Problem 94 - Intermediate Algebra

Question

Answer the question with an algebraic expression. Larry's annual salary is \(d\) dollars. What is his monthly salary?

Step-by-Step Solution

Answer

\(\frac{d}{12}\)

Step 1: Understand the Problem

We know Larry's annual salary is given as \(d\) dollars. We need to find his monthly salary.

Step 2: Recognize the Concept of Time Periods

Larry's salary is currently given for a whole year. Since a year has 12 months, we need to find the salary for one month.

Step 3: Division by Time Period

To find the monthly salary, we divide the annual salary by the number of months in a year. Thus, his monthly salary is \(\frac{d}{12}\).

Key Concepts

Annual Salary

When we talk about annual salary, we're referring to the total amount of money a person earns over an entire year. An annual salary is typically expressed in a yearly sum, like "Larry's annual salary is \(d\) dollars."
Understanding one's annual salary is crucial because it offers a complete picture of earnings and helps in planning long-term finances.

• It acts as a baseline for budgeting and saving.
• It's also used to assess financial performance and determine credit eligibility.

Many jobs pay on an annual basis, yet money might be received more frequently, such as monthly or bi-weekly.
This salary structure allows employees and employers to understand the earning potential and financial commitments for the year.

Monthly Salary

Understanding how to calculate a monthly salary from an annual salary provides clearer insights into monthly earnings. A monthly salary is simply the amount you earn in one month and is derived by dividing the annual salary by 12, the number of months in a year.
This division is useful for understanding monthly budgets and expenses.

• If Larry's annual salary is \(d\) dollars, his monthly salary would be \(\frac{d}{12}\).
• This calculation helps assess how much you can spend or save each month.

Knowing the monthly salary also aids in setting realistic financial goals since most bills and expenses are calculated monthly.

Division in Algebra

Division in algebra can help break down complex ideas into manageable pieces, such as dividing annual salaries to find out monthly salaries. Algebraic division involves dividing an algebraic expression by a number or another expression.
To divide algebraically:

• Identify the total amount, like \(d\), which is Larry's annual salary.
• Decide the divisor, the number you're dividing by, which here is 12 months.
• The result gives how much is earned per month, \(\frac{d}{12}\).

Using algebra to solve real-world problems helps with logical reasoning and practical applications like financial planning. It's an essential skill that shows the power of mathematics in everyday life.