Maths formulas for class 8 include the formulas from all the chapters in NCERT class 8 Maths book. Here you will find all the formulas in a PDF file, including Rational Number, Algebraic Expressions, Exponents and Powers, Mensuration, and other chapters.

These formulas for class 8 are beneficial while preparing for your exam. You can get the printout or read the formulas online. Please note that you need to practice more and more to memorize all the maths formulas. You can also review the essential maths formulas for upcoming classes (i.e., Class 9 and Class 10). We have prepared this formula PDF sheet based on the NCERT & CBSE syllabus. We will soon update Hindi medium study materials.

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Rational Numbers Maths Formulas for Class 8

In class 8, you will learn about another type of number. i.e., Rational Numbers. In this section, we have provided maths formulas for class 8 to study rational numbers. You will also find essential properties of rational numbers and other numbers.

If r = p/q, then r is a rational number.

Where p and q are integers and q≠0.

Properties of Numbers

Closure

Number Type	Operation	Condition	Conclusion
	Addition	for two whole numbers a and b, a+b is also a whole number.	Whole numbers are closed under addition
Whole Numbers	Subtraction	a-b is not always a whole number (e.g., 4-6 = -2)	Whole number are not closed under subtraction
	Multiplication	3×5 = 15, a whole number	Whole numbers are closed under multiplication
	Division	4÷6 = 2÷3, not a whole number	Whole numbers are not closed under division

	Addition	for two integers a and b, a+b is also an integer	Closed under addition
Integers	Subtraction	4-6 = -2, an integer	Closed under subtraction
	Multiplication	-3×5 = -15, an integer	Closed under multiplication
	Division	4÷6 = 2÷3, not a whole number	Not closed under division

	Addition	(1/2) + (2/3) = 7/6, a rational number	Rational numbers are closed under addition
Rational Numbers	Subtraction	(5/2) – (1/2) = 2, a rational number	Closed under subtraction
	Multiplication	(3/2) x (1/5) = 3/10, a rational number	Closed under multiplication
	Division	(2/5) ÷ 0, not defined	Rational numbers are not closed under division

Commutativity

Number Type	Operation	Condition	Conclusion
	Addition	a + b = b + a	Addition is commutative
Whole Numbers	Subtraction	a – b ≠ b – a	Subtraction is not commutative
	Multiplication	a x b = b x a	Multiplication is commutative
	Division	a ÷ b ≠ b ÷ a	Division is not commutative

	Addition	a + b = b + a	Addition is commutative
Integers	Subtraction	a – b ≠ b – a	Subtraction is not commutative
	Multiplication	a x b = b x a	Multiplication is commutative
	Division	a ÷ b ≠ b ÷ a	Division is not commutative

	Adition	(-3/8) + (1/9) = 1/9 + (-3/8)	Addition is commutative for rational numbers
Rational Numbers	Subtraction	(1/2) – (2/5) ≠ (2/5) – (1/2)	Subtraction is not commutative for rational numbers
	Multiplication	(2/5) x (3/8) = (3/8) x (2/5)	Multiplication is commutative for rational numbers
	Division	(2/5) ÷ (4/7) ≠ (4/7) ÷ (2/5)	Division is not commutative for rational numbers.

Associativity for Whole Numbers & Integers

Operation	Condition	Conclusion
Addition	(a + b) + c = a + (b + c)	Associative
Subtraction	(a – b) – c ≠ a – (b – c)	Not Associative
Multiplication	(a x b) x c = a x (b x c)	Associative
Division	(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)	Not Associative

Addition

\[\left( \frac{1}{3} + \frac{3}{5} \right) + \frac{4}{7} = \frac{1}{3} + \left( \frac{3}{5} + \ \frac{4}{7} \right)\]

Hence, Addition is associative for Rational Numbers.

Subtraction

\(\left( \frac{1}{3} – \frac{3}{5} \right) – \frac{4}{7}\) ≠ \(\frac{1}{3} – \left( \frac{3}{5} – \ \frac{4}{7} \right)\)

Subtraction is not associative for Rational Numbers.

Multiplication

\(\left( \frac{- 1}{3}x\frac{3}{5} \right)x\frac{4}{7}\) = \(\frac{- 1}{3}x\left( \frac{3}{5}\text{x }\frac{4}{7} \right)\)

Multiplication is associative for rational numbers.

