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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, .
Summarizing, we have
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, .
Summarizing, we have
Observing these two examples, we can suggest these relationships:
Find the sums.
Add these absolute values.
The common sign is “+.”
Thus, , or .
Find the sums.
The addition , 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.
Subtract absolute values: .
Attach the proper sign: "+."
Thus, or .
Subtract absolute values: .
Attach the proper sign: " ."
Thus, .
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 .
Subtract absolute values: .
Attach the proper sign: "+."
Thus, .
Find the sums.
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 |
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-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.
Find the sums in the following 27 problems. If possible, use a calculator to check each result.
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 .
( [link] ) Round 0.01628 to the nearest tenth.
( [link] ) Find the value of .
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