Associative Property Of Rational Numbers Associative Property Of Rational Numbers We know that the rational numbers are the numbers which can be written in the form of p/q, where p and q are integers and the denominator q <> 0. All natural numbers, whole numbers, integers and all fraction numbers with their additive inverse as the elements of the set of rational numbers. There are different properties of rational numbers. In this session we will learn about the Associative Property of Rational Numbers. We will be checking that if the Associative property holds true for all the mathematical operators namely Addition, subtraction, multiplication and division or not . Let us first define what is the Associative property of Rational numbers. According to the Associative Property of Rational Numbers, we mean that: Know More About Calculus Limit Worksheet

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if p1/q1 , p2/q2 and p3/q3 are any three rational numbers, then we have Associative Property of Addition of Rational Numbers, by which we have (p1/q1 + p2/q2) + p3/q3 = p1/q1 + (p2/q2 + p3/q3). Eg if we have p1/q1 = 1/7 , p2/q2 = 3/7, and p3/q3 = 2/7 then we have ( p1/q1 + p2/q2 ) + p3/q3 = (1/7 + 3 / 7) + 2/7 = 4/7 + 2/7 = 6/7 Also we have p1/q1 + (p2/q2 + p3/q3) = 1/7 + (3/7 + 2/7) = 1/7 + 5/7 = 6/7 In both the cases we get the same result. Thus we can say that the Associative property of Addition holds true for the rational numbers. if p1/q1 , p2/q2 and p3/q3 are any two rational numbers, then we have Associative Property of Multiplication of Rational Numbers, by which we have (p1/q1 * p2/q2) * p3/q3 = p1/q1 * (p2/q2 * p3/q3). Eg if we have p1/q1 = 1/7 , p2/q2 = 3/7, and p3/q3 = 2/7 then we have ( p1/q1 * p2/q2 ) * p3/q3 = (1/7 * 3 / 7) * 2/7 = (3/49) * (2/7) = ( 6 / 343) Also we have p1/q1 * (p2/q2 * p3/q3) = 1/7 * (3/7 * 2/7) = (6 / 343) In both the cases we get the same result. Thus we can say that the Associative property of Multiplication holds true for the rational numbers. On the another hand if we try the Associative property for the subtraction and division of the rational numbers Read More About Antiderivative Of 0

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if p1/q1 , p2/q2 and p3/q3 are any two rational numbers, then we have Associative Property of subtraction of Rational Numbers, by which we have (p1/q1 - p2/q2) p3/q3 = p1/q1 - (p2/q2 - p3/q3). Eg if we have p1/q1 = 1/7 , p2/q2 = 3/7, and p3/q3 = 2/7 then we have ( p1/q1 - p2/q2 ) - p3/q3 = (1/7 - 3 / 7) - 2/7 = (-2/7) - (2/7) = ( -4/ 7) Also we have p1/q1 - (p2/q2 - p3/q3) = 1/7 - (3/7 - 2/7) = 1/7 -1/7 = 0 The two results are not equal. Similarly it is not true for division. Thus we come to a conclusion that the Associative property does not hold true for Division.

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