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The addition of the two positive numbers 2 and 3 is performed on the number line as follows.
Begin at 0, the origin.
Since 2 is positive, move 2 units to the right.
Since 3 is positive, move 3 more units to the right.
We are now located at 5.
Thus, $\text{2}+\text{3}=\text{5}$ .
Summarizing, we have
$(\text{2 positive units})+(\text{3 positive units})=(\text{5 positive units})$
The addition of the two negative numbers -2 and -3 is performed on the number line as follows.
Begin at 0, the origin.
Since -2 is negative, move 2 units to the left.
Since -3 is negative, move 3 more units to the left.
We are now located at -5.
Thus, $(-2)+(-3)=-5$ .
Summarizing, we have
$(\text{2 negative units})+(\text{3 negative units})=(\text{5 negative units})$
Observing these two examples, we can suggest these relationships:
$(\text{positive number})+(\text{positive number})=(\text{positive number})$
$(\text{negative number})+(\text{negative number})=(\text{negative number})$
Find the sums.
$3+7$
$\left(\begin{array}{ccc}\left|3\right|& =& 3\\ \left|7\right|& =& 7\end{array}\right\}$ Add these absolute values.
$3+7=10$
The common sign is “+.”
Thus, $\text{3}+\text{7}=+\text{10}$ , or $\text{3}+\text{7}=\text{10}$ .
$(-4)+(-9)$
$\left(\begin{array}{ccc}|-4|& =& 4\\ |-9|& =& 9\end{array}\right\}$ Add these absolute values.
$4+9=13$
The common sign is “ $-$ .“
Thus, $(-4)+(-9)=-\text{13}$ .
Find the sums.
$\text{8}+\text{6}$
14
$\text{41}+\text{11}$
52
$(-4)+(-8)$
-12
$\left(-\text{36}\right)+\left(-9\right)$
-45
$-\text{14}+\left(-\text{20}\right)$
-34
$-\frac{2}{3}+\left(-\frac{5}{3}\right)$
$-\frac{7}{3}$
$-2\text{.}8+(-4\text{.}6)$
$-7\text{.}4$
$0+(-\text{16})$
$-\text{16}$
The addition $\text{2}+(-6)$ , two numbers with unlike signs , can also be illustrated using the number line.
Begin at 0, the origin.
Since 2 is positive, move 2 units to the right.
Since -6 is negative, move, from 2, 6 units to the left.
We are now located at -4.
We can suggest a rule for adding two numbers that have unlike signs by noting that if the signs are disregarded, 4 can be obtained by subtracting 2 from 6. But 2 and 6 are precisely the absolute values of 2 and -6. Also, notice that the sign of the number with the larger absolute value is negative and that the sign of the resulting sum is negative.
Find the following sums.
$\text{7}+(-2)$
$\underset{\text{value. Sign is positive.}}{\underset{\text{Larger absolute}}{\underbrace{\left|7\right|=7}}}$ $\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{|-2|=2}}}$
Subtract absolute values: $7-2=\text{5}$ .
Attach the proper sign: "+."
Thus, $\text{7}+(-2)=+5$ or $\text{7}+(-2)=\text{5}$ .
$\text{3}+(-11)$
$\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{\left|3\right|=3}}}$ $\underset{\text{value. Sign is negative.}}{\underset{\text{Larger absolute}}{\underbrace{|-11|=11}}}$
Subtract absolute values: $11-3=\text{8}$ .
Attach the proper sign: " $-$ ."
Thus, $3+(-11)=-8$ .
The morning temperature on a winter's day in Lake Tahoe was -12 degrees. The afternoon temperature was 25 degrees warmer. What was the afternoon temperature?
We need to find $-12+\text{25}$ .
$\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{|-12|=12}}}$ $\underset{\text{value. Sign is positive.}}{\underset{\text{Larger absolute}}{\underbrace{\left|25\right|=25}}}$
Subtract absolute values: $25-12=\text{16}$ .
Attach the proper sign: "+."
Thus, $-12+\text{25}=\text{13}$ .
Find the sums.
$\text{4}+(-3)$
1
$-3+5$
2
$\text{15}+(-\text{18})$
-3
$0+(-6)$
-6
$-\text{26}+\text{12}$
-14
$\text{35}+(-\text{78})$
-43
$\text{15}+(-10)$
5
$1\text{.}5+(-2)$
-0.5
$-8+0$
-8
$\text{0}+(0\text{.}\text{57})$
0.57
$-\text{879}+\text{454}$
-425
Calculators having the key can be used for finding sums of signed numbers.
Use a calculator to find the sum of -147 and 84.
Display Reads | |||
Type | 147 | 147 | |
Press | -147 | This key changes the sign of a number. It is different than $-$ . | |
Press | + | -147 | |
Type | 84 | 84 | |
Press | = | -63 |
Use a calculator to find each sum.
$\text{673}+(-721)$
-48
$-\mathrm{8,261}+\text{2,206}$
-6,085
$-\mathrm{1,345}\text{.}6+(-\mathrm{6,648}\text{.}1)$
-7,993.7
Find the sums in the following 27 problems. If possible, use a calculator to check each result.
$4+\text{12}$
16
$8+6$
$\left(-3\right)+\left(-\text{12}\right)$
-15
$\left(-6\right)+\left(-\text{20}\right)$
$\text{10}+\left(-2\right)$
8
$8+\left(-\text{15}\right)$
$-\text{16}+\left(-9\right)$
-25
$-\text{22}+\left(-1\right)$
$0+\left(-\text{12}\right)$
-12
$0+\left(-4\right)$
$0+\left(\text{24}\right)$
24
$-6+1+\left(-7\right)$
$-5+\left(-\text{12}\right)+\left(-4\right)$
-21
$-5+5$
$-7+7$
0
$-\text{14}+\text{14}$
$4+\left(-4\right)$
0
$9+\left(-9\right)$
$\text{84}+\left(-\text{61}\right)$
23
$\text{13}+\left(-\text{56}\right)$
$\text{452}+\left(-\text{124}\right)$
328
$\text{636}+\left(-\text{989}\right)$
$\mathrm{1,}\text{811}+(-\text{935})$
876
$-\text{373}+\left(-\text{14}\right)$
$-\mathrm{1,}\text{211}+\left(-\text{44}\right)$
-1,255
$-\text{47}\text{.}\text{03}+\left(-\text{22}\text{.}\text{71}\right)$
$-1\text{.}\text{998}+\left(-4\text{.}\text{086}\right)$
-6.084
In order for a small business to break even on a project, it must have sales of $21,000. If the amount of sales was $15,000, by how much money did this company fall short?
Suppose a person has $56 in his checking account. He deposits $100 into his checking account by using the automatic teller machine. He then writes a check for $84.50. If an error causes the deposit not to be listed into this person’s account, what is this person’s checking balance?
-$28.50
A person borrows $7 on Monday and then $12 on Tuesday. How much has this person borrowed?
A person borrows $11 on Monday and then pays back $8 on Tuesday. How much does this person owe?
$3.00
( [link] ) Find the reciprocal of $8\frac{5}{6}$ .
( [link] ) Find the value of $\frac{5}{\text{12}}+\frac{7}{\text{18}}-\frac{1}{3}$ .
$\frac{\text{17}}{\text{36}}$
( [link] ) Round 0.01628 to the nearest tenth.
( [link] ) Convert 62% to a fraction.
$\frac{\text{62}}{\text{100}}=\frac{\text{31}}{\text{50}}$
( [link] ) Find the value of $\mid -\text{12}\mid $ .
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