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QuestionCreate and solve a real-world addition problem with a rational number and its additive inverse, like x+(−x)x + (-x).

Studdy Solution

STEP 1

Assumptions1. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. . The additive inverse of a number is the opposite of that number, such that when it is added to the original number, the sum is zero.

STEP 2

Let's create a real-world problem using these concepts. Suppose you have a debt of 50(whichwe′llrepresentas−50,sinceowingmoneycanbethoughtofashavingnegativemoney).Then,youreceiveagiftof50 (which we'll represent as -50, since owing money can be thought of as having negative money). Then, you receive a gift of 50 (which is a positive50).The problem can be stated as follows "If you owe 50andthenreceiveagiftof50 and then receive a gift of 50, what is your new financial status?"

STEP 3

To solve this problem, we add the debt (a negative number) to the gift (a positive number).
Financial status=Debt+GiftFinancial\, status = Debt + Gift

STEP 4

Now, plug in the given values for the debt and gift to calculate the financial status.
Financial status=−$50+$50Financial\, status = -\$50 + \$50

STEP 5

Calculate the financial status.
Financial status=−$50+$50=$0Financial\, status = -\$50 + \$50 = \$0So, after receiving the gift, you no longer have any debt. You are at a financial status of $0.

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