Division

\(\left( \frac{- 1}{3} \div \frac{3}{7} \right) \div \frac{4}{5}\) ≠ \(\frac{- 1}{3} \div \left( \frac{3}{7} \div \frac{4}{5} \right)\)

Division is not associative for rational numbers.

Other Rational Number Properties

1 is the multiplicative identity of any rational number. i.e., for any rational number a,
- ax1 = 1xa = a
For a rational number a/b, – a/b is the negative inverse or additive inverse. i.e., (a/b) + (-a/b) = 0
For two rational number a/b and (c/d), if (a/b) x (c/d) = 1, then c/d is called reciprocal or multiplicative inverse of a/b.
Rational number can be represented on the number line and there can be infinite number of rational numbers between two numbers.
Two find the rational numbers between any two given number, convert the given numbers to rational number with same denominator and then find the numbers between them.

Linear Equations in one Variable

To solve a linear equation having the variable only at one side of the equation such as,

7x + 3 = 6

Add the negative invers of the constant to both sides,

i.e., 7x + 3 – 3 = 6 – 3

or 7x = 3, or x = 3/7

If a linear equation is given as

6x + 9 = 2x – 6

Then, to solve the above equation follow the below steps:

Transpose the variable to one side and constant to another side,

i.e., 6x – 2x = –6–9 (sign will change)

or 4x = – 15 or x = –15/4

Quadrilaterals Formulas for Class 8

Learn about different types of quadrilaterals and solve angle sum-related problems quickly with these maths formulas of class 8. Please make sure you practice more to memorize all the properties of Parallelogram, Rhombus, Square, and other quadrilaterals.

Polygons

Number of sides	Classification	Sum of interior angles
3	Triangle	180°
4	Quadrilateral	360°
5	Pentagon	540°
6	Hexagon	720°
7	Heptagon	900°
8	Octagon	1080°
9	Nonagon	1260°
10	Decagon	1440°
n	n-gon	(n-2) x 180°

Convex Polygon: No portion of diagonal is outside the polygon
Concave Polygon: Some part of the diagonal is outside the polygon

Angle Sum Property

Sum of interior angles of a polygon = (n – 2) x 180°, where n is the number of sides.

e.g., Sum of all interior angles of a triangle = (3 – 2) x 180 = 180°

Sum of all interior angles of a quadrilateral = (4 – 2) x 180 = 360°

Sum of all exterior angles of a polygon = 360°
Sum of angles of external and internal angles at any vertex = 180°

Quadrilaterals Properties

Type of Quadrilateral	Properties
Parallelogram (each pair of opposite sides is parallel)	1. Opposite sides are equal 2. Opposite angles are equal 3. Diagonals bisect each other 4. Adjacent angles are supplementary (i.e., their sum is 180°)
Rhombus (parallelogram with all sides of equal length)	1. All the properties of parallelogram 2. Diagonals are perpendicular to each other
Rectangle (Parallelogram with right angle)	1. All properties of a parallelogram 2. Each angle is a right angle 3. Diagonals are equal
Square (Rectangle with sides of equal length)	All the properties of Rhombus, Parallelogram, and Rectangle
Kite (exactly two distinct consecutive pairs of sides of equal length)	1. Diagonals are perpendicular to one another 2. One of the diagonals bisects the other 3. One pair of opposite angles are equal
Trapezium	1. One pair of opposite sides is parallel 2. If non-parallel sides are of equal length then it’s called Isosceles Trapezium

Data Handling & Graph

There are two chapters to understand the use of Graphs and data in class 8. Although there are not many formulas in this section, still you can learn the important terms to solve problems conveniently.

Data: Collected information with some value.
Pictograph: Pictorial representation of data using pictures.
Raw Data: Data in unorganized form
Bar Graph: Display of information using bars of uniform width, and height proportional to the respective values.
Double Bar Graph: A bar graph with two sets of data used for comparison.
Frequency: Number of times a particular entry occurs in a data.
Grouped Frequency Distribution: Representation and distribution of data on the basis of frequency.
Histogram: Representation of data in a bar graph using class-intervals.
Pie Chart: Data representation in circular form. The whole circle is divided in sectors and the angles for each sector can be found using the following method.
- Find the fraction of specific type.
- Multiply the fraction with total angle of circle i.e., 360°.
- Draw a circle and mark the first angle (usually the biggest)

A line graph displays data that changes continuously over periods of time. A line graph which is a whole unbroken line is called a linear graph.

