Integers In The Real World Connecting Integers

Integers in The Real World Connecting Integers T

Imagine that you have graduated and obtained your ideal job! This project will help you connect what you have learned about integers to personal finances. In this project, you will: learn to describe income using an equation, evaluate your income based on given hours per week or a goal amount of money, and make reasonable conclusions about finances. Additionally, you will connect the idea of positive and negative integers to credits and debits within accounts.

To complete this project, you will: complete the Ideal Job Worksheet to develop your budget, showing all work; and write a 2-page, double-spaced, APA-formatted report. In this report, you must present your findings and explain the connection between your calculations and integers. Your report should include: what types of transactions are positive or negative, how to write an expression to determine your income, and how to formulate an equation to solve for the hours you need to work or the money you need to reach your financial goals.

Paper For Above instruction

The integration of integers into personal financial planning offers a practical framework for understanding everyday economic transactions. Positive integers in finance typically represent credits or gains, such as income, deposits, or any inflow of money to an account. Conversely, negative integers symbolize debits or losses, including expenses, withdrawals, or any carbon of money leaving an account. Understanding this fundamental distinction provides clarity in managing and forecasting personal finances.

To illustrate, consider the concept of describing income using an algebraic expression. If an individual earns a fixed hourly wage, their total weekly income can be expressed as an algebraic equation such as I = h × r, where I is the total income, h is the number of hours worked per week, and r is the rate of pay per hour. This straightforward expression highlights how positive integers directly affect income calculation, and variations in hours worked or pay rate will proportionally alter the total income. For example, if the hourly rate is $15, and the person works 40 hours a week, their income can be calculated as I = 40 × 15 = $600.

Next, evaluating income based on weekly hours or reaching a financial goal involves establishing equations that incorporate both positive and negative integers. Suppose an individual aims to save a certain amount per month while managing expenses. Saving money can be viewed as a positive integer (income), while expenses or withdrawals can be modeled as negative integers. If the target savings goal is S dollars over a period, the total income minus expenses should equal S, which can be expressed as an equation: Total Income - Total Expenses = S. Working backwards, one can determine how many hours to work or the necessary rate to meet that goal.

For instance, if the goal is to save $2,000 over three months, and the individual expects to earn $600 per week, their total income over three months (approximately 12 weeks) is 12 × $600 = $7,200. If their total expenses over that period are $5,000 (modeled as a negative integer sum), then the net savings is $7,200 - $5,000 = $2,200, which exceeds the goal. Conversely, if expenses are higher or income lower, the equations help determine the necessary adjustments in working hours or pay rate.

Understanding the nature of transactions is crucial. Income sources such as salaries or bonuses are positive transactions, increasing account balances, while expenses, taxes, or fees are negative transactions that decrease balances. Developing an expression or an equation to manage these variables allows individuals to plan effectively and make informed financial decisions. For example, setting an equation like Total Income = Hours Worked × Hourly Rate allows for flexible planning: adjusting hours or pay rate can help meet financial targets efficiently.

Effective budgeting involves applying these principles, where each income or expense is represented as an integer—positive for inflows, negative for outflows. Formulating equations to solve for variables such as hours needed to work or additional sources of income enables individuals to reach their financial goals systematically. This approach not only clarifies how integers function in real-world contexts but also enhances financial literacy and planning skills.

References

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• Financial Awareness Foundation. (2019). Understanding Income and Expenses. Retrieved from https://financialawarenessfoundation.org.
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• Investopedia. (2023). Debit and Credit Explained. Retrieved from https://www.investopedia.com.
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• McGraw-Hill Education. (2015). Mathematics for Life Skills. New York: McGraw-Hill.
• National Endowment for Financial Education. (2018). Managing Money with Mathematics. Retrieved from https://www.nefe.org.
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• U.S. Securities and Exchange Commission. (2022). Personal Finance Tips. Retrieved from https://www.sec.gov.