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Rational Numbers - Coggle Diagram
Rational Numbers
What are Rational Numbers, standard form and their properties
What are Rational Numbers ?
The number which can be written in the p/q form, where p and q are integers and q is not equal to zero is called a rational number. Example - -6/7, -9/5 etc.
Standard Form :- The rational numbers are in the standard form if - 1. The numerator and denominator are coprime 2. The denominator is positive
Properties of rational numbers are closure, commutative, associative, distributive, additive identity and inverse, multiplicative identity and inverse
Closure Property
Addition - The closure property states that for any two rational numbers a and b, a + b is also a rational number.
Subtraction - The closure property states that for any two rational numbers a and b, a – b is also a rational number.
Multiplication - The closure property states that for any two rational numbers a and b, a × b is also a rational number.
Division - The closure property states that for any two rational numbers a and b, a ÷ b is also a rational number.
Commutativity
Addition - For any two rational numbers a and b, a + b = b+ a
Subtraction - For any two rational numbers a and b, a – b ≠ b – a.
Multiplication - For any two rational numbers a and b, a × b = b × a
Division - For any two rational numbers a and b, a ÷ b ≠ b ÷ a.
Associativity
Addition - For any three rational numbers a, b and c , a + (b + c) = (a +b) + c
Subtraction - For any three rational numbers a, b and c, a - (b - c) ≠ (a - b) - c
Multiplication - For any three rational numbers a, b and c, a × (b × c) = (a × b) × c
Division - For any three rational numbers a, b and c , a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Distributivity
For any three rational numbers a, b and c,
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