Explaining the Commutative Property in Math

ElevatEd
Math
January 15, 2025

Commutative property in Math, specifically in the addition or multiplication of two numbers, the sum will remain the same. In commutative property, numbers can be moved and swapped from their previous positions which will not make any difference in the final answer. This commutative property only works with addition and multiplication. It does not work the same for subtraction and division.

It is one of the essential properties of integers in mathematics. In arithmetic operations, the changing of operands does not change the result in addition and multiplication. This blog will help you understand commutative properties in Math. This article can assure you meet all your doubts once you read this.

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Definition Of Commutative Property

The commutative property mainly deals with the changing positions of numbers around. In mathematics changing operands does not change the results when it works with addition and multiplication. The literal meaning of the word refers to switching or moving positions. It depicts the numbers interchanging positions in addition and multiplication does not change the result.

In commutative property, while proceeding with addition generally two integers are used. After exchanging the position of numbers, the answer will remain unchanged.

Commutative Property Examples

Commutative property functions work with two conditions only, addition and multiplication.

In Addition

If the integers change positions, the final result will remain unchanged.

Suppose, A and B are the two integers, then we can write as A+B=B+A

1+2 or 2+1 =3

3+4 or 4+3= 7

10+15 or 15+10=25

In Multiplication

In the case of multiplication, two integers will show the same results even if numbers exchange their positions.

Suppose, A*B=B*A

1*2 or 2*1= 2

3*4 or 4*3= 12

10*15 or 15*10= 150

Important Facts About Commutative Property

Besides major properties such as addition and multiplication, there are other properties as well, associative property and distributive property.

1. Associative property: As per associative law in mathematics the numbers are grouped in any way the answers will remain the same.

Examples: A+ (B+C) = (A+B) +C

A*(B*C) =(A*B) *C

2. Distributive property: The distributive property of multiplication refers to the multiplication of each addend number and adding the actual value.

Examples: A*(B+C) = (A*B) +(A*C)

There are other properties, such as closure property and identity property that are introduced for integers.

3. Non-Commutative Property: In mathematics, there are non-commutative properties, such as subtraction and division. Unlike interchanging the position, subtraction, and division operations will provide different results.

Examples:

In subtraction, 3-2=1 and 2-3=-1

Again, in division, 10/2=5 and 2/10= 0.2

In short, the commutative property in Math refers that if the places of integers are changed or replaced with other number grouping the results will remain the same. This commutative property can only apply to addition and multiplication. In subtraction and division, the commutative property does work as a non-commutative property.

The different types of commutative properties, such as associative, distributive, and identity mainly govern the relationship with numbers. Learning commutative property is fun and children must learn it from their early ages. www.98thpercentile.com has introduced various courses on Math so that every kid can learn important facts.

FAQ (Frequently Asked Questions)

Q.1: What are the four different types of properties in mathematics?

Ans: The basic properties are commutative, associative, distributive, and identity.

Q.2: Why are subtraction and division non-commutative?

Ans: The interchanging places of numbers give different numbers each time.

Q.3: What is the commutative law in Math?

Ans: In Math, laws related to addition and multiplication are A+B=B+A and A*B=B*A.

Q.4: What is the difference between commutative property and associative property?

Ans: Commutative property refers to A+B=B+A and A*B=B*A. On the other hand, the associate property is represented as (A + B) + C = A + (B + C) = (A + C) + B.

Q.5: How to teach commutative property?

Ans: The best way to teach commutative property is by real-life objects such as pebbles, dice, seeds, etc.