Rational numbers
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, rational numbers can be written in the form a/b, where a and b are integers, and b is not equal to zero.
Examples of rational numbers include:
1/2, 3/4, -5/6, 7/8, 2/1, -3/5, 0/1, etc.
It is important to note that integers and fractions (proper and improper) are all considered rational numbers since they can be expressed in the form of a/b.
Properties of rational numbers:
1. Closure property: When two rational numbers are added, subtracted, multiplied, or divided, the result is always a rational number. For example, if you add 1/2 and 3/4, you get 5/4, which is also a rational number.
2. Commutative property: The order of numbers does not affect the result when adding or multiplying rational numbers. For example, if you multiply 3/4 by 2/3, you get 2/3 multiplied by 3/4, which is still equal to 1/2.
3. Associative property: The grouping of numbers does not affect the result when adding or multiplying rational numbers. For example, if you add (1/2 + 3/4) + 5/6, it is the same as adding 1/2 + (3/4 + 5/6), and the result is 17/12 in both cases.
4. Identity property: The sum of any rational number and zero is the number itself. For example, if you add 1/2 and 0, you get 1/2. Similarly, the product of any rational number and 1 is the number itself. For example, if you multiply 5/6 by 1, you get 5/6.
5. Inverse property: Every rational number has an additive inverse (opposite) and a multiplicative inverse (reciprocal). The sum of a rational number and its additive inverse is 0. For example, if you add 3/4 and -3/4, the result is 0. Similarly, the product of a rational number and its multiplicative inverse is 1. For example, if you multiply 2/3 by 3/2, the result is 1.
These properties make rational numbers very useful in various mathematical operations and calculations.
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