### Rational Numbers

Any number that can be written in the form of p ⁄ q where q ≠ 0 are rational numbers. It posses the properties of:

- Additive Identity: (a ⁄ b + 0) = (a ⁄ b)
- Multiplicative Identity: (a ⁄ b) × 1 = (a/b)
- Multiplicative Inverse: (a ⁄ b) × (b/a) = 1
**Closure Property – Addition:**For any two rational numbers*a*and*b, a + b*is also a rational number.**Closure Property – Subtraction:**For any two rational numbers*a*and*b, a – b*is also a rational number.**Closure Property – Multiplication:**For any two rational numbers*a*and*b, a × b*is also a rational number.**Closure Property – Division:**Rational numbers are not closed under division.**Commutative Property – Addition:**For any rational numbers a and b, a + b = b + a.**Commutative Property – Subtraction:**For any rational numbers a and b, a – b ≠ b – a.**Commutative Property – Multiplication:**For any rational numbers a and b, (a x b) = (b x a).**Commutative Property – Division:**For any rational numbers a and b, (a/b) ≠ (b/a).**Associative Property – Addition:**For any rational numbers a, b, and c,*(a + b)*+ c =*a + (b + c)*.**Associative Property – Subtraction:**For any rational numbers a, b, and c,*(a – b)*– c ≠*a – (b – c)***Associative Property – Multiplication:**For any rational number a, b, and c,*(a x b) x c*=*a x (b x c).***Associative Property – Division:**For any rational numbers a, b, and c,*(a / b)*/ c ≠*a / (b / c)*.**Distributive Property:**For any three rational numbers*a, b*and*c*,*a × ( b + c ) = (a × b) +( a × c)*.

**Number Formation**

- A two-digit number ‘ab’ can be written in the form: ab = 10a + b
- A three-digit number ‘abc’ can be written as: abc = 100a+10b+c
- A four-digit number ‘abcd’ can be formed: abcd = 1000a+100b+10c+d

### Laws of Exponents

- a
^{0}= 1 - a
^{-m}= 1/a^{m} - (a
^{m})^{n}= a^{mn} - a
^{m}/ a^{n}= a^{m-n} - a
^{m}x b^{m }= (ab)^{m} - a
^{m}/ b^{m }= (a/b)^{m} - (a/b)
^{-m}=(b/a)^{m} - (1)
= 1 for infinite values of^{n}*n*.

### Algebraic Identity

Algebraic Identities comprises of several equality equations which consist of different variables.

**a) Linear Equations in One Variable:**A linear equation in one variable has the maximum one variable of order 1. It is depicted in the form of ax + b = 0, where x is the variable.**b) Linear Equations in Two Variables:**A linear equation in two variables has the maximum of two variables of order 2. It is depicted in the form of ax^{2}+ bx + c = 0.

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - (x + a) (x + b) = x
^{2}+ (a + b)x + ab - (x + a) (x – b) = x
^{2}+ (a – b)x – ab - (x – a) (x + b) = x
^{2}+ (b – a)x – ab - (x – a) (x – b) = x
^{2}– (a + b)x + ab - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{3}= a^{3}– b^{3}– 3ab(a – b)

### Maths Formulas For Class 8 Square & Square Roots

If a natural number, m = n^{2} and n is a natural number, then m is said to be a square number.

- Every square number surely ends with 0, 1, 4, 5 6 and 9 at its units place.
- A square mysqladmin is the inverse operation of the square.

### Formula Of Maths Class 8 Cube & Cube Roots

Numbers, when obtained while multiplied by itself three times, is known as cube numbers.

- If every number in the prime factorization appears three times, then the number is a perfect cube.
- The symbol of the cube is ∛.
*Cube and Cube mysqladmin:*∛27 = 3 and 3^{3}= 27.

### 8th Class Maths Formulas Comparing Quantities

Discounts are the reduction value prevailed on the Marked Price (MP).

**Discount = Marked Price – Sale Price****Discount = Discount % of the Marked Price**

Overhead expenses are the additional expenses made after purchasing an item. These are included in the Cost Price (CP) of that particular item.

**CP = Buying Price + Overhead Expenses**

GST (Goods and Service Tax) is calculated on the supply of the goods.

**Tax = Tax % of the Bill Amount**

Compound Interest (CI) is the interest which is compounded on the basis of the previous year’s amount.

