Let's go through each part step by step to help Quiana with her loan calculations.
Part A
Write a rational number to express the initial loan amount as it relates to Quiana’s bank account.
The initial loan amount, from Quiana's perspective, can be expressed as: \[ -15,234.68 \] This negative sign indicates that this is money she owes.
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 is negative (-). This indicates that Quiana has a debt or liability; she does not have this amount in her bank account but owes it to the lender.
Part C
Write a rational number that represents the amount of the monthly payment from Quiana’s perspective.
The monthly payment can be expressed as: \[ -247.43 \] This negative sign indicates money being paid out of her account.
Part D
Quiana made five equal monthly payments from her bank account. Which rational number shows something being removed five times?
The total payment over five months is the monthly payment multiplied by 5: \[ 5 \times (-247.43) = -1,237.15 \]
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 expression that represents the net change to her loan would be: \[ -15,234.68 + (-1,237.15) \] This can also be written as: \[ -15,234.68 - 1,237.15 \]
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 -1 gives: \[ -(15,234.68 + 1,237.15) \]
Part I
Before we move on, what does multiplying a number by -1 mean?
Multiplying a number by -1 means changing its sign. A positive number becomes negative, and a negative number 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?
There will be no sign changes on the positive term itself since it's being grouped together. The overall expression remains negative because the outer operation is to negate the sum. Thus, the final expression will be 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?
First, we need to calculate the sum inside the parentheses: \[ 15,234.68 + 1,237.15 = 16,471.83 \]
Then the expression becomes: \[ -16,471.83 \] This means that after the five payments, the net change in the loan amount from Quiana’s viewpoint is a decrease in debt of $1,237.15, but her total remaining loan amount is now $16,471.83.
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.
Rating: 5
In this exercise, I learned how to handle negative values in the context of a loan and methodically break down the components of the problem. I found the calculations straightforward but keeping track of the sign changes while performing addition and subtraction with negative amounts required careful attention. Overall, this exercise has reinforced my understanding of rational numbers in financial situations.
2 answers