Transcript Algebra 2

Algebra 2
1.2: Operations on Real Numbers
Adding Two Negative Numbers
Add their absolute values, then put the negative
sign in front:
a) -12 + (-8)  (12  8)  20
b) -6 + (-3)  (6  3)  9
c) -1.2 + (-0.4)  (1.2  0.4)  1.6
5
1

d)        5  1    5  2    7
6  3
6
 6 3
6 6
Adding Numbers With Different Signs
Find the difference of the absolute values, then
give the answer the sign of the larger
absolute value:
a) -17 + 11  17  11  6
b) 4 + -1  4 1  3
c) -9 + 17  17  9  8
d)  4  2   12  10   12  10    2
5 3
15 15
15
 15 15 
Subtracting Real Numbers
Change the subtraction to an addition, then
follow the rules of addition:
a) 6 – 8  6  (8)  (8  6)  2
8  5  8 5 13
b)       
3  3 3 3 3
Adding and Subtracting Real Numbers
Work from left to right:
a) -8 + 5 – 6  (8  5)  6
 3  6
 9
b) 15 – (-3) – 5 – 12  (15  3)  5  12
 18  5  12
 13  12
1
Multiplying Real Numbers
The product of two numbers with the same sign is positive.
The product of two numbers with different signs is negative.
3
5

a)      15  5
4  3
12 4
b)
2  3
6
2
 3  3   1    3  2
 
3
Dividing Real Numbers
To divide, multiply by the reciprocal of the second number (the number
you are dividing by).
The quotient of two nonzero numbers with the same sign is positive.
The quotient of two nonzero numbers with different signs is negative.
1
12
a)  12  4  12 
   3
4
4
2
b)
3 2 5 2 9 18 6






5 3 9 3 5 15 5
9
CAUTION!!!
1. A number and its additive inverse always
have the opposite sign. However, a number
and its reciprocal always have the same sign.
2. Division by zero is undefined, however, zero
can be divided by a nonzero number.
Example:
6
 undefined
0
0
0
6
Equivalent Forms of a Fraction
x
x
x
 
y
y y
Also :
x x

y y