Properties of Rational Numbers Properties of Rational Numbers The rational numbers are closed under addition, subtraction, multiplication and division by nonzero rational numbers. The properties are called closure properties of rational numbers. If 'm' and 'n' are two rational numbers then the addition, subtraction, multiplication and division of these rational numbers is also a rational number, then these numbers satisfy the closure law. Letâ€™s take an example of addition which satisfies the closure properties, 3+4=7 shows the closure property of real number addition because when we add the real numbers to other real numbers the result is also real.
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This condition is necessary for all other operations like subtraction, multiplication and division. Identity Property of Rational Numbers Rational numbers are the numbers which can be expressed in the form x/y, provided y is not equal to zero and x,y are integers. Apart from the addition, subtraction, multiplication and division, rational numbers show a specific property which is called identity of rational numbers and such numbers are called identity property of rational numbers. There are two types of identity properties of rational numbers which are as follows: 1. Additive identity 2. Multiplicative identity Additive Identity of rational numbers: Additive identity of a rational number is basically a real number which when added to a rational number does not change its value, zero is called the additive identity for all rational numbers, for example letâ€™s say â€œQâ€? is a rational number equal to a/b Also if we add '0' to this rational number Learn More About Equivalent Rational Numbers Worksheets
Q+0 = Q or a/b+0 = a/b, as we see from the result we get the same rational number that is why zero is called the additive identity of rational numbers. Multiplicative Identity: Multiplicative identity of a rational number is such a real number which when multiplied by a rational number, its value remains unchanged, '1' is called the multiplicative identity for all rational numbers, ex. QĂ—1 = Q, or a/b Ă—1 = a/b, as we can see from the example when rational number 'q' is multiplied by 1, its value remains unchanged that is why 1 is called the multiplicative inverse of rational numbers.
If 'm' and 'n' are two rational numbers then the addition, subtraction, multiplication and division of these rational numbers is also a rati...