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Basic Math Formulas

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  • Difficulty Level : Basic
  • Last Updated : 17 Jun, 2022

Mathematics comes with an endless scope of research and study in the domain of numbers and their operations. Every branch of mathematics has something different to deal with. The branches explore new methods and standards of calculation for making daily trade even more convenient. 

Mathematics is divided into various branches as per the way of calculation involved and topics covered by them. The branches include geometry, algebra, arithmetic, percentage, exponential, etc. Mathematics also provides standard derived formulas to make the operations or calculation accurate. The given article provides all the basic formulas present in mathematics under its different branches or fields.

Basic math formulae

A formula is a mathematical expression or definite rule that is derived from the relation between two or more quantities and the derived final product is expressed in symbols. The formulas of mathematics included numbers known as constants, letters that represent the unknown values and are known as variables, mathematical symbols known as signs, and exponential powers in some cases.

Arithmetic

Arithmetic is the oldest method of calculation known till now. The word arithmetic is derived from the Greek words ‘arithmos’ which literally means numbers. Brahmagupta the Indian mathematician is known as the ‘father of arithmetic‘. And, the Fundamental theory of number theory was proposed by Carl Friedrich Gauss in 1801.

The basic operations involved in arithmetic are addition, subtraction, multiplication, and division.

Arithmetic formula

Arithmetic mean (average) = Sum of values/Number of values.

Algebra

Algebra is an elementary subject of mathematics that deals with the study of the evaluation of numbers and symbols. The algebraic operations are carried out to determine the unknown values which are expressed by letters. Algebraic equations are the expressions formed by the combination of variables, constants, factors, and coefficients of variables.

Basic algebra formula

  • a2 – b2 = (a – b)(a + b)
  • (a + b)2 = a2 + 2ab + b2
  • a2+ b2 = (a + b)2 – 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
  • (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
  • (a + b)3 = a3 + 3a2b + 3ab2 + b2
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  • a4– b4 = (a – b)(a + b)(a2 + b2)
  • (am)(an) = am + n
  • (ab)m = ambm
  • (am)n = amn

Geometry

Geometry is a part of mathematics that is concerned with the study of shapes, sizes, parameters, measurement, properties, and dimensions. There are generally three types of geometry. They are Euclidean geometry, Spherical geometry, and Hyperbolic geometry.

Basic geometry formula

  • Rectangle
  1. Perimeter of Rectangle = 2(l + b)
  2. The area of Rectangle  = l × b

Where ‘l’ is Length and ‘b’ is Breadth

  • Square
  1. The area of Square = a2
  2. The perimeter of Square = 4a

Where ‘a’ is the length of the sides of a Square

  • Triangle

Area of Triangle= 1/2 × b × h

Where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle

  • Trapezoid

Area of Trapezoid = 1/2 × (b1 + b2) × h

Where b1 and b2 are the bases of the Trapezoid

And, h = height of the Trapezoid

  • Circle
  1. Area of Circle = π × r2
  2. Circumference of Circle = 2πr

Where ‘r’ is the radius of a Circle

  • Cube

Surface Area of Cube = 6a2

Where ‘a’ is the length of the sides of the Cube

  • Cylinder
  1. The curved surface area of Cylinder = 2πrh
  2. The total surface area of Cylinder = 2πr(r + h)
  3. The volume of Cylinder = V = πr2h

Where ‘r’ is the radius of the base of the Cylinder

And, ‘h’ is the height of Cylinder

  • Cone
  1. The curved surface area of a cone = πrl
  2. Total surface area of cone = πr(r + l) = πr[r + √(h2 + r2)]
  3. Volume of a Cone = V = 1/3× πr2h

Here, ‘r’ is the radius of the base of Cone and h = Height of the Cone

  • Sphere
  1. Surface Area of a Sphere = S = 4πr2
  2. Volume of a Sphere = V = 4/3 × πr3

Where, r = Radius of the Sphere

Probability

Probability is the mathematical term used to determine the chance of occurring a particular event. Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of theoretical probability, experimental probability, and subjective probability.

Basic probability formula

P(A) = n(A)/n(S)

Where,

P(A) is the probability of an event.

n(A) is the number of favorable outcomes

n(S) is the total number of events

Fraction

A fraction is a number expressed with integers in which a numerator is divided by the denominator. A fraction is basically the quotient of a division. 

Basic fractions formula

  • (a + b/c) = (a × c) + b/c
  • (a/b + d/b) = (a + d)/b
  • (a/b + c/d) = (a × d + b × c/b × d)
  • a/b × c/d = ac/bd
  • (a/b)/(c/d) = a/b × d/c

Percentage

A percentage is a numerical value or ratio expressed as a fraction of 100. It is generally symbolized by the sign %.

Basic percentage formula

Percentage = (Amount in the category/Total value) × 100

Sample problems

Question 1: Determine the probability to get an ace from a card taken from a deck.

Solution:

Given:

Total number of favorable outcomes n(S) = 52

Number of face cards  in the deck = 12

Number of favorable outcomes n(A) = 12

Now,

P(A) = n(A)/n(S)

=> 12/52

=> 3/13

Hence, the probability to get a face card from a card deck is 3/13.

Question 2: Simplify 3/(x – 1) + 1/(x(x – 1) = 2/x

Solution:

=> 3x + 1/x(x – 1) = 2(x – 1)/x(x – 1)

=> 3x + 1 = 2(x – 1)

=> x = -3

Question 3: If x + 1/x = 3. Find the value of x2 + 1/x2.

Solution:

=> (x + 1/x)2 = (3)2

=> x2 + 2 × x × 1/x + (1/x)2 = 9

=> x2 + 1/x2 + 2 = 9

=> x2 + 1/x2 = 7

Question 4: If the radius of a circle is 21cm. Find the area of the given circle.

Solution:

Given:

The radius of the circle is 21cm.

We have,

Area of the circle (A) = πr2

=> 22/7 × 21 × 21

=> 1386cm2

Hence, the area of the given circle is 1386cm2

Question 5: Find the area of a triangle having a base of 100cm and a height of 20cm.

Solution:

Given:

The base of the triangle is 100cm.

The height of the triangle is 20cm.

We have,

Area(A) = 1/2 × b × h

=> 1/2 × 10 × 20

=> 1000cm2

Question 6: Punam has 4/5 parts of the field among which she uses 2/5 parts for farming. How much part of the farm is left for other purposes?

Solution:

Given: 

The total fraction of land 4/5.

The total fraction used for farming 2/5.

Now,

=> 4/5 – 2/5

=> 4 – 2/5

=> 2/5

Hence, 2/5 part of the field left.

Question 7: What will be the 20% of 240kg?

Solution:

=> 20/100 × 240

=> 48kg

Hence, the 20% of 240kg will be 48kg.


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