Which law is shown by (a+b=b+a)?
Answer and explanation
Correct answer: Commutative law
The equation \(a+b=b+a\) says that the two addends may exchange their positions without changing the sum. This property concerns the order of terms, not the way a sum is multiplied or expanded. For example, \(3+5=5+3\), and both sides equal 8. The letters may represent any suitable real numbers, so the rule is general.
This property is called the commutative law of addition. The word “commutative” means that the order can be changed. It is different from the distributive law, such as \(a(b+c)=ab+ac\), and from an exponent law. Therefore the statement matches option A, the commutative law. The equality is not claiming that addition and multiplication are interchangeable; it only changes the order of the addends.
Frequently asked questions
What is the correct answer to this question?
Commutative law
Why is this the correct answer?
The equation \(a+b=b+a\) says that the two addends may exchange their positions without changing the sum. This property concerns the order of terms, not the way a sum is multiplied or expanded. For example, \(3+5=5+3\), and both sides equal 8. The letters may represent any suitable real numbers, so the rule is general.
This property is called the commutative law of addition. The word “commutative” means that the order can be changed. It is different from the distributive law, such as \(a(b+c)=ab+ac\), and from an exponent law. Therefore the statement matches option A, the commutative law. The equality is not claiming that addition and multiplication are interchangeable; it only changes the order of the addends.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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