Probability

Probability of an even E, P(E) = \(\frac{\text{Number of outcomes that make an event}}{\text{Total number of outcomes of the experiment}}\)

Square and Square Roots

Square number table

Number	Square	Number	Square	Number	Square
1	1	8	64	15	225
2	4	9	81	16	256
3	3	10	100	17	289
4	16	11	121	18	324
5	25	12	144	19	361
6	36	13	169	20	400
7	49	14	196	21	441

Every square number has 1,3,4,5,6,9,0 in its unit place.
Square numbers can only have even numbers of zero at the end.
Sum of first n odd numbers is n².
The square number must be the sum of successive odd numbers starting from 1. i.e., after subtracting successive odd numbers from a square number, the result must be 0, otherwise the number is not perfect square.
Product of two consecutive even or odd numbers = (a + 1)(a – 1) = (a² – 1)

Non-Square numbers between two squares

Between n² and (n+1)², there are 2n non-square numbers. e.g., between 5² and 6², there are 2×5 = 10 non-square numbers.
Difference of two squares – 1 = total number of non-square numbers between those two square numbers.

Pythagorean Triplet

If for any natural number m>1, (2m)² + (m² – 1)² = (m² + 1)² then, 2m, m² – 1, and m² + 1 forms a Pythagorean triplet.

In Pythagorean triplets, sum of two square numbers = third square number

e.g., 3² + 4² = 5² and 6² + 8² = 10²

Smallest 3-digit perfect square = 100
Greatest 3-digit perfect square = 961
Smallest 4-digit perfect square = 1024
Greatest 4-digit perfect square = 9801

Square Root Table

Square Number	Square Root	Square Number	Square Root
1	√1 = 1	64	√64 = 8
4	√4 = 2	81	√81 = 9
9	√9 = 3	100	√100 = 10
16	√16 = 4	121	√121 = 11
25	√25 = 5	144	√144 = 12
36	√36 = 6	169	√169 = 13
49	√49 = 7	196	√196 = 14

Finding square roots using Repeated Subtraction

Subtract the successive odd numbers starting from 1
Repeat the process until you get 0
Count the total number of steps taken to reach 0 or total number of odd numbers subtracted. That is the square root of the number.

You can also find the square root of a number by prime factorization. Find the prime factors and then pair them with the same factors to find the square root of a number.

e.g., prime factorisation of 324 = 2x2x3x3x3x3 = (2×2) x (3×3) x (3×3) = 2² x 3² x 3² = (2x3x3)²

or √324 = 18

Cube and Cube Root

Cube Numbers

Number	Cube	Number	Cube	Number	Cube
1	1	8	512	15	3375
2	8	9	729	16	4096
3	27	10	1000	17	4913
4	64	11	1331	18	5832
5	125	12	1728	19	6859
6	216	13	2197	20	8000
7	343	14	2744	21	9261

Cube of an even number is always even
Cube of an odd number is always odd
There are only 10 perfect cubes from 1 to 1000
Each prime factor appears three times in a cube

Cube Roots

The symbol ³√ denotes ‘cube-root.’

Cube Number	Cube Root	Cube Number	Cube Root
1	³√1 = 1	216	³√216 = 6
8	³√8 = 2	343	³√343 = 7
27	³√27 = 3	512	³√512 = 8
64	³√64 = 4	729	³√729 = 9
125	³√125 = 5	1000	³√1000 = 10

Comparing Quantities

Ratio

Comparing two quantities by using fractions, such as

= p:q or ‘p is to q’, where p and q are different quantities. e.g., ratio of 25 mangoes to 40 apples will be, 25/40 = 5/8 = 5:8

Percentage

P% = p/100

Percentage	Value	Percentage	Value
10%	10/100 = 1/10	60%	60/100 = 3/5
20%	20/100 = 1/5	50%	50/100 = 1/2

Discounts

Discount = Marked price – Sale price

e.g., Marked Price = ₹2,000, Sale price = 1,500, Discount = 2000 – 1500 = ₹500.

