1. Summary

    Rational numbers :
    Numbers that can be expressed in the form  p q , where p and q are integers and q ≠ 0, are known as rational numbers. The collection of rational numbers is denoted by Q.

    These rational numbers satisfies various laws or properties that are listed below:

    • Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number, then we say that rational numbers satisfy the closure law.

      whole numbers, Integers, Rational Numbers, Closure Property, Closure law, closed under addition, closed under subtraction, closed under multiplication, closed under division, properties of rational numbers

    • Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:
      Commutative law under addition: a + b = b + a
      Commutative law under multiplication: a x b = b x a

      commutative property, commutative law, commutative under addition, commutative under multiplication, commutative under division, properties of rational numbers

    • Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:
      Associative law under addition: a + (b + c) = (a + b) + c
      Associative law under multiplication: a(bc) = (ab)c

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    • 0 is the additive identity for rational numbers.

    • 1 is the multiplicative identity for rational numbers.

    • The additive inverse of a rational number  p q  is -  p q , and the additive inverse of - p q is p q.

    • If  p q x  a b = 1, then a b  is the reciprocal or multiplicative inverse of p q , and vice versa.

    • For all rational numbers, p, q and r,  p(q + r ) = pq + pr  and  p(q - r ) = pq - pr , is known as the distributive property.

                distributive property, distributive law, distributive property of multiplication over addition, distributive property of multiplication over subtraction, multiplication is distributive over addition, multiplication is distributive over subtraction, properties of rational numbers
                distributive property, distributive law, distributive property of multiplication over addition, distributive property of multiplication over subtraction, multiplication is distributive over addition, multiplication is distributive over subtraction, properties of rational numbers
               
               




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