Page 39 - Algebra 1

Adding Real Numbers
Example
2
Find the sum. a. (-12) + 21
SOLUTION Since the numbers have different signs, find the difference of their absolute values. The sum is positive because ⎪-12⎥ < ⎪21⎥.
(-12) + 21 = 9
c. (3.2) + (-5.1)
SOLUTION Since the numbers have different signs, find the difference of their absolute values. The sum is negative because ⎪3.2⎥ < ⎪-5.1⎥.
(3.2) + (-5.1) = -1.9
Identifying Sets of Real Numbers Closed
Under Addition
Determine whether each statement is true or false. Give a counterexample for false statements.
a. The set of integers is closed under addition.
SOLUTION The statement is true because the sum of any two integers will
be an integer.
b. The set of real numbers is closed under addition.
SOLUTION The statement is true because the sum of any two real numbers will be a real number.
Application: Football
On the first down, the Cougars lost 4 yards. They gained 7 yards on the second down. Use addition to find the total number of yards lost or gained on the first two downs.
SOLUTION A loss of 4 yards can be expressed as -4. (-4) + 7 = 3
The Cougars gained a total of 3 yards on the first two downs.
b. (-19) + (-8)
SOLUTION Since the numbers have the same sign, find the sum of their absolute values. The sum is negative because both addends are negative.
(-19) + (-8) = -27 d. (-_3)+(-_1)
SOLUTION Since the numbers have the same sign, find the sum of their absolute values. The sum is negative because both addends are negative.
55
(-_3 )+ (-_1 )= (-_4 ) 555
Example
3
Math Language
A set of numbers is closed under a given operation if the outcome of the operation on any two members of the set is also a member of
the set.
Example
4
24 Saxon Algebra 1