Ellipse: Do you know the orbit of planets, moon, comets, and other heavenly bodies are elliptical? Mathematics defines an ellipse as a plane curve surrounding...

Ellipse: Definition, Properties, Applications, Equation, Formulas
April 14, 2025Harvest Smarter Results!
Celebrate Baisakhi with smarter learning and steady progress.
Unlock discounts on all plans and grow your way to success!
Ellipse: Definition, Properties, Applications, Equation, Formulas
April 14, 2025Altitude of a Triangle: Definition & Applications
April 14, 2025Manufacturing of Sulphuric Acid by Contact Process
April 13, 2025Refining or Purification of Impure Metals
April 13, 2025Pollination and Outbreeding Devices: Definition, Types, Pollen Pistil Interaction
April 13, 2025Acid Rain: Causes, Effects
April 10, 2025Congruence of Triangles: Definition, Properties, Rules for Congruence
April 8, 2025Complementary and Supplementary Angles: Definition, Examples
April 8, 2025Compounds of Phosphorus
April 8, 2025Nitro Compounds: Types, Synthesis, Properties and Uses
April 8, 2025Commutative Property: The property of commutative explains that the order of terms doesn’t matter while performing a mathematics operation. The commutative property is otherwise called Commutative Law.
On this page, we will provide you with all the necessary information about commutative property meaning, definition, formulas. Read on to find out more.
Commutative Property Definition: “Any mathematics operation is commutative if changing the order of the operands does not change the result”.
The commutative property is applicable for Addition and Multiplication. The commutative property of Division and Subtraction doesn’t apply while performing mathematics operations.
Let’s understand the topic in details by checking out this example of communicative property.
If 2 + 3 = 6, we can change the order of the operands to check if the results are the same.
Example 1: Commuative Property of Addition
2 + 3 = 6
3 + 2 = 6
Which means 2 + 3 = 3 + 2
Example 2: Commuative Property of Mulitiplication
2 x 3 = 6
3 x 2 = 6
Which means 2 x 3 = 3 x 2
Commutative Property Meaning: Commutative is originated from the French word “Commute” which means switch or move around. Whereas the word “ative” which is the suffix of commutative means “tend to“. The word commutative means that we can switch the positions of integers while performing an operation and the resultant product will be the same.
The sum of 2 numbers will be the same in whatever order they are added.
A + B = B + A |
Example:
2 + 3 = 3 + 2 = 5
5 + 6 = 6 + 5 = 11
7 + 8 = 8 + 7 = 15
The product of 2 numbers will be the same in whatever order they are multiplied.
A.B = B.A |
Example:
2 x 3 = 3 x 2 = 6
3 x 9 = 9 x 3 = 27
7 x 4 = 4 x 7 = 28
As discussed above, the commutative property is not applicable for Division and Subtraction problems.
The difference between 2 numbers will not be the same if they are subtracted in a different order.
Example:
2 – 3 = -1 Whereas 3 – 2 = 1
5 – 9 = – 4 ≠ 9 – 5 = 4
9 – 6 = 3 ≠ 6 – 9 = -3
The quotient and the remainder will not be the same if we perform division operation by changing the order of the numbers.
8 ÷ 2 = 4 which is not equal to 2 ÷ 8 = 0.25
6 ÷ 2 = 3 ≠ 2 ÷ 6 = 1/3
The formulas of commutative property are given below:
A + B = B + A A × B = B × A |
Question 1: Does 12 x 3 satisfies commutative law?
Answer: Yes, 12 x 3 satisfies the commutative law. Because when 12 multiplied by 3, the result is 36 and when 3 multiplied by 13, the product is 36.
12 x 3 = 3 x 12 = 36.
Question 2: Does 4 + 20 obey the commutative laws?
Answer: Yes, 4 + 20 obey’s commuatative law.
4 + 20 = 20 + 4 = 24.
Question 3: Does 4 – 5 statisfiees commutative law?
Answer: No, commutative law does not obey subtraction.
Question 4: Which of the following obeys commutative law?
1. 34 + 5
2. 8 ÷ 6
3. 4 x -5
4. 3 – 6
Answer: The commutative law obeys only while performing multiplication and addition operations. Thus only option 1 and option 3 provided above obeys commutative law.