Discount percentage = \(\frac{\text{Discount}}{\text{Marked Price}} \times 100\)

Cost and Profit

Overhead charge: expanses added to the buying or selling price. E.g., repair cost, labor cost, etc.

Profit

When Cost price < Selling price, CP<SP

Profit (P) = SP – CP

Profit Percentage (P%) = \(\frac{P}{\text{CP}} \times 100\)

Cost price may include additional expanses

Loss

When Cost Price > Selling Price, CP > SP

Loss (L) = SP – CP

Loss % = \(\frac{L}{\text{CP}} \times 100\)

Sales Tax (Value Added Tax)

Collected by the shopkeeper and transferred to the government. Tax is always applicable on the selling price. E.g., if the selling price of a chair is ₹800 and 10% tax is added to it,

then it will cost, 800 + \(\frac{10}{100} \times 800\) = 800 + 80 = ₹880 to the customer.

Simple Interest and Compound Interest

Simple Interest (SI) = P x r x t, where p = principal amount, r = rate of interest, t = time

Compound Interest

Interest calculated on the previous year’s amount, A = P + I

Amount when interest is compounded annually = \(P\left( 1 + \frac{R}{100} \right)^{n}\) where P = Principal, R = rate of interest, n = time-period / number of years

Amount when interest is compounded half-yearly,

= P\(\left( 1 + \frac{R}{200} \right)^{2n}\), where \(\frac{R}{2}\) is half yearly rate, and 2n = number of half-years

Algebraic Expressions & Identities

Expressions: Formed using variables and constants

Terms: Added to form expressions. Terms are the product of factors

e.g., for an algebraic expression, x² + 2xy + 9, x = variable, numbers = constants, X², 2xy, 9 = terms

Coefficient: Numerical factor of a term is called a coefficient.

Monomial: Expression with only one term
Binomial: Expression with two terms
Trinomials: Expression with three terms

Monomial, binomial, and trinomial are also called polynomials.

Like Terms: Terms with the same variable are called like terms. E.g., 2xy and 8yx are like terms, 5x² and 6x² are like terms.

5x² and 2xy are not like terms, 9x and 9x² are not like terms.

Addition and subtraction is performed on the coefficient of like terms. E.g., 2xy – xy = xy

Similarly, 9x² + 4x² = 13x²

Multiplication

Coefficients of product = coefficient of first term x coefficient of second term
Algebraic facto or product = algebraic factor of first term x algebraic factor of second term.

e.g., 9x² . 4x = 9.4.x.x.x = 36x³ where . ‘dot’ represent the product.

(a + b).c = ac + bc
(a + b)(c + d) = ac + ad + bc + bd or a(c + d) + b(c + d), using the distributive law
(a + b) (c² + cd + d) = a(c² + cd + d) + b(c² + cd + d), using the distributive law

Algebraic Identities

(a + b)² = a² + b² + 2ab
(a – b)² = a² + b² – 2ab
(a + b)(a – b) = a² – b²
(x + a)(x + b) = x² + (a + b)x + ab

Mensuration Maths Formulas For Class 8

Here you will find area and volume formulas for class 8 and learn about solving various 2D and 3D (solid) shapes. These formulas are essential and you need to put more efforts so that you can solve questions without making any calculation mistakes. Download all mensuration formulas for class 8 and take a printout for the easy access to all formulas.

2D Shapes

Shape	Area	Perimeter
Rectangle	a x b	2(a + b)
Square	a x a = a²	4a
Triangle	(1/2) b x h (b = base, h = height)	a + b + c (a,b,c are sides)
Parallelogram	b x h	2 (s + b)
Circle	πr2	2πr

Area of trapezium = \(h \cdot \frac{\left( s + b \right)}{2}\) = \(height \cdot \frac{\left( \text{sum of two parallel sides} \right)}{2}\)

Area of general quadrilateral = \(\frac{1}{2}d(h_{1} + h_{2})\) where d = length of diagonal

Area of rhombus = \(\frac{1}{2}d_{1}d_{2}\) ,

where d₁, d₂ are diagonals of rhombus.