**Formula of Amount (Compounded Annually):** **\(A = P \left (1 + \frac{R}{100} \right )^t\)**

P = Principal,

r = Rate of Interest, and

t = Time Period

**Formula of Amount (Compounded Half Yearly):** **\(A = P \left (1 + \frac{R}{200} \right )^{2t}\)**

R/2 = Half-yearly Rate,

2t = Number of Half-Years

### Maths Formulas For Class 8 Data Handling & Probability

Any useful information that can be utilized for some specific use is known as Data. These data can be represented either graphically (Pictograph/Bar Graph/Pie Charts) or symmetrically (Tabular form). Find the important Class 8 Maths formulas for Data Handling and Probability.

- A class interval is the specific range of numbers such as 10-20, 20-30, 30-40, and so forth.
- For a Class Interval of 10-20, Lower Class Limit = 10 and Upper-Class Limit = 20
- Frequency is the number of times a particular value occurs.

*Probability = Number of Favourable Outcomes / Total Number of Outcomes*

### Math Formula Class 8 Geometry

Here, we will define the geometrical formulas consistently used in Mathematics Class 8. We will use the following abbreviations for convenience:

- 1. LSA – Lateral/Curved Surface Area
- 2. TSA – Total Surface Area

Name of the Solid Figure | Formulas |

Cuboid | LSA: 2h(l + b)TSA: 2(lb + bh + hl)Volume: l × b × hl = length, b = breadth, h = height |

Cube | LSA: 4a^{2}TSA: 6a^{2}Volume: a^{3}a = sides of a cube |

Right Pyramid | LSA: ½ × p × lTSA: LSA + Area of the baseVolume: ⅓ × Area of the base × hp = perimeter of the base, l = slant height, h = height |

Right Circular Cylinder | LSA: 2(π × r × h)TSA: 2πr (r + h)Volume: π × r^{2} × hr = radius, h = height |

Right Circular Cone | LSA: πrlTSA: π × r × (r + l)Volume: ⅓ × (πr^{2}h)r = radius, l = slant height, h = height |

Right Prism | LSA: p × hTSA: LSA × 2BVolume: B × hp = perimeter of the base, B = area of base, h = height |

Sphere | LSA: 4 × π × r^{2}TSA: 4 × π × r^{2}Volume: 4/3 × (πr^{3})r = radius |

Hemisphere | LSA: 2 × π × r^{2}TSA: 3 × π × r^{2}Volume: ⅔ × (πr^{3})r = radius |

## List of Important Class 8 Math Formulas

Consistent practise is essential for success in math. Students are encouraged to solve as many problems as they can, since this will expose them to a variety of formulas. This is a fantastic technique to recall formulas without having to mumble them down. Here is a summarized list of Class 8 math formulas that can be used.

- Additive inverse of rational number: a/b = -b/a
- Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
- Distributivity a(b – c) = ab – ac
- Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
- Compound Interest formula = Amount – Principal, Amount in case the interest is to be calculated annually = Principal ( 1 + Rate/100)
^{n}, where ‘n’ is the time period. - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - Euler’s Formula: For any polyhedron, Number of faces + Number of vertices – Number of edges = 2
- Volume of a Cone = (1 / 3 )πr
^{2}h - Volume of a Sphere = (4/3) π r
^{3}

### Maths Formulas For Class 8: Important FAQs On Class 8 Maths All Formulas

Here are some important frequently asked questions related to Class 8 Maths formulas.

** Q: How to memorize Class 8 Maths formulas?** Just refer to the formula sheet as you solve questions. Eventually, you will memorize them and master their application.

A:

** Q: Is NCERT enough for Class 8 Maths exam?** Yes, for Class 8, NCERT Maths textbook is enough.

A:

*Q: Which book should I prefer for learning Class 8 maths formulas?*** A:** We advise you to go for NCERT books if you want to know all the important Class 8 Maths formulas.

*Q: Is there any website that offers free Class 8 practice questions?*** A:** Embibe provides free Class 8 practice questions to learn and score well in your examinations.

*Q: How to make the best use of these maths formulas?*** A:** These Class 8 Maths formulas will help you when you get stuck in some questions while practicing the subject. The formulas and properties will help you in quick revision. This way you can prepare well and score better.

