Question

question 1 - 6
bryan and jeanette were playing the integer card game. they were practicing adding and subtracting integers.
jeanette had a score of - 10. bryan took away one of jeanettes cards. he showed it to her. it was a - 8.
jeanette recalculated her score to be - 2, but bryan disagreed. he said that her score should be - 18 instead.
read their conversation and answer the question below.

o jeanette, removing a negative card means the same thing as subtracting a positive. so, negative 10 minus
negative 8 is negative 18.\
\it does not! removing a negative card is the same as adding the same positive card. my score will go up. negative
10 minus negative 8 is negative
2.\
based on their disagreement, who, if anyone, is right? explain why.

• show your thinking on your scratch sheet of paper.
• be sure to neatly organize your work.
• write your answer in the space below.

Explanation:

Step1: Analyze the operation

The original score is \(-10\). Removing a card with value \(-8\) means performing the operation \(-10-(-8)\).

Step2: Apply the rule for subtracting integers

The rule for subtracting integers is \(a - b=a+(-b)\). So, \(-10-(-8)=-10 + 8\).

Step3: Calculate the result

\(-10+8=-(10 - 8)=-2\) (using the rule for adding a negative and a positive integer: \(\vert - 10\vert=10\), \(\vert8\vert = 8\), and since \(10>8\), the result has the sign of the number with the larger absolute value).

Answer:

Jeanette is right. When we remove a negative card (subtract a negative number), according to the rule \(a-(-b)=a + b\). Here \(a=-10\) and \(b = 8\), so \(-10-(-8)=-10 + 8=-2\). Bryan made a mistake in applying the subtraction rule for integers.