## List of Maths formulas for class 6

**Formulas Related to Number System**

Integer Properties : For any integers a and b, |

Addition of integers is commutative a + b = b + a |

Addition of integers is associative a + ( b + c ) = ( a + b) + c |

0 is the identity element under addition a + 0 = 0 + a = a |

Multiplication of integers is commutative. a x b = b x a |

1 is the identity element under multiplication 1 x a = a x 1 = a |

### Mensuration Formulas for Two dimensional Figures

2-Dimensional Figures | Area (Sq.units) | Perimeter (Units) |

Square | (side)^{2} | 4 x side |

Triangle | ½ ( b x h ) | Sum of all sides |

Rectangle | length x breadth | 2 ( length + breadth ) |

Circle | πr^{2} | 2πr |

### Basic Algebra Formula:

Consider the simple quadratic equation** ax2+bx+c=0**

Where, a is the coefficient of x^{2}

b is the coefficient of x

c is a constant term

The quadratic formula to find the variable x is,

### Knowing The Numbers

Numbers starting from 1, 2, 3, 4, … and so on are known as natural numbers. A group of digits together forms a number where the digits can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

1. There are two methods of representing a number:

- a) Indian System of Numeration
- b) International System of Numeration

2. Place Value of a digit in a number = Face Value × Position Value

3. For two numbers, the number with more digits is always the greater number. In case, two numbers have the same digit, then you can start comparing the leftmost digit of the two numbers.

4. If you want to make the smallest number, then you have to start by choosing 1 in the leftmost part and adding zeroes. For example, the smallest four-digit number is 1000.

5. If you want to make the largest number, then you have to start by choosing 9 in the leftmost part. For example, the largest four-digit number is 9999.

6. Quantity weights:

- a) 1 kilometre (km) = 1000 Metres (m)
- b) 1 Metre (m) = 100 Centimetre (cm)
- c) 1 Centimetre (cm) = 10 Millimetre (mm)
- d) 1 Kilogram (kg) = 1000 Grams (gm)
- e) 1 Litre (l) = 1000 Millilitres (ml)

7. Roman Numerals:

- a) I – 1
- b) II – 2
- c) V – 5
- d) X – 10
- e) L – 50
- f) C – 100
- g) D – 500
- h) K – 1000

8. You can add or subtract the roman numerals by writing the desired quantity in either left or right; such as, 21 can be written as XXI and 49 ILIX.

### Whole Numbers

Numbers starting from 0, 1, 2, 3, … and so on are known as whole numbers. A number that divides the other number without leaving any remainder is the factor of that number.

1. A multiple of a number is exactly divisible by the number.

2. Number ‘1’ is said to be the factor of every number and is the number that has exactly one factor.

3. Numbers which are divisible by 2 are known as even numbers while numbers which are not divisible by 2 are known as odd numbers.

4. Divisibility rules:

- a) A number is divisible by 2 if the unit’s digit number is 0, 2, 4, 6 and 8.
- b) A number is divisible by 3 if the sum of all its digits is divisible by 3.
- c) A number is divisible by 4 if the digit in its tens and units place is divisible by 4.
- d) A number is divisible by 5 if the unit’s digit of the number is 0 and 5.
- e) A number is divisible by 6 if it holds the divisibility rule for 2 and 3 true.
- f) A number is divisible by 8 if the number formed in its hundreds, digits and units place is divisible by 8.
- g) A number is divisible by 9 if the sum of the digits of the number is divisible by 9.
- h) A number is divisible by 10 if the unit’s place digit is 0.
- i) A number is divisible by 11 if the difference of the sum of its digits in odd places and the sum of its digits in even places is either 0 or divisible by 11.

5. LCM (Least Common Multiple) of two numbers a and b is the smallest positive integer which is divisible by both a and b.

6. HCF (Highest Common Factor) of two numbers a and b is the largest positive integer that divides each of these given integers.

7. If a, b and c are the whole numbers, then

Property | Implementation |

Closure Property of Addition | a + b |

Closure Property of Multiplication | a × b |

Associativity of Addition | (a + b) + c = a + (b + c) |

Associativity of Multiplication | a × (b × c) = (a × b) × c |

Distributive of Multiplication over Addition | a × (b + c) = a × b + a × c |

Distributive of Multiplication over Subtraction | a × (b – c) = a × b – a × c |

Existence of Multiplicative Identity | a + 0 = a = 0 + a |

Existence of Multiplicative Identity | a × 0 = 0 = 0 × a |

Unit Multiplication | a × 1 = a = 1 × a |

### 6th Class Maths Formulas Geometry

Geometry is the study of different shapes or figures.

1. A line segment corresponds to the shortest distance between two points. The line segment joining points A and B is denoted by AB¯AB¯

2. Two distinct lines meeting at a point are called intersecting lines. Two parallel lines will never intersect each other.

3. A polygon is a simple closed figure comprising different line segments.

- a) The line segments are the sides of the polygon.
- b) Any two sides with a common endpoint are said to be adjacent sides.
- c) The point where a pair of sides meet is called a vertex.
- d) The endpoints located on the same sides are adjacent vertices.
- e) The line segment joining the endpoints of any two non-adjacent vertices is called a diagonal.

### Integers

The numbers −∞,…,−3,−2,−1,0,1,2,3,….,∞−∞,…,−3,−2,−1,0,1,2,3,….,∞ are considered as integers. where 1, 2, 3, … are positive integers and -1, -2, -3, … are negative integers.

1. 0 is less than every positive integer and greater than every negative integer.

