In mathematics, the rational number is the type of real number which can be perfectly represented in the form of P/Q where Q will not be equal to 0 at any point in time. Any fraction which comes with non-zero denominators should go with the option of being categorised into the rational number in the whole process. The very basic example is 3/4, 1/2, 1/5 and so on. Zero is also considered to be a type of rational number because people can perfectly represent it into several formats for example 0/1, 0/3 and so on. It is very much important for people to be well-versed with the properties of rational numbers so that they can make the right kind of decisions in the whole world of mathematics and can indulge in proper simplified procedures in the whole process.
Identification of the rational numbers will always be based upon two main points which or explained as:
- It will be represented in the form of P/Q where Q is not equal to 0
- It will be represented in the form of the ratio of P/Q which can be further simplified and represented in decimal format.
The set of rational numbers can always be:
- Inclusive of positive, negative and zero numbers
- Can be expressed as the fraction
Following are some of the very basic categories of the numbers about which everyone should be clear:
- Real numbers will include all the rational numbers
- Real numbers will include the integers
- Integers will include all the natural numbers
- Every whole number is a rational number because every whole number can be perfectly expressed in the form of a fraction.
The standard form of the rational number can be perfectly defined and it will not include any kind of common factors aside from one between the dividend and the divisor because the divisor has to be positive in the whole process.
Following are some of the basic points associated with the negative and positive rational numbers:
- If the numerator and denominator are of the same signs then it will be a positive rational number but if the numerator and denominator are of the opposite signs then it will be a negative rational number.
- All positive rational numbers will be greater than zero and all negative rational numbers will be less than zero.
- An example of positive rational number can be 12/17 and an example of a negative rational number can be -2/17
Following are some of the very basic arithmetic operations which can be carried out on rational numbers:
- Kids can very easily go with the option of application of the laws of addition of the rational numbers so that they can indulge in adding fractions.
- Kids can go with the option of implementing the subtraction concept on rational numbers very easily.
- Multiplication can also be easily applied to rational numbers so that there is no query in the minds of people.
- Division can also be implemented on rational numbers very easily.
Following are the basic properties of the rational numbers about which everybody should be clear:
- The result will always be a rational number if people go with the option of multiplying, adding or subtracting any two rational numbers
- The rational number will remain the same if people divide or multiply both the numerator and nominator with the same factor
- If we add 0 to a rational number then one will get the same number itself
- Rational numbers are always closed under subtraction, multiplication and addition
Hence, being clear about the concept of rational numbers and irrational numbers is very much important in the whole process so that there is no issue at any point in time and apart from this people also need to be clear about the concept of number line. So, to have a good command of all these kinds of things people need to register themselves on platforms like Cuemath to ensure success.
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