Directions

Question

Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
Quiana took out a loan to pay for a new car. Initially, she owed the lender $15,234.68. She has repaid $247.43 of the loan each month for the past 5 months. What is the net change to the loan from Quiana’s perspective over the past 5 months?

Complete the steps below to help Quiana calculate the loan amount that she’s repaid to the lender.

Part A
Write a rational number to express the initial loan amount as it relates to Quiana’s bank account.

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Part B
What is the sign of the rational number you wrote in part A for Quiana’s loan? What does the sign represent?

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Part C
Write a rational number that represents the amount of the monthly payment from Quiana’s perspective.

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Part D
Quiana made five equal montly payments from her bank account. Which rational number shows something being removed five times?

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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.

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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.

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Part G
Next, rewrite the expression by grouping the -1s and grouping the numbers that are not -1s.

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Part H
Now find the product of the values that are not -1s and rewrite the expression using this product.

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Part I
Before we move on, what does multiplying a number by -1 mean?

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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?

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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?

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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.

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Answer 1

Part A

To express the initial loan amount from Quiana’s perspective, we can represent it as a negative value because it represents money that she owes. Therefore, the rational number is:

-15,234.68

Part B

The sign of the rational number written in Part A is negative. This sign represents that Quiana's loan is a liability; it indicates money that she owes to the lender.

Part C

The rational number that represents the amount of the monthly payment from Quiana’s perspective is also negative, since it represents an outflow of cash. Therefore, it is:

-247.43

Part D

The rational number that shows something being removed five times is:

-247.43 * 5

Part E

To represent the net change to Quiana’s loan as a result of her payments, we can combine the amounts paid:

-15,234.68 + (-247.43 * 5)

Part F

Factoring out a -1 from the negative payment we have:

-15,234.68 - 1(247.43 * 5)

Part G

Now, we group the -1s and the numbers that are not -1s:

-1(247.43 * 5) - 15,234.68

Part H

Finding the product of the values that are not -1s:

First calculate \(247.43 * 5 = 1,237.15\).

Now we can write the expression as:

-1(1,237.15 + 15,234.68)

Part I

Multiplying a number by -1 means to change its sign. Thus, it converts a positive number to a negative one and vice versa.

Part J

When simplifying the expression in part H, the sign of the positive term will change one time due to the multiplication by -1. Therefore, the final expression will be negative.

Part K

Simplifying the expression from Part H leads to:

-1(1,237.15 + 15,234.68) = -1(16,471.83) = -16,471.83

The net change in the loan amount from Quiana’s viewpoint after her five payments is:

-1,237.15 (down from 15,234.68)

Self-Evaluation

I would rate my work a 5. I approached each question systematically and was able to follow the logic of the financial transactions clearly. I learned how to express loan amounts and payments as rational numbers and how to manipulate these numbers algebraically. The challenge was ensuring I did not confuse the signs when expressing outflows and simplifying products. Overall, I feel I grasped the concepts well and applied them correctly.