Exercises

1. Use the concept of money, such as assets and debts, to explain your answers for each of the following subtractions:
   1. \(5-2\)
   2. \(9-12\)
   3. \((-3)-5\)
   4. \((-7)-(-3)\)
2. In each of the following, predict the sign of the answer and then evaluate the difference.
   1. \(7-10\)
   2. \(17-25\)
   3. \(50-125\)
   4. \((-8)-(-5)\)
   5. \((-15)-(-18)\)
3. The difference between two integers is \(0\).  What is always true about the values of these two integers?
4. The difference between two integers is \(-6\).  One of the integers is \(-9\).  What are the possible values of the other integer?
5. The summit of Mount Everest, the highest point on Earth, is \(8848\) metres above sea level.  The lowest point on Earth, \(10~994\) metres below sea level, is found in the Marianas Trench in the western Pacific Ocean.  What is the change in elevation between these two extremities on Earth?  Represent the change in elevation as a difference of integers.
6. Patricia has two sets of numbers. In the first set are the numbers from \(-356\) to \(-234\) and in the second set are the numbers from \(-120\) to \(-64\). Patricia chooses one number from each set and can subtract the numbers in either order.
   1. What is the greatest difference that she can make?
   2. What is the least difference that she can make?
7. On the number line, an increase in value corresponds to moving to the right, whereas a decrease in value corresponds to moving to the left. Use a number line to complete the table and indicate whether the difference between the two integers is less than or greater than the first integer.

   Sign of First Integer \(-\) Sign of Second Integer		Value Compared to First Integer
   positive \(-\) positive		less than integer 1
   positive \(-\) negative
   negative \(-\) positive
   negative \(-\) negative

8. Addition is commutative, but subtraction is not commutative.  However, we can rewrite any subtraction problem as the addition of the first integer and the opposite of the second integer. For example, \(7-8=7+(-8)=(-8)+7\). Try two more examples and then explain, in words, why rewriting the subtraction of two integers in this way does not contradict the statement that "subtraction is not commutative."