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We know from experience with arithmetic that the subtraction $5-2$ produces 3, that is $5-2=\text{3}$ . 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 $5-2$ is the same as $\text{5}+(-2)$ . 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.
$5-3=5+(-3)=2$
$4-9=\text{4}+(-9)=-5$
$-4-6=-4+(-6)=-\text{10}$
$-3-(-\text{12})=-3+\text{12}=9$
$0-(-15)=\text{0}+\text{15}=\text{15}$
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.
$26-(-7)=\text{26}+\text{7}=\text{33}$
Thus, the expected temperature drop is 33°F.
$\begin{array}{ccc}-6-(-5)-10& =& -6+5+(-10)\hfill \\ & =& (-6+5)+(-10)\hfill \\ & =& -1+(-10)\hfill \\ & =& -11\hfill \end{array}$
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.
$\mathrm{3,}\text{187}-\mathrm{8,}\text{719}$
Display Reads | ||
Type | 3187 | 3187 |
Press | - | 3187 |
Type | 8719 | 8719 |
Press | = | -5532 |
Thus, $\mathrm{3,}\text{187}-\mathrm{8,}\text{719}=-\mathrm{5,}\text{532}$ .
$-\text{156}-(-\text{211})$
Method A:
Display Reads | ||
Type | 156 | 156 |
Press | -156 | |
Type | - | -156 |
Press | 211 | 211 |
Type | -211 | |
Press | = | 55 |
Thus, $-\text{156}-(-\text{211})=\text{55}$ .
Method B:
We manually change the subtraction to an addition and change the sign of the number to be subtracted.
$-\text{156}-\left(-\text{211}\right)$ becomes $-\text{156}+\text{211}$
Display Reads | ||
Type | 156 | 156 |
Press | -156 | |
Press | + | -156 |
Type | 211 | 211 |
Press | = | 55 |
Use a calculator to find each difference.
$\text{12}\text{.}\text{756}-\text{15}\text{.}\text{003}$
-2.247
$-\text{31}\text{.}\text{89}-\text{44}\text{.}\text{17}$
-76.06
For the following 18 problems, perform each subtraction. Use a calculator to check each result.
$\text{12}-7$
$\text{14}-\text{30}$
$-1-\text{12}$
$-\text{11}-\left(-8\right)$
$0-\text{15}$
$0-\left(-\text{10}\right)$
$\text{142}-\text{85}$
$\text{105}-\text{421}$
$-\text{15}\text{.}\text{016}-\left(4\text{.}\text{001}\right)$
For the following 4 problems, perform the indicated operations.
$-\text{15}-\text{21}-\left(-2\right)$
$-\text{104}-\left(-\text{216}\right)-\left(-\text{52}\right)$
164
$-0\text{.}\text{012}-\left(-0\text{.}\text{111}\right)-\left(0\text{.}\text{035}\right)$
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 $-4\xb0$ F and the high was $-\text{42}\xb0$ F. What is the temperature difference?
( [link] ) Convert $\text{16}\text{.}\text{02}\frac{1}{5}$ to a decimal.
16.022
( [link] ) Find 4.01 of 6.2.
( [link] ) Convert $\frac{5}{\text{16}}$ to a percent.
31.25%
( [link] ) Use the distributive property to compute the product: $\text{15}\cdot \text{82}$ .
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