2. The sum of all the positive integers and negative integers is zero.

3. The absolute value of an integer |a| is the numerical value of an integer without regard to its sign.

- a) |a| = a, if a is positive
- b) |a| = – a, if a is negative

4. The sum of two integers (same sign) results to an integer of the same sign to which the total absolute value is equal to the sum of the absolute values of two integers.

### Mensuration

1. Perimeter is the distance covered by going along the boundary of a closed figure till the point from where you started.

- (a) Perimeter of a rectangle = 2 × (length + breadth)
- (b) Perimeter of a square = 4 × length of its side
- (c) Perimeter of an equilateral triangle = 3 × length of a side

2. Figures in which all sides and angles are equal are called regular closed figures.

3. The amount of surface enclosed by a closed figure is called its area.

4. To calculate the area of a figure using a squared paper, the following conventions are adopted:

- (a) Ignore portions of the area that are less than half a square.
- (b) If more than half a square is in a region. Count it as one square.
- (c) If exactly half the square is counted, take its area as 1/2 sq units.

5. Area of a rectangle = length × breadth

6. Area of a square = side × side = (side)^{2}

### Algebra

Algebra is the study of unknown quantities. The letters used to represent some numbers are known as literals.

1. The combination of literal numbers obey all the basic rules of addition, subtraction, multiplication and division along with the properties of such operation.

2. x × y = xy; such as 5 × a = 5a = a × 5.

3. a × a × a × … 9 times = a^{12}

4. Let’s suppose a number is x^{8}, then x is the base and the exponent is 8.

5. A constant is a symbol with a fixed numerical value.

### Ratio And Proportion

The ratio of any number “a” to another number “b” (where b ≠ 0) is basically the fraction abab. It is written as a : b.

1. The ratio of two numbers is always expressed in their simplest form. For example, 68 will be further reduced to 34.

2. An equality of two ratios is known as the proportion such that a : b = c : d if and only if ad = bc.

3. If a : b = b : c, then a, b and c are in continued proportion.

4. If a, b and c are in continued proportion, a : b :: b : c, then b is represented as the mean proportional between a and c.

### FAQs On Maths Formula

Here are some of the frequently asked questions and their answers:

** Q1. Where do I get Maths Formulas Classwise?** All class-wise Maths formulas are available on Embibe.

A1.

*Q2. Where can I get all Important Formulas for Class 6 to Class 12?*** A2. **You can get all the important formulas for Class 6 to 12 at Embibe.

** Q3. How can I memorize the Maths formulas for Class 6?** The best way to memorize the Class 6 Maths formulas is by solving practice questions. Refer to the formulas as you solve questions. The more questions you solve, the better you will get at understanding their applications.

A3.

** Q4. Is solving Maths questions from NCERT books enough for Class 6?** Yes, for Class 6, Maths NCERT textbook is enough. Just make sure you have a clear understanding of the concepts before you move on to solving questions.

A4.

**Q1: What are the important properties of proportion?**

A1: The following are the important properties of proportion:

- Addendo – If a : b = c : d, then a + c : b + d
- Subtrahend – If a : b = c : d, then a – c : b – d
- Dividendo – If a : b = c : d, then a – b : b = c – d : d
- Componendo – If a : b = c : d, then a + b : b = c+d : d
- Alternendo – If a : b = c : d, then a : c = b: d
- Invertendo – If a : b = c : d, then b : a = d : c
- Componendo and dividendo – If a : b = c : d, then a + b : a – b = c + d : c – d

**Q2: What are the Natural Numbers and Whole Numbers Properties?**

A2: The various properties of Natural numbers and Whole numbers are as follows:

**Addition Property**- When two natural numbers are added, the result is a natural number.

Eg: 34+145 = 179

- Similarly, when two whole numbers are added, the result is a whole number.

Eg: 6+10= 16

**Subtraction Property**- The subtraction of two natural numbers may or may not result in a natural number.
- Eg: 5 –12 = -9 is not natural number
- But 11– 5 = 6 is a natural number
- The subtraction of two whole numbers may or may not result in a whole number.
**Multiplication Property**- Multiplication of two natural numbers always results in a natural number
- Eg: 12 X 6 = 72 is a natural number
- Multiplication of two whole numbers always results in a whole number
- Ex: 14 X 0 = is a whole number, where 4 and 0 are also whole numbers.
**Division Property**- Division of two natural numbers may always not always result in a natural number.
- Division of two whole numbers may always not always result in a whole number.

This is because if the result is in fraction or decimal, then they are not considered as natural or whole numbers.

Eg: 4/2 = 2 is natural as well as the whole number.

But 5/2 = 2.5 is neither natural nor the whole number.

**Q3: What are the important formulas of mensuration?**

A3: Some important formulas of mensuration are as follows:

- Square – Area – (side)
^{2}, Perimeter – 4 x side - Triangle – Area – ½ ( b x h ) , Perimeter – Sum of all sides
- Rectangle – Area – length x breadth , Perimeter – 2 * ( length + breadth )
- Circle – Area – πr
^{2}, Perimeter – 2πr

**Q4: What is the order of operations in algebra?**

A4: The order of operation in algebra is given as follows:

- First preference is given to all the operations inside the brackets.
- Then all the operations on roots and exponents must be performed.
- This is followed by the division and multiplication operations moving from left to right.
- Then all the addition and subtraction operations must be performed from left to right.

NOTE: Students must ensure that all the operations must be performed according to BODMAS: Brackets, Of( Multiplication), Division, Multiplication, Addition and Subtraction.

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