What is a rational number?
Rational numbers are Rational Number for class 8 those that can be represented in the form p/q, where p and q are integers and q≠0. Integers, whole numbers, and natural numbers are all examples of rational numbers. Numbers that may be expressed as fractions are known as rational numbers.
Some examples of rational numbers are = 0/4,4/3,-9/-5……etc
It is to be noted that q should not be equal to zero. Rational Number for class 8 It is because any number divided by 0 is equal to infinity. It means that it cannot be defined. So, q≠0.
Also read: How to clean glass reactor?
Some key factors to keep in mind: By Number
- Always remember that zero is a rational number.
- A rational number is any integer.
- Natural numbers, whole numbers, integers, and decimals are not in the form of p/q, but they may be expressed as p/q, which makes them rational numbers.
- Every fraction is a number that may be expressed as a rational number.
- Rational numbers include non-terminating decimals with repeated decimal patterns.
- Any integer that may be stated as fractions is a rational number.
- In addition, rational numbers can be stated in decimal form.
Properties of Rational Numbers-
The below are the six properties of rational numbers:
- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- Multiplicative Property
- Additive Property
- Closure Property – The closure property of rational numbers asserts that any two rational numbers added, subtracted,Rational Number for class 8 or multiplied will produce a rational number in all three circumstances. For example-
- When x and y are added then (x+y) will be a rational number only.
- ⅙ +⅛ = 4+3/24 = 7/24 which is a rational number.
- Subtraction –
- When x is subtracted from y then (y-x) is a rational number only.
- ¾-½ = 6-4/8 = 2/8 which is a rational number.
- When x is multiplied by y then (x*y) is a rational number only.
- ¾*½ = ⅜
2. Commutative Property –
The commutative property of rational numbers asserts that adding or multiplying any two rational numbers in any order produces the same result. However, if the order of the numbers is altered in subtraction and division, the result will vary as well.
- Addition –
- For x and y, x + y = y+ x (x and y are rational numbers)
- ½ +⅛ and ⅛+½ = ⅝
- Subtraction –
- For x and y, y – x ≠ x – y. (x and y are rational numbers)
- 5/3-¼ = 17/12
- ¼-5/3 = -17/12
- For x and y, x*y= y*x. (x and y are rational numbers)
- For x and y, x ÷ y ≠ y ÷ x. (x and y are rational numbers)
- 5/3÷ ¼ = 20/3
- ¼ ÷ 5/3 =3/20
3. Associative Property –
The associative characteristic of rational numbers asserts that no matter how numbers are grouped, the outcome stays the same when any three rational numbers are added or multiplied. However, if the order of the numbers is altered in subtraction and division, the result will vary as well.
- The associative property for addition is provided for any three rational integers as X, Y, and Z, (X + Y) + Z = X + (Y + Z).
- The associative property for subtraction is provided for any three rational integers as X, Y, and Z, (X – Y) – Z ≠ X – (Y – Z)
- The associative property for multiplication is provided for any three rational integers as X, Y, and Z (X × Y) × Z = X × (Y × Z)
- The associative property for division is provided for any three rational integers as X, Y, and Z (X ÷ Y) ÷ Z ≠ X ÷ (Y ÷ Z)
- Distributive Property-
Any statement with three rational numbers X, Y, and Z written in the form
X (Y + Z) is resolved as X (Y + Z) = XY + XZ or X (Y – Z) = XY – XZ,
according to the distributive principle of rational numbers. This signifies that operand X is shared amongst the other two operands, Y and Z. Multiplication distributivity over addition or subtraction is another name for this feature.
- Multiplicative Property –
The additive identity characteristic of rational numbers asserts that any rational number multiplied by 1 equals the rational number. For rational integers given in x/y form, 1 is the multiplicative identity.
- Additive property –
According to the additive identity feature of rational numbers, the sum of any rational number (x/y) and zero equals the rational number itself.
This is all about the basics of rational numbers for class 8. Learning theory and property is crucial before practicing the questions. Through this article, we want to tell you about the basics of a rational number.
Though the rational number is not a tough topic still you should practice well to solve its question easily. For further information check out the Frequently asked questions (FAQs) section of the article.
Frequently Asked Questions (FAQs)-
- From which book should we study?
One can study from NCERT and RS Aggarwal maths book for class 8. Both the books are competent with their board’s syllabus. The students should practice from both books thoroughly to gain good marks in their exams.
- Should we go through sample papers and papers from past years?
Without a doubt. You should use sample papers and even take mock examinations to prepare for your exams. This will assist you in evaluating your preparation before the exam. You can also get an idea of the exam’s format and difficulty. Solving practice papers can help you improve your accuracy and speed. As a result, you should solve example papers.
- Where can I get RS Aggarwal class 8 solutions?
Solutions to the RS Aggarwal book for class 8 may be found on several websites. You may need to go to the website and look for the appropriate question. In the event of a doubt, it is extremely simple to consult an internet answer.
- What are the advantages of studying from RS Aggarwal Class 8 Solutions?
There are various advantages to studying from RS Aggarwal Solutions Class 8 Rational Numbers and solutions. There are several references, practice exercises, sample papers, and question papers from prior years.