Commutative Property of Addition
According to the commutative property of addition, the sum of two or more numbers is the same regardless of how they are grouped. In this post, we will learn more about the commutative property of addition.
What is the Commutative Property of Addition?
According to the commutative property of addition, the result of adding or totaling two or more numbers is the same regardless of how the numbers are organized. In this context, grouping refers to the placement and arrangement of brackets in the provided addition problem. Consider the following illustration to comprehend the commutative property of addition.
5 + 6 = 6 + 5
11 Equals 11
Here, it is evident that when all the numbers arranged differently are added together, the sum is the same.
Commutative Property of Addition Formula?
According to the commutative property, the order of operands does not affect the final result. The addition commutative property formula is provided below.
Commutative Property of Addition Formula
The commutative property of addition states that the order in which the addends are added has no effect on the sum.
A + B = B + A
Application of Commutative Property of Addition
The commutative law of addition is only relevant when the intended result may be obtained in any arrangement, i.e., LHS = RHS. Try to explain why and how the commutative property only applies to multiplication and addition. We shall apply the general commutative property law to each of the four fundamental operations separately. To further clarify the commutative property of multiplication, we shall present an example from the real world.
For Addition: the commutative property is written as a + b = b + a. As an illustration, (15 + 9) = (9 + 15) = 24. We declare that the addition of the given set of numbers is commutative.
For Multiplication: the commutative property is expressed as A B = B A. As an illustration, (15 6) = (6 15) = 90. Here, we determine that multiplication is commutative for the given number set.
Here, we will examine the real-world application of the commutative property of addition.
Example: Seven chocolate and five pizzas are present. Determine the sum of the items using the commutative property of addition for the reverse combinations of things that are available for purchase.
Solution: If you have 7 chocolate, you can choose 5 pizzas for a total of 7 + 5 = 12 items.
Also, with 5 pizzas, you can choose 7 chocolate; this gives you a total of 12 items (5 + 7)
The commutative property of addition between 7 chocolates and 5 pizzas is exemplified by both of these combinations.
Consider some examples to understand better the commutative feature of addition.
Examples of Commutative Property of Addition
Example 1: If (8 + 4) = 12, then prove (4 + 8) also results in 12 using the commutative property of the addition formula
Solution:
Since addition satisfies the commutative property
Hence (8 + 4) = (4 + 8) = 12.
Example 2: Erik’s mother asked him whether p + q = q + p is an example of the commutative property of addition. Can you help Erik find out whether it is commutative or not?
Solution:
We know that the commutative property for multiplication states that changing the order of the addends will not change the value of the sum.
p+q = q+p
So, we see that changing the order will not alter the sum value.
So this is an example of the commutative property of addition.
Answer: p + q = q + p is an example of the commutative property of addition.
FAQ ( Frequently Asked Questions )
Q.1 What is the Commutative Property Law of Addition?
The addition formula for the commutative property is defined as the sum of two or more numbers that remain unchanged regardless of the sequence of the operands and addends. For addition, the formula for the commutative property is (A + B) = (B + A).
Q.2 How Do You Find the Commutative Property of Addition?
According to the commutative property of addition, if a and b are two numbers, then a plus b equals b plus a. If the LHS and RHS terms are equal after solving the provided numerical values, the equality can be verified.
Q.3 What is an Example of Commutative Property of Addition?
(A + B) = (B + A) exemplifies the commutative feature of addition. Here A equals 8 and B 9, on solving we get 8 + 9 = 9 + 8 = 17. Thus demonstrated, LHS is equal to RHS.
Q.4 What is the Commutative Property of Addition for Fractions?
The expression for the commutative property of addition for fractions is (P + Q) = (Q + P). Here, the values of P and Q are represented as a/b. For example, if P = 7/8 and Q = 5/2, we obtain (7/8 + 5/2) = (5/2 + 7/8) = 27/8 by swapping the numbers in (P + Q) = (Q + P).
Q.5 What is the Commutative Property of Addition for Integers?
The expression for the commutative property of addition for integers is (P + Q) = (Q + P). For example, if P is equal to -3 and Q is equal to -9, then (-3 + (-9)) = (-9 + (-3)) = -12. Hence LHS = RHS.