*Q: How will these Class 8 maths formulas help me?***A:** These Maths formulas are taken from the standard Class 8 NCERT book. Therefore, it’ll prove to be useful for you no matter what education board you are studying in. These formulas are present on a page so that you don’t have to go back and forth. Hence, this will come in handy at the time of revision.

## Geometry Formulas for Class 8

To recall, geometric shapes are of two types which are 2D shapes and 3D shapes (or solid shapes). The list for all the 2D and 3D geometric shapes are:

### Geometry Shapes Formulas for Solid Shapes:

Name of the Solid | Lateral / Curved Surface Area | Total Surface Area | Volume |
---|---|---|---|

Cuboid | 2h (l + b) | 2 (lb + bh + hl) | l × b × h |

Cube | 4a^{2} | 6a^{2} | a^{3} |

Right Prism | Perimeter of Base × Height | Lateral Surface Area + 2(Area of One End) | Area of Base × Height |

Right Circular Cylinder | 2 (π × r × h) | 2πr (r + h) | πr^{2}h |

Right Pyramid | ½ (Perimeter of Base × Slant Height) | Lateral Surface Area + Area of the Base | ⅓ (Area of the Base) × Height |

Right Circular Cone | πrl | πr (l + r) | ⅓ (πr^{2}h) |

Sphere | 4πr^{2} | 4πr^{2} | 4/3 (πr^{3}) |

Hemisphere | 2πr^{2} | 3πr^{2} | ⅔ (πr^{3}) |

### Geometry Shapes Formulas for 2D Shapes:

Geometric Area | Geometric Area Formula |
---|---|

Square | a^{2} |

Rectangle | a × b |

Circle | πr^{2} |

Ellipse | πr_{1}r_{2} |

Triangle | ½(b × h) |

## Algebra Formulas for Class 8

Some important 8th class formulas related to Algebra are:

Algebraic Identities For Class 8 |
---|

(a + b)^{2 }= a^{2 }+ 2ab + b^{2} |

(a − b)^{2 }= a^{2 }− 2ab + b^{2} |

(a + b) (a – b) = a^{2 }– b^{2} |

(x + a) (x + b) = x^{2 }+ (a + b)x + ab |

(x + a) (x – b) = x^{2 }+ (a – b)x – ab |

(x – a) (x + b) = x^{2 }+ (b – a)x – ab |

(x – a) (x – b) = x^{2 }– (a + b)x + ab |

(a + b)^{3 }= a^{3 }+ b^{3 }+ 3ab (a + b) |

(a – b)^{3 }= a^{3 }– b^{3 }– 3ab (a – b) |

## List of Important Class 8 Math Formulas

Here is a summarized list of Class 8 math formulas that can be used.

- Additive inverse of rational number: a/b = -b/a
- Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
- Distributivity a(b – c) = ab – ac
- Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
- Compound Interest formula = Amount – Principal, Amount in case the interest is to be calculated annually = Principal ( 1 + Rate/100)
^{n}, where ‘n’ is the time period. - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - Euler’s Formula: For any polyhedron, Number of faces + Number of vertices – Number of edges = 2
- Volume of a Cone = (1 / 3 )πr
^{2}h - Volume of a Sphere = (4/3) π r
^{3}

### Rational Numbers Class 8 Math Formulas

Integers, real numbers, natural numbers, whole numbers, fractional numbers, prime numbers, composite numbers are the different types of numbers in arithmetic. Rational Numbers Class 8 math formulas cover the different entities of rational numbers that will help the students understand the concept of rational numbers, their uniqueness from the rest of the numbers and their usage in higher arithmetic.

Any number that can be written in the form of a ⁄ b where b ≠ 0 are rational numbers. The properties of rational numbers are as follows:

- Additive Identity states (a ⁄ b + 0) = (a ⁄ b)
- Multiplicative Identity states (a ⁄ b) × 1 = (a/b)
- Multiplicative Inverse states (a ⁄ b) × (b/a) = 1

### Geometry Solid Shapes Class 8 Math Formulas

Solid geometry plays an important part in everyday life since it aids in understanding the various shapes that surround us and their qualities. Students will benefit from a strong understanding of visualization of solid objects in learning more complicated geometry concepts, and in solving real-world problems. Hence, it becomes essential to learn about the various formulas associated with different solids that will help in everyday calculations.

- Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, where ‘r’ is its base radius and ‘l’ its slant height. ‘l’ = √(r
^{2}+ h^{2}) - Volume of a Cuboid = Base Area × Height = Length × Breadth × Height
- Volume of a Cone = (1 / 3 )πr
^{2}h - Volume of a Sphere = (4/3) π r
^{3} - Volume of a Hemisphere = (2/3) πr
^{3}

### Data Handling Formulas for Class 8 Maths

Any problem that we need to investigate necessitates the gathering of data, which must then be displayed in such a way that it gives a clear visual of the problem’s details while also analyzing the solutions that are possible. For this the students need to familiarize themselves with various concepts related to data handling. One such concept that falls within data handling is probability which helps in the prediction of events. Probability is the mathematical term for possibility of occurrence.

Probability = Number of outcomes making up an event / Total number of outcomes, if the outcomes are equally likely.

### Exponents Formulas for Class 8 Maths

An exponent represents the value which refers to the number of times a number is multiplied by itself. For example, 5 × 5 × 5 can be written as 53. Even very small numbers can be expressed in the form of negative exponents. Here is a list of some of the laws related to exponents:

- Law of Product: a
^{m}× a^{n}= a^{m + n} - Law of Quotient: a
^{m}/a^{n}= a^{m – n} - Law of Zero Exponent: a
^{0}= 1 - Law of Negative Exponent: a
^{-m}= 1/a^{m} - Law of Power of a Power: (a
^{m})^{n}= a^{mn} - Law of Power of a Product: (ab)
^{m}= a^{m}b^{m} - Law of Power of a Quotient: (a/b)
^{m}= a^{m}/b^{m}

### Comparing Quantities Formulas for Class 8 Maths

The following formulas will help students understand the basics of simple arithmetic involving money.

- Discount = Marked Price – Sale Price
- Simple Interest = ( Principal × Rate × Time )/100
- Compound Interest Formula = Amount – Principal

If the interest is to be calculated annually, then Amount = Principal ( 1 + Rate/100)^{n}, ‘n’ is the time period.

### Algebra for Class 8 Maths

Algebraic expressions and Identities are one of the most important and interesting concepts to understand the nature of mathematics. Factorization of an algebraic expression results in a product of factors. These factors can be numbers, algebraic variables or expressions. The following three identities hold true for any value of the variables.

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2}

## Applications of Class 8 Maths Formulas

Math is present in practically every activity that we engage in our daily lives. The formulation of these arithmetic formulas was based on an analytical examination of how to address challenges encountered in everyday life.

- The class 8 maths formulas related to data handling and probability help in taking out meaningful inferences and the prediction of events.
- The class 8 maths formulas related to exponents and powers help in making the complex calculations encountered in mathematics very easy. The laws of exponents are a quick way to understand the mathematics of large numbers.
- The algebraic entities are an interesting way to solve the value of the unknown for any given problem.

**Example 1:** Solve the given expression using the law of exponents: 40^{5} × 40^{2}

**Solution: **

We will solve the expression using the Law of Product: a^{m} × a^{n} = a^{m+n}

40^{5} × 40^{2} = 40^{5+2}

= 40^{7}

**Example 2 :** The height of a cylinder needs to be calculated whose radius is 6 cm and the total surface area is 900 cm^{2}

**Solution: **Let us assume the height of the cylinder = h, radius = 6 cm

Total surface area of cylinder = 2πr (h + r)

Substituting the values in the given equation:

900 = 2 × 22/7 × 6 (h + 6)

h = 17.87

Hence, the height of the cylinder is 17.87 cm.

## List of 8th Class Maths Formulae

## FAQs on Class 8 Maths Formulas

### What are the Important Formulas for Class 8 Maths?

Class 8 maths formulas help in forming a solid base for the board examinations that the students usually face in class 9 and class 10. Here is a quick overview of some of the important formulas that could help in the problem solving process:

- Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
- Distributivity a(b – c) = ab – ac
- Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
- Compound Interest formula = Amount – Principal, Amount in case the interest is to be calculated annually = Principal (1 + Rate/100)
^{n}, where ‘n’ is the time period. - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - Euler’s Formula: For any polyhedron, Number of faces+Number of vertices-Number of edges = 2
- Volume of a Cone = (1 / 3 )πr
^{2}h

### What are the Basic Formulas in Class 8 Maths?

The basic formulas covered in class 8 maths are from the topics of rational numbers, algebraic identities, comparing quantities, solid geometry, data handling and probability, exponents and powers. The entities related to rational numbers and algebraic expressions help in factorization and calculations of complex numbers and equations. The class 8 math formulas related to the law of exponents help ease out the calculations involved with large numbers. The formulas related to data handling and probability help out making important inferences from the data presented.

