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When it comes to integers, the four fundamental mathematical operations — addition, subtraction, multiplication, and division — as well as the properties associated with these operations, can be applied to them.
Throughout this post, we will go over the rules for multiplying integers with one another. The basic characteristics of multiplication such as commutative property, associative property, and so on need be learned before we may multiply any two integers together. Students in Grades 1 through 10 will benefit from learning these properties, which will make it easier for them to answer multiplication issues.
Multiplication of integers
Multiplication is essentially the process of adding numbers over and over again. In the case of 2 multiplied by 3, this indicates that 2 is multiplied by itself three times, and so on.
3 x 3 = 3+ 3+ 3 = 12
As a result, the repeated addition of integers is referred to as the multiplication of integers.
Integers are multiplied together.
In this case, a and n are both positive integers.
What are the properties of the integer multiplication operation?
The following are the properties of integer multiplication:
- Property for sale in the event of a closure
- The property of commutativity
- The property of association
- The distributive property is defined as follows:
- Multiplication by zero is a mathematical operation.
- An identity that is multiplicative
There are several similarities between the properties of addition and those of multiplication, such as the commutative and associative properties, and these are discussed below. As a result, it becomes easier to recall such characteristics.
Closure Property of Multiplication
The Closure Property of Multiplication is a mathematical property that describes how a number is closed.
It follows that if two integers are multiplied by each other, then the resulting a + b is also an integer, according to this property. As a result, when integers are multiplied, they become closed.
For every integer, a and b, the product a b is an integer.
Examples:
- 2 x -2 = -4
- 4 x 9 = 36
Commutative Property of Multiplication
Multiplication has the property of being commutative.
The commutative property of integer multiplication asserts that changing the order of the operands or the order of the integers has no effect on the outcome of the multiplication operation.
For any integer a and b, the expression a * b = b* a
Examples:
- 3 x 5 = 5 x 3 (=15)
- 5 x 3 = 3 x 5 (=15)
Associative Property of Multiplication
Multiplication has the property of being associative.
The result of the product of three or more integers is independent of the way in which the integers are grouped together. In general, if three integers a, b, and c are present, then
a × (b × c) = (a × b) × c
Examples:
- 1 x (4 x 5) = (1 x 4) x 5 (=20)
- -2 x (1 x -3) = (-2 x 1) x -3 (= 6)
The Distributive Property of Multiplication is a mathematical property that describes how a number is distributed.
The distributive property of multiplication of integers states that if three integers a, b, and c are multiplied together, the result is
a * (b + c) = (a *b) + (a *c)= a* (b + c)
Example:
- 5x 0 = 0
- -1 x 0 = 0
- 110 x 0 = 0
Multiplication by zero
Multiplication by zero is a mathematical operation.
No matter what integer is multiplied by zero, the result is always zero. In general, if a and b are two numbers, then the expression is
a* 0 = 0 *a = 0
Examples:
7x 0 = 0
10 x 0 = 0
As a result, we can observe that when any integer is multiplied by zero, regardless of whether it is the smallest or the largest, the outcome is always zero.
Multiplicative Identity of Integers
The Identity of Integers Can Be Multiplicative
When you multiple any integer by one, the outcome is always the same as the original integer. In general, if a and b are two numbers, then the expression is
b × 1 = 1 × b = b
As a result, integer 1 is known as the Multiplicative Identity of Integers.
Examples:
- 13 x 1 = 23
- 74 x 1 = 44\
Conclusion
In mathematics, integers are defined as the sum of all whole numbers and all negative numbers. The set of all integers is represented by the symbol
In mathematics, multiplication is defined as the addition of an integer to itself a specified number of times. When compared to the other four fundamental operations on integers, the multiplication of integers is one of the more intriguing operations on integers. First, let’s take a quick look at what the concept of integer multiplication operations is all about before we get too far into the subject.