Solid Shapes (3D)

Cuboid

l, b, h are the edges of a cuboid

Surface area of a cuboid = 2(lb + bh + hl)
Perimeter of cuboid = 4(l + b + h)
Longest diagonal length in a cuboid = √(l² + b² + h²)
Volume of a cuboid = l x b x h

Cube

Surface area of a cube = 6a²
Perimeter of a cube = 12a
Volume of cube = a³
Diagonal of cube = √(3a)

Cylinder

Curved surface area of a cylinder = 2πrh
Total surface area of cylinder = 2πr(r + h)
Volume of cylinder = πr²h
Area of two circular bases in a cylinder = πr² + πr² = 2πr²

Exponents and Powers

a^m x aⁿ = a^m+n
a^m ÷ aⁿ = a^m-n
(a^m)ⁿ = a^mn
a^m x b^m = (ab)^m
a⁰ = 1
a^m / b^m = (a/b)^m
a^-m = 1/a^m
a^m = 1/a^-m

Direct and Inverse Proportions

x and y are in direct proportion if (x/y) = k, or x = ky, where k is any constant.

When x and y are in direct proportion, we can write \(\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}\) or \(x_{1}y_{2}\) = \(y_{1}x_{2}\)

x and y are inversely proportional if xy = k,

we can also write, \(x_{1}y_{1}\) = \(x_{2}y_{2}\) or \(\frac{x_{1}}{x_{2}} = \frac{y_{1}}{y_{2}}\)

Test for Divisibility of Numbers

You have already learned about various divisibility rules in the previous class. Now is the time to revise those again. How many of the divisibility rules do you remember?

Divisibility by 10

A number having 0 at the end is divisible by 10. i.e., 10,20,900,5640, are divisible by 10.

Divisibility by 2

A number having 0,2,4,6, or 8 in its one’s place is divisible by 2. E.g., 24,2596, 4590, 5788 are divisible by 2.

Divisibility by 3

If the sum of digits in a number is multiple of 3 then the number is divisible by 3.

E.g., 729 has digits sum as 7+2+9 = 18 which is a multiple of 3. Hence, 729 is divisible by 3.

Divisibility by 4

A number having 3 or more than 3 digits is divisible by 4 if the number formed by the last two digits (i.e., ones and tens) is divisible by 4.

E.g., 9928 is divisible by 4 because 28 is divisible by 4. Similarly, 316 is divisible by 4 because 16 is divisible by 4.

Divisibility by 5

If a number has 0 or 5 at one’s place, then the number is divisible by 5.

e.g., 255, 1250, 300, 995 are divisible by 5.

Divisibility by 6

If a number is divisible by both 2 and 3, then it is also divisible by 6.

e.g., 216 is divisible by 2 and 3. Hence, it is also divisible by 6.

Divisibility by 7

A number is divisible by 7 if the difference between twice of unit digit and the remaining part of the number is divisible by 7.

e.g., suppose we have 343. Now, twice of the unit digit, 3×2 = 6.
Difference between remaining part and twice of the unit digit, 34 – 6 = 28, which is divisible by 7. Hence, 343 is also divisible by 7.

Another example with, 819. Twice of the unit digit, 9×2 = 18.
The difference, 81-18 = 63, which is divisible by 7. Hence, 819 is also divisible by 7.

Divisibility by 8

A number with 4 or more digits is divisible by 8 if the number formed by the last 3 digits is divisible by 8.

e.g., 8216 is divisible by 8 because 216 is also divisible by 8.

Divisibility by 9

It is similar to the divisibility by 3 rule. If the sum of digits in a number is multiple of 9, then the number is divisible by 9.

e.g., 4608 is divisibly by 9 because the sum (4+6+0+8 = 18) is multiple of 9.

Divisibility by 11

Follow the steps below to test the divisibility by 11 for any number:

From the right, find sum of digits at odd place (ones, hundred, ten thousand, etc.)
From the right, find sum of digits at even place (ten, thousand, lakh, etc.)
Find the difference between both sums.
If the difference is 0 or divisible by 11, then the number is also divisible by 11.

e.g., suppose we have 61809. Now,
the sum of odd place digits, 9+8+6 = 23, the sum of even place digits, 0+1=1.
The difference between both sums, 23-1 = 22, which is a multiple of 11, Hence 61809 is divisible by 11.

Numbers in General Form

Two digit number, ab = 10a + b
Three digit number, abc = 100a + 10b + c
Four digit number, abcd = 1000a + 100b + 10c + d
Five digit number, abcde = 10000a + 1000b + 100c + 10d + e

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Maths Formulas for Class 8 PDF