Numbers that appear to the Left of a given number are Less Than (
Zero is both a whole number and an even integer, but it is neither positive nor negative all factors of 12 since they all divide evenly into 12
Rational Numbers These are any numbers that can be expressed as a fraction, which includes all integers and most decimals Examples include - 1 2 , 208,
The integers are represented on the number line as follows : Fig 3 1 • All the positive integers lie to the right of 0 and the negative integers
Everyone has taken at least one class Or Everyone except one student in your class has an inter- universe of discourse is the set of all integers
The second digit can be any digit except equal to the first one, so it has 9 choices too There are 9 · 9 = 81 choices total Page 2 3-digit integers:
Q16 A monotonic integer is made of digits 1, 2, , 9, such that each subsequent digit is All of the following could be a possible value of v EXCEPT
A positive integer that is divisible by exactly two positive numbers, 1 and itself The result of adding all numbers and then dividing by the number of
Two quantifiers are nested if one is within the scope of the other Example: x y (x + y = 0) For every real numbers x and y, if x is positive and y
integers, maintaining all the fundamental laws of arithmetic multiplicative identity, meaning that a×1 = a for all integers a, but integer
7004_6math0300_integers_and_the_number_line.pdf
Integers and the Number Line
Positive Numbers (n): are numbers greater than zero; Negative Numbers (n): are numbers less than zero;
Math Symbols:
Read As
Extended definition n > 0; n is greater than zero Greater than (>): the open end contains the greater number sign (+) positive or plus Give value to a number or describes an mathematical operation n < 0; n is less than zero Less than (<): the closed end contains the lesser number sign (-) negative or minus Give value to a number or describes an mathematical operation -8 0 8
1. On the number line numbers get larger to as we move from Left to Right.
2. Numbers that appear to the Right of a given number are Greater Than (>) the given number.
3. Numbers that appear to the Left of a given number are Less Than (<) the given number.
Integers are -4, -3, -2, -1, 0, 1, 2, 3, 4
Zero is not negative or positive. Zero is the origin on the number line.
Example:
1a. On the number line what number is 5 units to the right of negative (-2)
-4 -3 -2 -1 0 1 2 3 4 5 spaces
Solution:
3 is 5 units to the right of (-2)
Math 0300Student Learning Assistance Center - San Antonio College1
Opposites
The distance from 0 to 3 on the number line is (3) three units. The distance from 0 to -3 on the number line is (3) three units. Two numbers that are the same distance from zero on the number line, but on opposite sides of zero are called
Opposites.
Example 1:
(-3) is opposite of (3) and (3) is opposite of (-3)
Note:
For a number (n): the opposite of (n) is (-n)
and the opposite of (-n) is (n)
Example 2:
a. - (3) = -3 The opposite of positive three is a negative three. b. - (-3) = 3 The opposite of negative three is a positive three.
Using Symbols:
Equation
Read As
1. 6 + 2 six plus two
2. +2 positive two
3. 6 - 2 six minus two
4. -2 negative two
Absolute Value:
Absolute Value of a number is the distance from zero to that number on the number line. a. That distance is never negative. b. The symbol for Absolute Value is " | | ". Math 0300Student Learning Assistance Center - San Antonio College2
Example of Absolute Value:
a. The distance from 0 to 3 is three units. Thus the | 3 | = 3 [The Absolute Value of 3 is 3]
b. The distance from 0 to -3 is three units. Thus the | - 3 | = 3 [The Absolute Value of - 3 is 3]
Note:
The Absolute Value of a positive number is positive. | 5 | = 5 The Absolute Value of a negative number is positive. | -5 | = 5 The Absolute Value of a Zero is Zero. | 0 | = 0 Math 0300Student Learning Assistance Center - San Antonio College3