This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to subtract signed numbers. By the end of the module students should understand the definition of subtraction, be able to subtract signed numbers and be able to use a calculator to subtract signed numbers.
Section overview
- Definition of Subtraction
- The Process of Subtraction
- Calculators
Definition of subtraction
We know from experience with arithmetic that the subtraction
produces 3, that is
. We can suggest a rule for subtracting signed numbers by illustrating this process on the number line.
Begin at 0, the origin.
Since 5 is positive, move 5 units to the right.
Then, move
2 units to the left to get to 6. (This reminds us of addition with a negative number.)
From this illustration we can see that
is the same as
. This leads us directly to the definition of subtraction.
Definition of subtraction
If
and
are real numbers,
is the same as
, where
is the opposite of
.
The process of subtraction
From this definition, we suggest the following rule for subtracting signed numbers.
Subtraction of signed numbers
To perform the subtraction
, add the opposite of
to
, that is, change the sign of
and add.
Sample set a
Perform the indicated subtractions.
The high temperature today in Lake Tahoe was 26°F. The low temperature tonight is expected to be -7°F. How many degrees is the temperature expected to drop?
We need to find the difference between 26 and -7.
Thus, the expected temperature drop is 33°F.
Practice set a
Perform the indicated subtractions.
Calculators
Calculators can be used for subtraction of signed numbers. The most efficient calculators are those with a
key.
Sample set b
Use a calculator to find each difference.
Display Reads |
Type |
3187 |
3187 |
Press |
- |
3187 |
Type |
8719 |
8719 |
Press |
= |
-5532 |
Thus,
.
Method A:
Display Reads |
Type |
156 |
156 |
Press |
|
-156 |
Type |
- |
-156 |
Press |
211 |
211 |
Type |
|
-211 |
Press |
= |
55 |
Thus,
.
Method B:
We manually change the subtraction to an addition and change the sign of the number to be subtracted.
becomes
Display Reads |
Type |
156 |
156 |
Press |
|
-156 |
Press |
+ |
-156 |
Type |
211 |
211 |
Press |
= |
55 |
Practice set b
Use a calculator to find each difference.
Exercises
For the following 18 problems, perform each subtraction. Use a calculator to check each result.
For the following 4 problems, perform the indicated operations.
When a particular machine is operating properly, its meter will read 34. If a broken bearing in the machine causes the meter reading to drop by 45 units, what is the meter reading?
The low temperature today in Denver was
F and the high was
F. What is the temperature difference?
Exercises for review
(
[link] ) Convert
to a decimal.
(
[link] ) Convert
to a percent.
(
[link] ) Use the distributive property to compute the product:
.
(
[link] ) Find the sum:
.