NCERT Solutions for Class 6 Social Science Geography Chapter 4

August 8, 202239 Insightful Publications

**Maths Formula for Class 6**: Students must make it a point to follow the Maths formula for Class 6 to prepare for the exam. It will also help them answer the questions effectively. Students must ensure that they keep their formulas in one place. Having the formulas in handy will make it easier for students to memorise the graphs, relevant diagrams and more.

Some of the important Maths formula for Class 6 that the students must follow include that of chapters like Algebra, Decimals, Ratio, Proportion, Geometry and Mensuration. Following the Class 6 Maths formula can help the student grasp the concepts of Maths easily. Students must ensure that they are following the formula for each chapter thoroughly. Read the article gven below to get more information on formulas for CBSE Class 6 Maths.

In this article, we have provided the important formulas for CBSE Class 6. With the help of these formulas, you can analyse the concepts, compute them and reach the solution. Given below is the list of Class 6 chapter-wise Maths formulas:

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 on either left or right; such as 21 can be written as XXI and 49 ILIX.

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 that are divisible by 2 are known as even numbers while numbers that 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 between 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 |

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 \(\bar{AB}\)

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.

4. A quadrilateral is a four-sided polygon. In a quadrilateral ABCD, \(\bar{AB}\) & \(\bar{DC}\) and \(\bar{AD}\) & \(\bar{BC}\) are pairs of opposite sides. \(\angle A\) & \(\angle C\) and \(\angle B\) & \(\angle D\) are pairs of opposite angles. \(\angle A\) is adjacent to \(\angle B\) & \(\angle D\); similar relations hold for the other three angles as well.

The numbers \(-\infty, …, -3, -2, -1, 0, 1, 2, 3, …., \infty\) 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 \(\left | a \right |\) is the numerical value of an integer without regard to its sign.

- a) \(\left | a \right |\) = a, if a is positive
- b) \(\left | a \right |\) = – a, if a is negative

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

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 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.

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

1. The ratio of two numbers is always expressed in their simplest form. For example, \(\frac{6}{8}\) will be further reduced to \(\frac{3}{4}\).

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.

- 5. \(Value\,of\,one\,article=\frac{Value\,of\,given\,number\,of\,articles}{Number\,of\,articles}\) (Unitary Method)
- where more the number of articles, more is the value and vice-versa.

**Q.1: Where do I get the list of Class 6 chapter-wise Maths formulas?Ans:** The list of Maths formulas for Class 6 for all chapters are available on Embibe.

**Q.2: Where can I get all the important formulas for Class 6 to Class 12?Ans:** You can get all the important formulas for classes 6 to 12 at Embibe.

**Q.3: Is Class 6 CBSE Maths difficult to remember?Ans:** No, it is not difficult. With regular practice, students can improve their skills in mathematics.

**Q.4: How can I memorise the Mathematics Maths formulas for Class 6?Ans:** 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.

**Q.5: Is solving Maths questions from NCERT books enough for Class 6?Ans:** Yes, for Class 6, the Maths NCERT textbook is enough. Just make sure you have a clear understanding of the concepts before you move on to solving questions.