Properties of Division Properties of Division We will discuss different properties of rational numbers in this session. Rational numbers are the numbers which can be expressed in the form of p/q, where p and q are the integers and q in not equal to zero. Here we will take the properties of rational numbers: 1. Closure property: We mean by closure property that if there are two rational numbers, then Closure property of addition holds true, which means that the sum of two rational numbers is also a rational number. Closure property of subtraction holds true, which means that if there exist two rational numbers, then the difference of the two rational numbers is also a rational number. Closure property of multiplication holds true, which means that if there exist two rational numbers, then the product of the two rational numbers is also a rational number. Closure property of division holds true, which means that if there exist two rational numbers, then the quotient of the two rational numbers is also a rational number. 2. Commutative property of rational number: Commutative property of rational numbers holds true for addition and multiplication but does not hold true for subtraction and division. It means that if p1/q1 and p2/q2 are any two rational numbers, then according to commutative property of rational numbers, we mean that : P1/q1 + p2/q2 = p2/q2 + p1/q1 Know More About :- Subtraction Definition

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(P1/q1 - p2/q2) - p3/q3 <> P1/q1 - (p2/q2 - p3/q3 ) (P1/q1 ÷ p2/q2) ÷ p3/q3 <> P1/q1 ÷ (p2/q2 ÷ p3/q3 ) 7. Distributive property of multiplication over addition and subtraction of rational numbers holds true, which states: P1/q1 * ( p2/q2 + p3/q3) = (p1/q1 * p2/q2) + (p1/q1 * p3/q3) P1/q1 * ( p2/q2 - p3/q3) = (p1/q1 * p2/q2) - (p1/q1 * p3/q3) P1/q1 * p2/q2 = p2/q2 * p1/q1 P1/q1 - p2/q2 <> p2/q2 - p1/q1 P1/q1 ÷ p2/q2 <> p2/q2 ÷ p1/q1 3. Additive Identity of Rational numbers: According to additive identity property, If we have a rational number p/q, then there exist a number zero (0), such that if we add the number zero to any number, the result remains unchanged. So we write it as : p/q + 0 = p/q 4. Multiplicative identity of Rational numbers: According to multiplicative identity property of rational numbers, If we have a rational number p/q, then there exist a number one (1), such that if we multiply the number one to any number, the result remains unchanged. So we write it as : p/q * 1 = p/q 5. Power of zero: By the property Power of zero, we mean that there exists a number zero, such that if we multiply zero to any rational number, then the product id zero itself. So if we have p/q as a rational number, then we say: p/q * 0 = 0 . 6. Associative property of Rational numbers: Associative property of rational numbers holds true for addition and multiplication but does not hold true for subtraction and division. It means that if p1/q1 , p2/q2 and p3/q3 are any three rational numbers, Read More About :- Dividing Whole Numbers by Decimals

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