Problem 7 - Prealgebra

Question

Find the percent of change. Round to the nearest tenth, if necessary. Then state whether the percent of change is a percent of increase or a percent of decrease. from \(25 \mathrm{cm}\) to \(36 \mathrm{cm}\)

Step-by-Step Solution

Answer

The percent change is 44%, and it is an increase.

Step 1: Determine the Change in Value

To find the percent of change, we first need to find the difference between the two values given. Here, subtract the original value from the new value: \[ 36 \text{ cm} - 25 \text{ cm} = 11 \text{ cm} \]

Step 2: Calculate the Percent Change

Next, to find the percent change, divide the change in value (found in Step 1) by the original value. Then, multiply the result by 100 to convert it to a percentage: \[ \frac{11}{25} \times 100 = 44 \% \]

Step 3: Identify the Type of Change

Determine whether this percent change is an increase or decrease. Since the final value of 36 cm is greater than the original value of 25 cm, this is a percent increase.

Key Concepts

Understanding Percent Increase

The concept of percent increase is fundamental in recognizing how a value grows over time or in different scenarios. To understand it, let's delve into a situation where we have an initial and a new value. In our exercise, the initial value is 25 cm, and the new value is 36 cm. The percent increase tells us how much larger the new value is compared to the original value in terms of percentage.
To find the percent increase, follow these steps:

• First, calculate the change in value. Subtract the original value from the new value: \(36 \text{ cm} - 25 \text{ cm} = 11 \text{ cm}\).
• Next, to convert this change to a percentage, divide the change by the original value: \(\frac{11}{25}\).
• Finally, multiply by 100 to get a percent: \(\frac{11}{25} \times 100 = 44\%\).

So, a 44% increase means the new value is 44% more than the original. Remember, if the new value is larger, it's a percent increase. If smaller, it would be a percent decrease.

Applying Mathematical Operations

Mathematical operations are essential tools for calculating the percent of change. In this specific exercise, several basic mathematical operations are employed, including subtraction, division, and multiplication. Each operation plays a crucial role in finding the percent of change accurately.
The subtraction step helps us find the change or difference in values. This initial computation gives us an understanding of how much the quantity has changed.
Next, division is used to determine how significant this change is in relation to the original amount. When you divide the change (11 cm) by the original amount (25 cm), you find the proportion of change relative to the start value.
Lastly, the multiplication by 100 converts this proportion into a percentage, making it a meaningful and easy-to-understand figure that represents the percent of change. Using these operations in sequence helps you unlock the solution and apply the concept of percent change in various contexts.

Enhancing Problem Solving Skills

Problem solving skills are nurtured by practicing exercises involving percent change. This type of problem prepares you for real-life scenarios by building analytical thinking skills and the ability to comprehend and calculate changes quantitatively.
To effectively solve a percent change problem, it's crucial to:

• Break down the problem into manageable steps (finding the change, original value, and performing calculations).
• Understand the relationships between values and recognize whether the change is an increase or decrease.
• Check your calculations to ensure the accuracy of the results.

Moreover, each problem-solving experience helps in honing skills that are applicable beyond math class. From budgeting personal finances to interpreting statistical data, the capability to assess percent changes can significantly enhance decision-making processes in everyday life.