### What are the important formulas covered in class 8 Comparing quantities?

Comparing quantities is a fundamental concept in many higher math disciplines, as well as a useful skill to have when solving real-world problems. The formulas shown below will assist students in grasping the fundamentals of simple mathematics which involves calculations involving money:

- Discount = Marked Price – Sale Price
- Simple Interest = ( Principal × Rate × Time )/100
- Compound Interest Formula = Amount – Principal
- Amount = Principal ( 1 + Rate/100)
^{n}

### How Many Formulas are there in Class 8 Maths?

There are around thirty important formulas covering the class 8 maths syllabus. Each of the topics of rational numbers, algebraic identities, comparing quantities, solid geometry, data handling and probability, exponents and powers has around four to five basic formulas that if understood well will ease out the problem solving process.

### How can I Memorize Class 8 Maths formulas?

Class 8 Maths formulas can be easily revised with the help of the following tips:

- The students are advised to revise one topic at a time instead of studying all the formulas in a single day.
- Also, keeping only one list of formulas for reference will be extremely beneficial. It can be something like a formula wallpaper on their phone or laptop. Since everyone has continuous access to these devices throughout the day, hence a quick glance at the wallpaper will ensure a consistent revision throughout.
- Finally, continuous practice goes a long way toward excelling in arithmetic. Students are encouraged to solve as many problems as they can, as this will expose them to a variety of formulas. This is a fantastic technique to recall formulas without having to mumble them down.

**Q1. How many chapters are there in CBSE Class 8 Maths NCERT textbook?**

Ans: As per the latest CBSE syllabus, the NCERT textbook for Class 8 Maths includes 16 chapters. Following are the chapters’ names:

- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterals
- Practical Geometry
- Data Handling
- Squares and Square Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identities
- Visualizing Solid Shapes
- Mensuration
- Exponents and Powers
- Direct and Inverse Proportions
- Factorization
- Introduction to Graphs
- Playing with Numbers

Students can find chapter-wise formulas of Class 8 Maths on Vedantu’s site. This will help students while learning and practising the chapters.

**Q2. How can I score well in the Class 8 Maths exam?**

Ans: Students need to practice and understand each and every concept taught in Class 8 Maths precisely to score well in the exams. In order to get good grades in the Maths paper, it is important to keep formulas in mind. However, there is no need to mug up the formulas. Students must have a thorough understanding of the chapters. Having a strong foundation of the subject is crucial as it makes it easy to understand how formulas are formed. Students should try to understand how certain formulas are derived. Once you know the derivation, you can easily figure out the formulas even if you forget. If you practice a lot of questions based on these formulas, you can score well in the exams.

**Q3. Which platform caters to online chapter-wise formulas of CBSE Class 8 Maths?**

Ans: There are certain online educational platforms available that provide chapter-wise CBSE Class 8 Maths formulas. Vedantu is one such platform which caters to top-quality free PDFs of online materials. At Vedantu, you can find the formulas of NCERT CBSE Maths for Class 8 students. The advantage of using Vedantu’s platform is all the formulas are 100% correct. Also, any explanation regarding the formulas that are required is also given to solve problems. These chapter-wise formulas are available in the form of PDF files. So, it can be downloaded by students to access all the formulas at one place. Class 8 CBSE students can download such material that can be used offline at once convenience while practising Maths.

**Q4. How can online formulas for Class 8 Maths be useful for students?**

Ans: Online platforms like Vedantu provide free PDFs of Class 8 Maths formulas to ensure that students have all the formulas at one place. The online repository of formulas helps in revision during exam time and practising questions based on them. After downloading these files, students are no longer required to refer to the textbook for formulas. Vedantu lists out all the chapters’ formulas so students must not waste their time in writing down all the formulas and can access chapter-wise formulas online or download the files for offline use. The platform also provides chapter-wise NCERT Solutions, Important questions, sample papers, etc. for helping students during exam preparation.

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