Write the properties of rational numbers Grade :- 8
Answers
Answer:The properties of rational numbers are:
Closure Property.
Commutative Property.
Associative Property.
Distributive Property.
Identity Property.
Inverse Property.
Step-by-step explanation:
Explanation: A rational number is any number that can be expressed as a fraction/ratio, with both the numerator and denominator being integers.
The properties of rational numbers are :-
1. Closure Property
2. Commutative Property
3. Associative Property
4. Distributive Property
5. Identity Property
6. Inverse Property
1. Closure property
For two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example:
(7/6)+(2/5) = 47/30
(5/6) – (1/3) = 1/2
(2/5). (3/7) = 6/35
2. Commutative 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:
2/5 × 3/7 = 3/7 × 2/5 = 6/35
3. 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
4. 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
5. Identitive Property
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]
6. Inverse Property
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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