Table of Contents
Properties of Multiplication of Integer
The product of two integers is always an integer.
The product of two negative integers is always a negative integer.
The product of two positive integers is always a positive integer.
The product of a positive and a negative integer is always a negative integer.
What Is The Meaning of An Integer?
An integer is a number that can be written without a decimal point and has no fractional parts. Integers include the natural numbers (1, 2, 3,…) and their negatives (-1, -2, -3,…).
Basic Properties of the Integers
Integers are whole numbers and their opposites. The set of all integers is denoted by \mathbb{Z}. The first few integers are:
\mathbb{Z} = {…, -3, -2, -1, 0, 1, 2, 3, …}
Integers have the following properties:
They are whole numbers.
Their opposites are also integers.
Integers can be added, subtracted, multiplied, and divided.
Integers are closed under addition, subtraction, multiplication, and division. This means that the sum, difference, product, and quotient of two integers is always another integer.
Closure Property
The Closed property indicates whether the text box is currently closed.
public bool Closed { get; }
The Closed property is a bool that indicates whether the text box is currently closed.
Closure Property Under Multiplication:
If a and b are two positive real numbers and a*b = c, then c is also a positive real number.
Commutative Property
of Addition
The commutative property of addition states that the order of addition does not affect the result. In other words, a + b is the same as b + a.
Multiplication is commutative for integer numbers.
This means that the order of multiplication does not affect the result: a×b=b×a.
Associative Property
The associative property states that when two or more items are combined, the order of the items does not matter. For example, if you are adding three numbers together, the order in which you add them does not matter.
3 + 4 + 5 = 12
12 + 3 = 15
15 + 4 = 19
19 + 5 = 24
Associative property under multiplication:
For all real numbers a, b, and c,
a(bc) = (ab)c.
Distributive Property
The distributive property states that for any real numbers a, b, and c,
a(b+c) = ab+ac.
Distributive Property of Multiplication Over Addition:
For any real numbers a, b, and c,
(a + b) * c = a * c + b * c.
