The document defines and provides examples of absolute value, operations on real numbers including addition, subtraction, multiplication and division of signed numbers, powers and roots. Absolute value of a number is its distance from the origin on a number line. Rules for addition and subtraction of signed numbers include adding/subtracting absolute values and determining the sign based on unlike or like signs. Multiplication and division of signed numbers involves multiplying/dividing absolute values and determining the sign based on the numbers having the same or different signs.

1. Absolute Value
The absolute value of a real number x, written as | x |, is the undirected distance of x from the
origin, thus
x if x > 0
| x | = 0 if x = 0
-x if x < 0
Examples:
a. | 11 | = 11
b. - | 4 | = -4
c. | 0 | = 0
d. |-66| = 66
e. - | -30 | = 30
f. - | 7 – 12 | = 5
g. | 45 – 28 | = 17
h. - |11 – 5 | = -6
i. - | -(-9) + (6) | = -15
j. | 4 – 7(2) – 4 | = 14
Operation on Real Numbers
1. Addition
To add two (or more) numbers of the same signs (like signs), add their absolute values
and affix to the sum the common sign.
To add two (or more) numbers of different signs (unlike signs), subtract the smaller
absolute value from the bigger absolute value and affix to the difference the sign of the
bigger absolute value.

2. Examples:
a. 15 + 31 = 46
b. (-5) + (-2) = -7
c. 6 + (-6) + (-6) = -6
d. 16 + 4(-4) + 16 = 16
e. (-4) + 6 + (-3) = -1
f. 6 + 2 + (-8) = 0
g. (-20) + (-16) + 2 = -34
h. 2 + 6 + (-4) + (-10) = -16
i. 4 + (-8) + (-5) = -9
j. 118 + (-60) + (-40) = 18
2. Subtraction
To subtract two signed numbers, change the signed of the subtrahend and proceed to
algebraic addition.
Examples:
a. 16 – 34 = 16 + (-34) = -18
b. 68 - (-47) = 68 + 47 = 115
c. (-21) – 34 = (-21) + (-34) = -55
d. (-46) – 76 = (-46) + (-76) = -122
e. 15 – 4 – (-24) =15 + (-4) + (-24) = -13
3. Multiplication
To multiply two signed numbers, multiply their absolute values and affix a positive sign
to the product if the numbers are of the same sign; otherwise, affix a negative sign.
Example:
a. (6)(5) = 30
b. (-32)(4) = -128
c. (-4)(-23) = 92
d. (7)(-89) = -623
e. (-6)(8)(-5) = 240

3. 4. Division
To divide two signed numbers, divide their absolute values and affix a positive sign to the
quotient if the numbers are of the same sign; otherwise, affix a negative sign.
Examples:
a. 66 ÷ 3 = 22
b. 99 ÷ (-11) = -9
c. (-224) ÷ (-8) = 28
d. 1000 ÷ (-250) = -4
e. (-480) ÷ (-16) = 30
Powers
an is read as “a to the nth power”; an = a * a * a * … * a …......
n factors
Any number raised to a zero, power is one.
Examples:
a. 25 = 2 x 2 x 2 x 2 x 2 = 32
b. 43(-5) = 4 x 4 x 4 x -5 = -320
c. 6(-6)0 = 6 x 1 = 6
d. (-14)0 = 1
e. (18)(-2)2 = 18 x -2 x -2 = 72
Roots
The nth root of a number a is a number which when raised to a power n, gives a, denoted
by √푎 푛 .
Examples:
a. √125 3 = 5 53 = 125
b. √225 = 15 152 = 225
c. √81 4 = 3 34 = 81
d. √400 = 20 202 = 400
e. √512 3 = 8 83 = 512