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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.
From this definition, we suggest the following rule for subtracting signed numbers.
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.
Perform the indicated subtractions.
Calculators can be used for subtraction of signed numbers. The most efficient calculators are those with a key.
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 |
Use a calculator to find each difference.
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?
-11
The low temperature today in Denver was F and the high was F. What is the temperature difference?
( [link] ) Find 4.01 of 6.2.
( [link] ) Use the distributive property to compute the product: .
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