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Let us add the two positive numbers 2 and 3. We perform this addition on the number line as follows.
We begin at 0, the origin.
Since 2 is positive, we move 2 units to the right.
Since 3 is positive, we move 3 more units to the right.
We are now located at 5.
Thus,
.
Summarizing, we have
Now let us add the two negative numbers and . We perform this addition on the number line as follows.
We begin at 0, the origin.
Since
is negative, we move 2 units to the left.
Since
is negative, we move 3 more units to the left.
We are now located at
.
Thus, .
Summarizing, we have
These two examples suggest that
Find the sums.
Find the sums.
Notice that
Now let us perform the addition . These two numbers have unlike signs. This type of addition can also be illustrated using the number line.
We begin at 0, the origin.
Since 2 is positive, we move 2 units to the right.
Since
is negative, we move, from the 2, 6 units to the left.
We are now located at
.
A rule for adding two numbers that have unlike signs is suggested by noting that if the signs are disregarded, 4 can be obtained from 2 and 6 by subtracting 2 from 6. But 2 and 6 are precisely the absolute values of 2 and . 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.
The morning temperature on a winter's day in Lake Tahoe was degrees. The afternoon temperature was 25 degrees warmer. What was the afternoon temperature?
We need to find .
Thus, the afternoon temperature is 13 degrees.
Find the sums.
Find the sums for the the following problems.
In order for a small business to break even on a project, it must have sales of . If the amount of sales was , how much money did this company fall short?
Suppose a person has in his checking account. He deposits into his checking account by using the automatic teller machine. He then writes a check for . If an error causes the deposit not to be listed into this person's account, what is this person's checking balance?
A person borrows on Monday and then on Tuesday. How much has this person borrowed?
A person borrows on Monday and then pays back on Tuesday. How much does this person owe?
( [link] ) Simplify .
( [link] ) Simplify .
( [link] ) Determine the value of .
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