![]() Hence, it is evident that all Rational Numbers except ‘0’ are closed under the Mathematical operation of division.Īccording to the Commutative Law, for Rational Numbers, the Mathematical operations of addition and multiplication are commutative.Īccording to the commutative law of addition, for two Rational Numbers, say, 'a' and 'b': a + b = b + a. We will now perform the Mathematical operation of division on these two numbers.Ī ÷ b = 1/2 ÷ 3/4 = 1/2 * 4/3 = 2/3, which is also a Rational Number. However, we can say that except '0,' all numbers are closed under the Mathematical operation of division. The reason why the Mathematical operation of division is not under the closure property is that division by zero isn't defined. Why is the Mathematical Operation of Division Not Under the Closure Property? Hence, it is evident that Rational Numbers are closed under the Mathematical operation of multiplication. We will now perform the Mathematical operation of multiplication on these two numbers.Ī * b = 1/2 * 3/4 = 3/8, which is also a Rational Number. ![]() Let us try to understand the concept of multiplication of Rational Numbers under the closure property with the help of an example. Multiplication of Rational Numbers Under the Closure PropertyĪccording to the closure property, the result of the multiplication of two Rational Numbers, say, for example, 'a' and 'b' is also a Rational Number, that is, a * b is also a Rational Number. Hence, it is evident that Rational Numbers are closed under the Mathematical operation of subtraction. We will now perform the Mathematical operation of subtraction on these two numbers.Ī - b = 1/2 - 3/4 = (1*2 - 3*1)/4 = -1/4, which is also a Rational Number. ![]() Let us try to understand the concept of subtraction of Rational Numbers under the closure property with the help of an example. ![]() Subtraction of Rational Numbers Under the Closure PropertyĪccording to the closure property, the result of the subtraction of two Rational Numbers, say, for example, 'a' and 'b' is also a Rational Number, that is, a - b is also a Rational Number. Hence, it is evident that Rational Numbers are closed under the Mathematical operation of addition. We will now perform the Mathematical operation of addition on these two numbers.Ī + b = 1/2 + 3/4 = (1*2 + 3*1)/4 = 5/4, which is also a Rational Number. Let us try to understand the concept of the addition of Rational Numbers under the closure property with the help of an example. Therefore, we can say that the Rational Numbers are closed under the Mathematical operations of addition, subtraction, and multiplication.Īddition of Rational Numbers Under the Closure PropertyĪccording to the closure property, the result of the addition of two Rational Numbers, say, for example, 'a' and 'b' is also a Rational Number, that is, a + b is also a Rational Number. So, let us go through these properties of Rational Numbers one by one.Īccording to the Closure Property, for two Rational Numbers, say, for example - 'a' and 'b,' the results of addition, subtraction, and multiplication operations shall always give another Rational Number. ![]() For understanding the properties of Rational Numbers, we will consider the general properties of integers, including commutative, associative, and closure properties. To be specific, Rational Numbers are integers that can be represented on the number line. In Mathematics, Rational Numbers are those numbers that can be expressed in the form of a/b where both ‘a’ and ‘b’ are integers, and b is not equal to 0. On this page not this question will be answered, you will also learn about other properties associated with Rational Numbers. Do you ever come across numbers expressed in fractional forms and wonder why haven’t they expressed as other whole numbers? What is its significance? To answer these questions Vedantu has brought this write-up for you. ![]()
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