Commutative Law of Addition
Commutative law of addition states that if two numbers are added then the result is equal to the addition of their interchanged position. In this article we will explore the commutative law of addition, commutative law for addition representation, and commutative law for addition examples. We will also solve some examples related to the commutative law of addition. Let’s start our learning on the topic “Commutative Law for Addition.”
What is Commutative Law?
Commutative law is a law in which the order of the two operands does not affect the result of the expression. In other words, the change in the place of the operand does not change the result of the expression. The operations like addition, multiplication, etc. satisfy the commutative law.
What is Commutative Law for Addition?
Commutative law for addition states that if two numbers are related by the addition operator, then by interchanging the numbers, the result does not change. In other words, if we change the position of the operands of addition, it does not affect the result of the addition.
Commutative Law for Addition Representation
Consider two numbers a and b then, commutative law of addition is represented as:
a + b = b + a
Commutative Law for Addition Examples
Some examples of commutative law for addition are listed below.
- 5 + 2 = 2 + 5 = 7
- (-17) + 7 = 7 + (-17) = -10
- (4 / 9) + (5 / 7) = (5 / 7) + (4 / 9)
Commutative vs Associative Law of Addition
Addition also follows associative law. Let’s see the comparison between Commutative and Associative law of addition.
|
Aspect |
Commutative Law |
Associative Law |
|---|---|---|
|
Definition |
It states that changing the order of number does not affect the sum |
It states that if there are three or more numbers, total sum remains same irrespective of the group in which numbers are arranged. |
|
Expression |
a + b = b + a |
(a + b) + c = a + (b + c) |
|
Example |
6 + 2 = 2 + 6 = 8 |
(2 + 5) + 6 = 2 + (5 + 6) = 13 |
Also, Check
Solved Examples on Commutative Law of Addition
Example 1: Prove that x + y = y + x if x = 10 and y = 20.
Solution:
LHS = x + y
x + y = 10 + 20
x + y = 30
RHS = y + x
y + x = 20 + 10
y + x = 30
x + y = y + x
LHS = RHS
Hence Proved
Example 2: Prove the Commutative Law of Addition if p = 14 and q = -23.
Solution:
Commutative Law of Addition: p + q = q + p
LHS = p + q
p + q = 14 + (-23)
p + q = -9
RHS = q + p
q + p = (-23) + 14
q + p = -9
p + q = q + p
LHS = RHS
Hence Proved
Example 3: Prove that u + v = v + u if u = -34 and v = -9.
Solution:
LHS = u + v
u + v = (-34) + (-9)
u + v = -43
RHS = v + u
v + u = (-9) + (-34)
v + u = -43
u + v = v + u
LHS = RHS
Hence Proved
Practice Problems on Commutative Law of Addition
Q1. Prove that a + b = b + a if a = -90 and b = 150.
Q2. Prove the commutative law of addition if r = 98 and s = 67.
Q3. Prove that c + d = d + c if c = -13 and d = -45.
FAQs on Commutative Law of Addition
What is Commutative Law for Addition?
The law in which the result is not affected by the changing the position of the operands in addition is called as commutative law for addition.
What is an Example of Commutative Law of Addition?
An example of commutative law for addition is: 5 + 4 = 4 + 5
What is the Commutative Law for Addition Formula?
The commutative law for addition formula is given by: a + b = b + a
Is commutative law also valid for subtraction?
No, commutative law is not valid for subtraction
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