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We know from our experience with arithmetic that the subtraction
$5-2$ produces 3, that is,
$5-2=3$ . Illustrating this process on the number line suggests a rule for subtracting signed numbers.
We begin at 0, the origin.
Since 5 is positive, we move 5 units to the right.
Then, we move
2 units to the left to get to 3. (This reminds us of addition with a negative number.)
This illustration suggests that
$5-2$ is the same as
$5+(-2)$ .
This leads us directly to the definition of subtraction.
The preceding definition suggests the rule for subtracting signed numbers.
Perform the subtractions.
$5-3=5+(-3)=2$
$4-9=4+(-9)=-5$
$-4-6=-4+(-6)=-10$
$-3-(-12)=-3+12=9$
$0-(-15)=0+15=15$
The high temperature today in Lake Tahoe was
${26}^{\circ}\text{F}$ . The low temperature tonight is expected to be
$-{7}^{\circ}\text{F}$ . How many degrees is the temperature expected to drop?
We need to find the difference between 26 and
$-7$ .
$26-(-7)=26+7=33$
Thus, the expected temperature drop is ${33}^{\circ}\text{F}$ .
$\begin{array}{lll}-6-(-5)-10\hfill & =\hfill & -6+5+(-10)\hfill \\ \hfill & =\hfill & (-6+5)+(-10)\hfill \\ \hfill & =\hfill & -1+(-10)\hfill \\ \hfill & =\hfill & -11\hfill \end{array}$
Perform the subtractions.
$9-6$
3
$6-9$
$-3$
$0-7$
$-7$
$1-14$
$-13$
$-8-12$
$-20$
$-21-6$
$-27$
$-6-(-4)$
$-2$
$8-(-10)$
18
$1-(-12)$
13
$86-(-32)$
118
$0-16$
$-16$
$0-(-16)$
16
$0-(8)$
$-8$
$5-(-5)$
10
$24-(-(-24))$
0
For the following exercises, perform the indicated operations.
$8-3$
5
$12-7$
$5-6$
$-1$
$14-30$
$2-15$
$-13$
$5-18$
$1-7$
$-6$
$4-11$
$-6-5$
$-11$
$-8-14$
$-1-12$
$-13$
$-4-4$
$-6-8$
$-14$
$-1-12$
$-5-(-3)$
$-2$
$-11-(-8)$
$-7-(-12)$
5
$-2-(-10)$
$-4-(-15)$
11
$-11-(-16)$
$-1-(-6)$
5
$-8-(-14)$
$-15-(-10)$
$-5$
$-11-(-4)$
$-16-(-8)$
$-8$
$-12-(-11)$
$0-6$
$-6$
$0-15$
$0-(-7)$
7
$0-(-10)$
$67-38$
29
$142-85$
$816-1140$
$-324$
$105-421$
$-550-(-121)$
$-429$
$-15.016-(4.001)$
$-26+7-52$
$-71$
$-15-21-(-2)$
$-104-(-216)-(-52)$
164
$-0.012-(-0.111)-(0.035)$
$\left[5+(-6)\right]-\left[2+(-4)\right]$
1
$\left[2+(-8)\right]-\left[5+(-7)\right]$
$\left[4+(-11)\right]-\left[2+(-10)\right]$
1
$\left[9+(-6)\right]-\left[4+(-12)\right]$
$(11-8)-(1-6)$
8
$(5-12)-(4-10)$
$(1-10)-(2-15)$
4
$(0-8)-(4-12)$
$(-4+7)-(2-5)$
6
$(-6+2)-(5-11)$
$\left[-8+(-5+3)\right]-\left[9-(-3-5)\right]$
$-27$
$\left[-4+(-1+6)\right]-\left[7-(-6-1)\right]$
$\left[2-(-6+10)\right]-\left[1-(2-11)\right]$
$-12$
$\left[5-(-2-5)\right]-\left[2-(-1-4)\right]$
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 $-{4}^{\circ}\text{F}$ and the high was ${42}^{\circ}\text{F}$ . What is the temperature difference?
( [link] ) Use the distributive property to expand $4x(5y+11)$ .
$20xy+44x$
( [link] ) Simplify $\frac{2{(3{x}^{2}{y}^{2})}^{3}{(2{x}^{4}{y}^{3})}^{0}}{27{x}^{4}{y}^{3}}$ . Assume $x\ne 0,y\ne 0$ .
( [link] ) Simplify $\left|-\left({4}^{2}+{2}^{2}-{3}^{2}\right)\right|$ .
11
( [link] ) Find the sum. $-8+(-14)$ .
( [link] ) Find the sum. $3+(-6)$ .
$-3$
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