The commulative law of addition for two rational numbers x and y is---
Answers
Answer:
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Step-by-step explanation:
ommutative Property
For rational numbers, addition and multiplication are commutative.
Commutative law of addition: a+b = b+a
Commutative law of multiplication: a×b = b×a
For example:
Commutative law example
Subtraction is not commutative property i.e. a-b ≠ b-a. This can be understood clearly with the following example:
Commutative law - subtraction LHS
Whereas
Commutative law - subtraction RHS
The division is also not commutative i.e. a/b ≠ b/a, since,
Commutative law - Division LHS
Whereas,
Commutative law - Division RHS
Associative Property
Rational numbers follow the associative property for addition and multiplication.
Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+z
For multiplication: x(yz)=(xy)z.
Example: 1/2 + (1/4 + 2/3) = (1/2 + 1/4) + 2/3
⇒ 17/12 = 17/12
And in case of multiplication;
1/2 x (1/4 x 2/3) = (1/2 x 1/4) x 2/3
⇒ 2/24 = 2/24
⇒1/12 = 1/12
Distributive Property
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
Example: 1/2 x (1/2 + 1/4) = (1/2 x 1/2) + (1/2 x 1/4)
LHS = 1/2 x (1/2 + 1/4) = 3/8
RHS = (1/2 x 1/2) + (1/2 x 1/4) = 3/8
Hence, proved
Identity and Inverse Properties of Rational Numbers
Identity Property: 0 is an additive identity and 1 is a multiplicative identity for rational numbers.
Examples:
1/2 + 0 = 1/2 [Additive Identity]
1/2 x 1 = 1/2 [Multiplicative Identity]
Inverse Property: For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.
Examples:
The additive inverse of 1/3 is -1/3. Hence, 1/3 + (-1/3) = 0
The multiplicative inverse of 1/3 is 3. Hence, 1/3 x 3 = 1
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Frequently Asked Questions – FAQs
What are the important properties of rational numbers?
The major properties are: Commutative, Associative, Distributive and Closure property.
When two rational numbers are added then it is equal to?
Two rational numbers when added gives a rational number. For example, 2/3 + 1/2 = 7/6.
What is the distributive property of rational numbers?
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
The commutative property of rational number is applicable to addition and multiplication only. True or false?
True. The commutative property of rational numbers is applicable for addition and multiplication only and not for subtraction and division.