(\$8.54\). We first calculated the difference: \[ 8.75 - 8.54 = 0.21 \text{ dollars} \] to find out how much the price had decreased. This step is crucial as it lays the foundation for further calculations. Subtract the final price from the initial price to find the decrease. Knowing how to calculate such changes in stock prices can help you make informed decisions in investing and finance. Always keep track of initial prices to determine the value change accurately.

headline of the respective core concept

Converting fractions to percentages is a valuable math skill. It involves expressing a fraction as a part of 100. In our example, the decrease of \(0.21\) dollars was divided by the initial amount of \(8.75\) dollars to create a fraction: \(\frac{0.21}{8.75}\). To convert this fraction to a percentage, multiply it by 100: \(\frac{0.21}{8.75} \times 100 = 2.4\text{%} \). The result tells you how much the price decreased relative to the original price. This step is particularly useful in finance, as percentages provide a clear and standardized way to communicate changes in values.