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2.3.1 Exercises

Add.

1. −6+ 19

2. 12 + (−4)

3. −34 + (−28)

4. 266 + (−265)

5. −133 + (−93)

6. −1001 + 909

Use an appropriate signed number addition for the following.

11. Find the temperature at noon in Anchorage if the temperature at dawn was −11 Fand, by noon,
◦
the temperature had risen by 36 F.
◦
12. Find the height (in feet above ground level) of an elevator which started 30 feet below ground level
and subsequently rose 70 feet.

2.3.2 Opposites, Identity

There are exactly two numbers at any given non-zero distance from 0,one negative and the other
√ √
positive. Pairs of numbers such as {−5, 5}, {− 2, 2}, {−π, π}, which are unequal but equidistant
from 0, and hence have the same absolute value, are called opposites.(0 is the only number which
is its own opposite, having absolute value 0.) To find the opposite of a nonzero number, we simply
change its sign.

Example 46. (a) The opposite of 11 is −11. (b) The opposite of −17 is 17.
Since there are only two possible signs, the opposite of the opposite of a number is the number we
started with.

The opposite of the opposite of N is N:

−(−N)= N.

Example 47. The opposite of the opposite of −5is −(−(−5)) = −5.

Suppose a nonzero number is added to its opposite, for example,3+(−3). Our rule for adding signed
numbers with opposite signs doesn’t quite work since it is not clear what the sign of the sum should
be. But in fact it doesn’t matter: the absolute value of the sum is 0, which has no sign. Accordingly,
−3 + 3 = 0. The tug-of-war picture helps here: if two people of exactly the same weight and strength
pull in opposite directions, the rope doesn’t move at all!

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