Algebra is a discipline of mathematics that is about the study of mathematical symbols, constants, and their operations. Algebra includes basic mathematical operations like addition, subtraction, multiplication, and division for the analysis of these symbols. Algebraic expressions have known values and unknown values. Various operations are conducted to determine the value of these unknown quantities. The expressions consist of variables (an unknown value), coefficients,s, and integers or constants. Generally, there are two types of integers positive and negative. The article is composed of brief details about integers and the greatest negative integer.

Integers

Integers are the numbers that include all the positive as well as negative whole numbers. The set of integers is denoted by the alphabetical letter ‘Z’. The set of integers include positive counting numbers, negative counting numbers, and zero.  The list of integers does not include any kind of decimal or fractional value. Some of the examples of integers are 0, -1, -5, 6, 7, 38, etc.

The term integer is actually a Latin word that means ‘whole’. These integers are used in mathematical operations such as addition, subtraction, multiplication, division, etc.  The integers are basically divided into three groups.

• Zero(0): Zero is a neutral mathematical value which neither stands for positive nor for negative value in operations. Zero lies at the center of the number line.
• Positive integers: The positive integers are the set of natural numbers counting from 1, 2, 3, and so on. The set is denoted by ‘+Z’. The positive integers lie on the right side from zero in the number line.
• Negative integers: The negative integers are the negative set of natural numbers counting from -1, -2, -3, and so on. The set is denoted by ‘-Z’. The negative integers lie on the left side from zero in the number line.

What is the greatest negative integer?

Answer:

-1 is the greatest negative integer. In a number line, the numbers to the right from 0 (zero) are the positive integers. And, the numbers left to 0 (zero) are the negative integers.

Negative integers are numbers that are less than zero. Now, when we move right in the number line from 0 we will find -1 to be the first one we will observe. So, -1 is the greatest of all the negative integers.

Sample Problems

Question 1: Is -0.4123 an integer?

Answer:

-0.4123 is a negative value but not an integer. It is a decimal value.

Question 2: What are positive integers?

Answer:

Positive integers are numbers that are greater than zero. Positive integers are placed to the left from 0 (zero).

Question 3: Does 0 count as an integer?

Answer:

Yes, 0 is an integer. As integers include all the negative and positive counting numbers along with zero.

Question 4: Mention the major properties of integers.

Answer:

The major properties of integers are:

• Closure Property
• Associative Property
• Commutative Property
• Distributive Property
• Additive Inverse Property
• Multiplicative Inverse Property
• Identity Property

Question 5: What will be the result if you add two positive integers with the same sign?

Answer:

If two positive integers with the same signs are added, then, the result will also be positive.

For example, (+2) + (+5) = (+7)

Question 6: What will be the result if you multiply two integers with the same sign?

Answer:

If two integers with the same sign are multiplied, then the result will be positive.

For example: (+2) × (+2) = 4

(-2) × (-2) = 4