Table of Contents
All Integer Numbers
Integers are all of the natural numbers and their negatives. The set of integers is {…, -3, -2, -1, 0, 1, 2, 3, …}. This set includes the counting numbers 1, 2, 3, etc., as well as the negative numbers -1, -2, -3, etc.
All About Integers
Integers are a set of whole numbers and their opposites. The set of integers is {…-3, -2, -1, 0, 1, 2, 3, …}
Integers can be positive or negative. 0 is the integer that represents no value.
Integers can be used in math operations, such as addition, subtraction, multiplication, and division.
Types of Integers
There are three types of integers: positive, negative, and zero. Positive integers are numbers that are greater than zero. Negative integers are numbers that are less than zero. Zero is the number that is equal to zero.
Arithmetic Rules for Integers
An integer is a whole number, and is represented by a number without a fractional component.
Integers can be addition, subtraction, multiplication, or division.
Addition:
The sum of two integers is the result of adding the two numbers together. For example, the sum of 3 and 5 is 8.
Subtraction:
The difference of two integers is the result of subtracting the two numbers. For example, the difference of 9 and 3 is 6.
Multiplication:
The product of two integers is the result of multiplying the two numbers. For example, the product of 3 and 5 is 15.
Division:
The quotient of two integers is the result of dividing the two numbers. For example, the quotient of 9 and 3 is 3.
Integers on a Number Line
-2, -1, 0, 1, 2
Graphing Integers on a Number Line
Integers can be graphed on a number line like this:
The integers on this number line are:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
Integer Operations
The six basic operations on real numbers are addition, subtraction, multiplication, division, square root, and cube root.
There are also a few other operations that can be performed on real numbers. These are the absolute value, the natural logarithm, and the exponential function.
The absolute value of a number is the distance of that number from zero on the number line. The natural logarithm of a number is the logarithm to the base of e. The exponential function of a number is the inverse of the natural logarithm.
Addition of Integers
The sum of two integers is the result of adding the two numbers together. For example, the sum of 5 and 7 is 12.
To add two integers, first line them up so that their columns match. Next, add the numbers in each column. Finally, bring the decimal place down one spot for each number in the sum.
For example, to add the numbers 5 and 7, first line them up like this:
5
7
Next, add the numbers in each column:
5 + 7 = 12
Finally, bring the decimal place down one spot:
1 + 2 = 3
Subtraction of Integers
To subtract two integers, find the difference between them.
For example, to subtract 5 from 8, find 5 − 8 = −3.
Rules of Integers
Integers are whole numbers that can be positive, negative, or zero.
Integers can be combined using the standard operations: addition, subtraction, multiplication, and division.
The order of operations applies when working with integers: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Properties of Integers
An integer is a whole number, and is represented by the symbol “∣”.
Integers can be positive or negative.
The set of all integers is denoted by the symbol ℤ.
Integers can be written in the form:
∣a
where a is an integer.
Integers can also be written in the form:
∣a±b
where a is an integer and b is a positive or negative number.
Comparing the Integers
The integers are all the whole numbers and their opposites. The following are all examples of integers:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
The following are not examples of integers:
6.5, -6.5, pi, -pi
Solved Examples
Question
A company has a debt of $10,000,000 and a market value of equity of $20,000,000. What is the company’s debt-to-equity ratio?
The company’s debt-to-equity ratio is 0.5.
