
Which property is illustrated by the following statement?
Answer
488.1k+ views
Hint:
Observe the two sides of the equation. Find the difference. We can see the only difference is and . Thus we can identify that the commutative property is used here. Explain the commutative property of addition in general.
Complete step by step solution:
Given that
The only difference we can see on both sides of the equation is the order of the numbers, and .
Subtracting from both sides we get,
This addition of two numbers does not depend on the order in which they are written.
This property is called Commutativity.
Commutative property of addition states that changing the order of addends does not change the sum.
In general we can say that, for any two numbers and , .
This property can be extended to any number of terms apart from binary addition.
Therefore the answer is Commutative property.
Additional information:
Commutative property is also applicable in case of multiplication. We know that for any two numbers and , .
But it does not hold in case of subtraction and division.
We have and in most cases.
But there are exceptional cases as well. If and are equal, then and .
Commutative property, associative property and distributive property are the three fundamental properties defined for any binary operation.
Note:
Don’t confuse commutative property with associative property. Associative property is used when there are three numbers and the operations are the same. It states that , for some operation .
Observe the two sides of the equation. Find the difference. We can see the only difference is
Complete step by step solution:
Given that
The only difference we can see on both sides of the equation is the order of the numbers,
Subtracting
This addition of two numbers does not depend on the order in which they are written.
This property is called Commutativity.
Commutative property of addition states that changing the order of addends does not change the sum.
In general we can say that, for any two numbers
This property can be extended to any number of terms apart from binary addition.
Therefore the answer is Commutative property.
Additional information:
Commutative property is also applicable in case of multiplication. We know that for any two numbers
But it does not hold in case of subtraction and division.
We have
But there are exceptional cases as well. If
Commutative property, associative property and distributive property are the three fundamental properties defined for any binary operation.
Note:
Don’t confuse commutative property with associative property. Associative property is used when there are three numbers and the operations are the same. It states that
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