Lindsay owes her cousin $9. This debt is represented by the integer -9. If Lindsay repays one third of this debt, which rational number represents her new debt to her cousin?

Answer 1

Lindsay's initial debt of $9 is represented by the integer -9. If she repays one third of this debt, we need to calculate how much she pays back.

One third of her debt is calculated as follows:

\[ \frac{1}{3} \times 9 = 3 \]

Now, if Lindsay pays back $3, we need to subtract this amount from her existing debt. To do this, we can represent the repayment of $3 as +3 (because paying back means reducing the debt).

So, we can express the new debt as:

\[ -9 + 3 = -6 \]

Therefore, after repaying one third of her debt, Lindsay's new debt to her cousin is represented by the rational number -6.