Properties of integers  absolute value, comparing, substraction, addition, double negative
The set of integers includes the whole numbers and their opposites; some common uses of integers include temperatures (24°F and 2°C) and finance (the Smiths' net worth is $83,500, and the Johnsons' net worth is $23,450)
The number line below illustrates the set of positive integers as well as the set of negative integers
Properties of integers table
ABSOLUTE VALUE of integers 
• The absolute value of a number is the distance the number is away from 0 on a number line • The absolute value of x is written in symbols as x; x = x if x > 0 or x = 0 and x = x if x < 0; that is, the absolute value of a number is always the positive value of that number EX: 6 = 6 and 6 = 6; the answer is positive 6 in both cases; this means the 6 and 6 are both 6 units away from 0 on a number line 
COMPARING and ORDERING INTEGERS 
• A number line can be used to help compare and order integers; on a horizontal number line, integers to the right are greater than integers to the left; when comparing two integers, use the symbols < (less than) and > (greater than); the symbol points to the lesser number

ADDITION of integers 
• If the signs of the numbers are the same, add; the answer has the same sign as the numbers • If the signs of the numbers are different, subtract; the answer has the sign of the number with the greater absolute value EX: (4) + (9) = 5 and (4) + (9) = 5 
SUBTRACTION of integers 
• Change subtraction to addition of the opposite number; a  b = a + (b); that is, change the subtraction sign to addition and also change the sign of the number directly after the subtraction sign to the opposite; then follow the addition rules EX: (8)  (12) = (8) + (12) = 4 and (8)  (12) = (8) + (12) = 20 and (8)  (12) = (8) + (12) = 4; note that the sign of the number in front of the subtraction sign never changes 
MULTIPLICATION and DIVISION 
• Multiply or divide, then follow these rules to determine the sign of the answer: • If the numbers have the same signs, the answer is positive • If the numbers have different signs, the answer is negative • It makes no difference which number is greater when you are trying to determine the sign of the answer EX: (2)(5) = 10 and (7)(3) = 21 and (18) + (6) = 3 
DOUBLE NEGATIVE of integers 
• (a) = a; that is, the sign in front of the parentheses changes the sign of the contents of the parentheses EX: (3) = 3 and (3) = 3 • (a + b) = a + (b) and (a  b) = a  (b) = a + b; that is, when a negative sign is in front of a quantity, the negative sign is distributed to each term in the quantity EX: 5(a + 6) = 5a  30 and 2(x  3) = 2x + 6 
RAISING A NEGATIVE TO A POWER 
• When a negative number is raised to a power, the negative number must be in parentheses; the values ax and (a)^{x} are not the same; in a^{x}, only a is raised to the power of x, and the final value is negative; in (a)^{x}, the final value is positive if x is even and negative if x is odd EX: 3^{4} = 81 and (3)^{4} = 81 
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