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Commutative property states that the change in the order of operands doesn’t have any impact on the final result. There is no change in the final result. Thus we know that change in the order of operands doesn’t change the final result. But this property works for only addition and multiplication and not for subtraction and division. Let’s see why it doesn't work in this article.
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Commutative Property of Addition:
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The commutative property of addition states that the change in the order of operands around the plus operator doesn’t have any impact on the final result of addition.
Formula for Commutative Property of Addition-
a+b=b+a
For example: take 1+2
We know that 1+2=3. Here, 3 is the final result.
Now, if we change the order of operands, then it will be 2+1
We also know—> 2+1=3 Here also, 3 is the final result.
There is no change in the final result of addition.
Commutative Property of Multiplication:
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The commutative property of addition states that the change in the order of operands around the multiplication operator doesn’t have any impact on the final result of addition.
Formula for Commutative Property of Multiplication-
a*b=b*a
For example: take 1*2
We know that 1*2=2. Here, 2 is the final result.
Now, if we change the order of operands, then it will be 2*1
We also know—> 2*1=2 Here also, 2 is the final result.
There is no change in the final result of multiplication.
Commutative Property of Subtraction:
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The commutative property of subtraction does not work. As the change in the order of operands around the minus operator has significant impact on the final result of subtraction.
Formula for Commutative Property of Subtraction–
a-b ≠ b-a
For example: take 1-2
We know that 1-2=-1. Here, -1 is the final result.
Now, if we change the order of operands, then it will be 2-1
We also know—> 2-1=1 Here also, 1 is the final result.
1≠ -1
Hence the commutative property of subtraction does not exist.
Commutative Property of Division:
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The commutative property of Division does not work. As the change in the order of operands around the division operator has a significant impact on the final result of division.
Formula for the commutative Property of Division–
a/b ≠ b/a
For example: take 4/8
We know that 4/8=½=0.5. Here, 0.5 is the final result.
Now, if we change the order of operands, then it will be 8/4
We also know—> 8/4=2 Here also, 2 is the final result.
0.5≠ 2
Hence the commutative property of Division does not exist.
Things to Remember
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- Commutative property states that the change in the order of operands doesn’t have any impact on the final result.
- The commutative Property of Addition: a+b=b+a
- The commutative Property of Multiplication: a*b=b*a
- The commutative property is not applicable for subtraction and division
- a-b ≠ b-a
- a/b ≠ b/a
Sample Questions:
Ques. Prove that 15 + 13 = 13 + 15 is true? (2 Marks)
Ans.
15+13 =28
13+15=28
Both of them yield the same result and by the commutative property of addition, a+b=b+a
Hence 15 + 13 = 13 + 15 is true.
Ques. Is 5 - 3 = 3 - 5 true? (2 Marks)
Ans. a-b is NOT equal to b-a.Commutative property is not applicable for subtraction and division.
5-3=2
3-5=-2
2 and -2 are not equal. Hence, it is not true.
Ques. Prove that 5 *3 = 3 *Is 5 true? (2 Marks)
Ans. 5*3 =15
3*5=15
Both of them yield the same result and by the commutative property of multiplication, a*b=b*a
Hence 5 *3 = 3 *5 is true.
Ques. Is 15/30 = 30/15 true? (2 Marks)
Ans. a/b is NOT equal to b/a. Commutative property is not applicable for subtraction and division.
15/30 = ½ =0.5
30/15=2
0.5 and 2 are not equal. Hence, it is not true.
Ques. Prove that 20+ 30= 30+ 20 is true? (2 Marks)
Ans.
20+30 =50
30+ 20 =50
Both of them yield the same result and by the commutative property of addition, a+b=b+a
Hence 20+ 30= 30+ 20 is true.
Ques. Is (-9) - 3 = 3 - (-9) true? (2 Marks)
Ans. a-b is NOT equal to b-a.Commutative property is not applicable for subtraction and division.
(-9) - 3 =-12
3 - (-9) = 12
12 and -12 are not equal. Hence, it is not true.
Ques. Prove that 5 *0 = 0*Is 5 true? (2 Marks)
Ans. 5*0 =0
0*5=0
Both of them yield the same result and by the commutative property of multiplication, a*b=b*a
Hence 5 *0 = 0*5 is true.
Ques. Is 9/3 = 3/9 true? (2 Marks)
Ans. a/b is NOT equal to b/a. Commutative property is not applicable for subtraction and division.
9/3 = 3
3/9=0.33333333333
3 and 0.33333333333 are not equal. Hence, it is not true.
Ques. Prove that 5 *-4 = -4 *Is 5 true? (2 Marks)
Ans.
5*-4 = -20
-4*5= -20
Both of them yield the same result and by the commutative property of multiplication, a*b=b*a
Hence 5 *-4 = -4 *5 is true.
Ques. Is commutative property applicable for rational numbers? (3 Marks)
Ans.
The commutative property is applicable for rational numbers and can be expressed only for addition and multiplication.
If we take A and B to be rational numbers, then commutative property can be expressed as (A+ B) = (B + A) or (A × B) = (B × A).
Here the values of A, B are
A=n/d
B= m/t where d ≠ 0, t≠ 0.
Ques. Why is commutative property not applicable for subtraction and multiplication? (5 Marks)
Ans.
Commutative Property of Subtraction:
For example: take 1-2
We know that 1-2=-1. Here, -1 is the final result.
Now, if we change the order of operands, then it will be 2-1
We also know—> 2-1=1 Here also, 1 is the final result.
1≠ -1
Hence the commutative property of subtraction does not exist.
Commutative Property of division:
For example: take 4/8
We know that 4/8=½=0.5. Here, 0.5 is the final result.
Now, if we change the order of operands, then it will be 8/4
We also know—> 8/4=2 Here also, 2 is the final result.
0.5≠ 2
Hence commutative property of Division does not exist.
From the examples, we can know that commutative property is not applicable for subtraction and multiplication.
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