Number system is a technique of writing to express numerals. It is the mathematical inscription used to express digits of a given group by using numerals or other characters. It has arithmetic functions to execute division, multiplication, addition, and subtraction between numbers.
Numbers and Digits
Digits are the calculations or dimensions used in mathematics, digits are used to represent numbers. A digit can be described as a character used for counting, for example, there are 45 books in the library, where 46 is the integer which is a mixture of integers 4 and 6. An integer is a single digit, the variety of digits form integers. In the decimal number system, there are 10 integers, they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
What are Rational Numbers?
A rational number is a digit that can be defined in a p/q format such that q is not equal to 0. The group of rational numerals Possesses positive, negative numerals, and zero and it is represented by Q. Rational number can also be represented as a fraction.
When a numeral is represented in a p/q format or in fraction format where both the numerator and the denominator element are integers, then the numeral is known as a rational number.
Some examples of rational numbers are: 2/3, -3/7, 8/13, -5/9, 16/44
The numeral“0” is also a rational number, as we can denote it in many formats such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational numerals because they provide us infinite values.
Note: Rational numerals can also be represented in decimal format.
Types of Rational Numbers
There are different types of rational numbers and they are:
Natural Numbers: All natural numerals are rational numerals because they can be documented in p/q format. Like 4 can be expressed in 4/1 (p/q) form.
Example – 1, 2, 3, 4, 5 …. etc.
Terminating Decimals: Rational numbers can also be expressed in decimal form because decimal numbers can be represented in p/q form. For example, 2.1 can be written as 2.1 = 21/10. Thus all terminating decimals are rational numbers.
Example – ( 0.55, 0.3456, 0.8755 etc. )
Non-Terminating Decimals: Non-Terminating decimals holding replicated numerals after the decimal point such as 0.88888….., 0,242424…. are also rational numbers. Since 0.88888… can be written as 1/8, therefore it is a rational number.
Example – ( 0.22222….., 0.121212….. etc. )
Fractions: When a numeral is described in a p/q format or in fraction format where both the numerator and the denominator element are integers, then it is a rational number.
Example – 3/4, 2/7, 7/10, -7/10, 14/99 (all of them are in p/q form)
Whole Numbers: All whole numbers are rational numerals because the whole numerals can be represented in p/q fraction format.
Example – 0 is a rational number because it can be written as a fin 0/1, 0/-2,… etc.
How to add the negative rational numbers
Step 1:- Determine the Final Sign(Positive or Negative) Same Signs Same, Different Keep the Larger
Step 2:- Add or Subtract Same Signs Add, Different Signs Subtract
Sample Problems
Problem 1: Add two rational numbers 1.2 and -3.4
Solution:
Step 1:- Determine the Final Sign(Positive or Negative) In this question it is Different Keep the Larger
Step 2:- Add or Subtract In this question it is Different Signs Subtract
= 1.2 + -3.4 (Different Signs Subtract)
= -2.2 (Different keep the larger i.e.,- )
Problem 2: Add two rational numbers -2.5 and -6.2
Solution:
Step 1:- Determine the Final Sign(Positive or Negative) In this question it is Same Signs Same.
Step 2:- Add or Subtract In this question it is Same Signs Add.
= -2.5 + -6.2 (same signs add)
= -8.7(same sign same i.e., -)
Problem 3: Add two Rational numbers 5/6 and -2/6
Solution:
Step 1:- Determine the Final Sign(Positive or Negative) In this question it is different keep the larger.
Step 2:- Add or Subtract In this question it is different sign subtract.
= 5/6 + -2/6 (different sign subtract)
= (3/6) / (3/3)(different keep the larger)
= 1/2
Problem 4: Add two rational numbers -2(1/3) + -1(2/3)
Solution:
Step 1:- Determine the Final Sign(Positive or Negative) In this question it is Same Signs Same.
Step 2:- Add or Subtract In this question it is Same Signs Add,
= -2(1/3) + -1(2/3) (Same Signs Add)
= -4 ( Same Signs Same)
How to subtract the negative rational numbers
Problem 5: Subtract two rational numbers -4.5 and -5.5
Solution:
In this question use, change the problem to addition(keep change )
This means changing the equation -4.5 – (-5.5) into -4.5 + (-5.5)
= -4.5 + (+5.5)
As now it is converted into an addition problem now, we can use the same step from before i.e.,
Step 1:- Determine the Final Sign(Positive or Negative) which is Different Keep the Larger
Step 2:- Add or Subtract In this equation it is Different Signs Subtract
= -4.5 + (+5.5) (Different Signs Subtract )
= 1 (Different Keep the Larger)
Problem 6: Subtract two rational numbers -3/8 and 4/8
Solution:
Use, change the problem to addition(keep change )
This means changing the equation -3/8 – 4/8 into -3/8 + (-4/8)
= -3/8 + (-4/8)
As now it is converted into an addition problem now, we can use the same step from before i.e.,
Step 1:- Determine the Final Sign(Positive or Negative) which is the same sign same
Step 2:- Add or Subtract In this equation it is Same Signs Add
=-3/8 + (-4/8) (Same Signs Add)
= -7/8 (same sign same)
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