§ 2.5 Subtraction of Signed
Numbers
Subtract signed
numbers
Again, we can understand subtraction
of signed numbers in terms of money. Here are two examples:
(A.) In the expression, -7 - 5, the -7 can be thought of as "owing"
$7 or as $7 "below zero." Now, if you subtract
or "lose" five more dollars, you now are $12 below
zero. So we write -7 - 5 = -12.
OK, this next example helps explain why
subtracting a negative is tantamount to adding a positve.
(B.) Suppose you owe $7 to the telephone
company. In your finances, you consider this debt as a -7 dollars. But suppose that I'm a nice guy and I
say that I will "take away" or "subtract"
your phone bill from you. In other words, I will subtract your
negative from you and pay your bill. The net effect for you
is positive. You are $7 better off than you were before!
Exercise 2.5
A. Compute the following word
problems. Experiment, use whatever method you like best. Use
signed numbers to express your answer.
[1.] The temperature was 7 degrees below
zero and then dropped 5 degrees. What was the net result? I.e., -7 - 5 = ?
(Note: "I.e."
is short for Id est,
= "That is").
[2.] Hypatia had $12 in debts. Philammon
took an $8 debt away from her and paid it. What was her net
balance? I.e., -12 - -8 = ?
[3.] Chimma had 6 cents but then lost 6
cents. What was his net result? I.e., 6 - 6 = ?
[4.] The temperature was 15° when a
cold front began to pass over. Afterwards, the temperature had
dropped 21. What was the final temperature? I.e., 15 - 21 = ?
[5.] Sweeney Todd had an $8 debt for
barber supplies. A customer said that, in exchange for a haircut,
he would subtract Sweeny's debt by paying it for him. What was
Sweeny's balance after his customer took his debt away? Hint: -8 - -8 = ?
[6.] The Chicago Bears gained 14 yards
on first down but lost 8 on the next play. What was the net
result of the two plays? I.e., 14 - 8 = ?
[7.] The Bears gained 15 yards on the
first play but lost 5 yards on the next down. What was the net
result of the two plays?
[8.] -45 - 6 = ? E.g., the Green Bay Packers got a 45
yard loss on first down, then lost 6 more yards on second down.
What was the net result of the two plays?
[9.] 0 - -12 = ? E.g., suppose that you have no assets or
debts when Omar says that he will take away the next $12
of debt you incur and pay it for you. How would you represent
this in your finance book?
[10.] Suppose that you have $7 of debt.
Now dream that Uncle Sam says he will subtract $8 of your debt.
What would be the net credit for you? Hint: -7 - -8 = ?
B. Compute the following subtraction
problems. Think in terms of money, temperature, or football if
helpful.
| [11.] 0 - -386 =
|
|
[12.] -34 - 0 = |
| [13.] 5 - -2 =
|
|
[14.] 0 - -34 = |
| [15.] 26 - 71 =
|
|
[16.] 15 - -2.25 = |
[17.] The coldest temperature ever
recorded in Madison was -37F. This happened on January 30th, 1951. The
normal low for that day was 7F. How much colder was the record?
Hint: Find the difference: 7 - -37. ___________
C. Answer "true" or
"false."
[18.] Subtracting negative from negative
is always negative. ___________
|