Also, Check:
Trigonometry Formulas | Algebra Formula |
Mensuration Formulas | Differentiation Formulas |
Factorisation Formulas | BODMAS Rules |
The frequently asked questions on Commutative Property are given below:
Q. Is commutative for whole numbers? A. Yes, Commutative property is applicable for the Whole number. |
Q. Why is there no commutative property for division? A. The commutative property of division is not applicable since the order matters while performing division operation. |
Q. Are integers commutative under subtraction? A. No Integers are not communicative under subtraction, because while performing subtraction operation of integers if the order gets changed even the results will get changed. |
Q. What is another name for the commutative property? A. The other name of the commutative property is “Commutative Law”. |
Q. What is the formula of commutative property? A. The formulas of Commutative property is: Commutative Property of Addition: A + B = B + A Commutative Property of Subtraction: A × B = B × A |
Students can also make use of Embibe’s Mathematics Study page which covers almost all the Mathematical Concepts right from Grade 11 and Grade 12. All these concepts come with video lectures which can be accessed for. Also, solve and take Maths Mock Tests on Embibe:
Now that you are provided with all the necessary information about Commutative Property and we hope this article is helpful to you. If you have any queries on Commutative Law, ping us through the comment section below and we will get back to you as soon as possible.
Ellipse: Do you know the orbit of planets, moon, comets, and other heavenly bodies are elliptical? Mathematics defines an ellipse as a plane curve surrounding...
Altitude of a triangle is the side that is perpendicular to the base. A triangle has three sides altitude, base and hypotenuse. The altitude of...
Manufacturing of Sulphuric Acid by Contact Process: Sulphuric acid is referred to as the king of chemicals. It is one of the most important chemical...
Refining or Purification of Impure Metals: Metals like Copper, Aluminium, Iron, etc., occur in nature in the combined state, in the form of their oxides,...
Pollination and Outbreeding Devices: Flowers are symbolic of beauty and have aesthetic, ornamental, social, religious and cultural value. But how are they formed? Let us...
Congruence of Triangles: The congruence of a triangle depends upon the measurements of sides and angles of the two triangles. There are a few criteria,...
Complementary and Supplementary angles are defined for the addition of two angles. If the sum of two angles so formed is \({90^ \circ }\), then...
Nitro compounds are a group of organic compounds having Nitro group \({\rm{( - O - N = O)}}\) as a part of its molecular structure....
Bond Linking Monomers in Polymers: Every living thing is made up of various proteins, enzymes, certain peptide hormones, carbohydrates, nucleic acids, polyphenolics etc. are important...
Higher animals possess an elaborated circulatory system that consists of a muscular and chambered heart, a network of blood vessels, and an extracellular fluid called...
Machines: Do you know we can easily lift heavy loads with a small effort? Do you know we can make the work easier with the...
Algebra of Complex Numbers: Complex numbers have wide applications in various fields of science, such as AC circuit analysis. Learning about the algebra of complex numbers...
The Lanthanoids: How many elements do you think there are in and around us? They can be counted, however counting them on your fingers is...
Important Trends and Anomalous Behaviour of Carbon: You know how important carbon is for our existence. Even our bodies are largely composed of carbon compounds....
Preparation of Colloidal Solutions: As we know, all solutions contain two entities in them, a solvent and a solute, mixed together to form a solution....
Deliquescence: We all must have seen tiny silica gel packets inside shoe boxes, new bags, and other gadgets, and they are there for a reason....
Periodic Trends in the Properties of Elements: The long form of the periodic table or the modern periodic table can also be called Bohr’s table...
Occurrence of Group 17 Elements: On the periodic table, the halogens are to the left of the noble gases. Fluorine \(\left( {\rm{F}} \right){\rm{,}}\) chlorine \(\left(...
Dinitrogen: Nitrogen is a colourless, odourless, and tasteless element that is plentiful in nature. Daniel Rutherford, a Scottish physician, was the first to discover it...
Drug-Target Interaction: As we've seen, chemistry plays a crucial role in practically every aspect of our lives. Medicinal chemistry is one such topic that is...
Biotechnology: The application of engineering science principles and technological methods on biological systems, like microorganisms, higher animals, and plants, intending to carry out chemical, environmental...
Health Organisations: Did you know that ischemic heart disease is the leading cause of disease worldwide? Last year heart disease killed \(4.77\) million people in...
Unleash Your True Potential With Personalised Learning on EMBIBE
Create Free Account