Sure, let's work through each part of the activity!
Activity
Part A
Write a rational number to express the initial loan amount as it relates to Quiana’s bank account.
The initial loan amount can be expressed as a negative rational number since it represents money owed. Thus, the initial loan amount is: -15,234.68
Part B
What is the sign of the rational number you wrote in part A for Quiana’s loan? What does the sign represent?
The sign of the rational number is negative (-). This negative sign represents that Quiana has a liability or debt – she owes this amount of money to the lender.
Part C
Write a rational number that represents the amount of the monthly payment from Quiana’s perspective.
The amount of the monthly payment that Quiana makes is: -247.43
Part D
Quiana made five equal monthly payments from her bank account. Which rational number shows something being removed five times?
To show the removal of the monthly payment five times, we can multiply the monthly payment by 5: -5 * 247.43
This means she is removing:
- (5 * 247.43) or -1237.15 (the total amount repaid after 5 months).
Part E
Now, write an expression using the two terms from parts C and D to represent the net change to Quiana’s loan as a result of her payments.
The net change in the loan from Quiana's perspective after 5 months of payments is: -15,234.68 + (- (5 * 247.43)) or -15,234.68 - 1237.15
Part F
One way to simplify expressions with negative terms is to distribute the -1s. Rewrite the expression from Part E, factoring out a -1 from any negative value.
Factoring out a -1, we get: -(15,234.68 + 1237.15)
Part G
Next, rewrite the expression by grouping the -1s and grouping the numbers that are not -1s.
This would be: -(15,234.68 + 1237.15)
Part H
Now find the product of the values that are not -1s and rewrite the expression using this product.
Calculate: 15,234.68 + 1237.15 = 16,471.83
Now express the equation: -16,471.83
Part I
Before we move on, what does multiplying a number by -1 mean?
Multiplying a number by -1 means changing its sign. If the number is positive, it becomes negative, and if it is negative, it becomes positive.
Part J
When simplifying the expression in part H, how many times will the sign change on the positive term? Will the final expression be positive or negative?
The sign will change once when factoring out the -1. Since the original expression is negative, the final expression will remain negative.
Part K
Simplify the expression in part H. Following the five payments, what is the net change in the loan amount from Quiana’s viewpoint?
The simplified expression is: -16,471.83
Thus, the net change to the loan following the five payments is a decrease of $16,471.83 from the original loan amount.
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
I would rate my work a 5. I clearly understood the process of representing the loan and payments as rational numbers and successfully simplified the expressions. I learned how important it is to keep track of both positive and negative values in a financial context, which can be challenging at times. Understanding how to work with negative numbers is crucial for modeling real-world financial situations accurately.
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