Class 6 Maths Formulas
All Important Formulas, Rules, Examples & Practice Questions
Make mathematics easier with simple explanations, colourful formula cards and interactive revision.
Numbers Fractions Geometry MensurationWelcome to Maths Wallah, your learning companion for mathematics. This Class 6 Maths Formula Guide brings together important mathematical rules, formulas, definitions and examples in one place. Use it for homework, school examinations, quick revision and building a strong foundation for higher classes.
📚 Table of Contents
1. Numbers and Place Value
Place value tells us the value of a digit according to its position in a number. For example, in 4,582, the digit 5 has a place value of 500.
Digit × Place
Place value = Digit × Position value Example: Place value of 7 in 3,742 = 7 × 100 = 700.Break the Number
5,326 = 5,000 + 300 + 20 + 6 Write each digit according to its place value.Nearest Ten or Hundred
If the next digit is 5 or greater, increase the retained digit by 1. If it is less than 5, leave the retained digit unchanged.Roman numerals: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.
Examples: VI = 6, IX = 9, XIV = 14, XL = 40.
2. Basic Arithmetic Operations
Addition
Sum = First number + Second number Example: 245 + 135 = 380.Subtraction
Difference = Minuend − Subtrahend Example: 850 − 325 = 525.Multiplication
Product = Multiplicand × Multiplier Example: 24 × 6 = 144.Division
Dividend = Divisor × Quotient + Remainder The remainder is smaller than the divisor when the divisor is a positive whole number.Example: 17 ÷ 5 gives quotient 3 and remainder 2.
17 = 5 × 3 + 2Important properties:
- Addition is commutative: a + b = b + a.
- Multiplication is commutative: a × b = b × a.
- Addition is associative: (a + b) + c = a + (b + c).
- Multiplication is associative: (a × b) × c = a × (b × c).
- Distributive property: a × (b + c) = ab + ac.
- Multiplying by 1 keeps a number unchanged: a × 1 = a.
- Adding zero keeps a number unchanged: a + 0 = a.
3. Factors, Multiples, HCF and LCM
Factors
A factor divides a number exactly, leaving no remainder.Example: Factors of 12 are 1, 2, 3, 4, 6 and 12.
Multiples
Multiples are obtained by multiplying a number by whole numbers.Example: First five positive multiples of 4 are 4, 8, 12, 16 and 20.
HCF and LCM
HCF = Greatest common factor LCM = Least common positive multiple Example: For 12 and 18, HCF = 6 and LCM = 36.For two positive integers a and b:
HCF(a, b) × LCM(a, b) = a × bThis identity is useful for two positive integers.
4. Integers and Negative Numbers
Integers include negative whole numbers, zero and positive whole numbers.
…, −3, −2, −1, 0, 1, 2, 3, …Addition
Same signs: add the absolute values and keep the common sign.
Example: −4 + (−3) = −7.
Different Signs
Subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.
Example: −8 + 5 = −3.
Subtraction
a − b = a + (−b)Example: 6 − 9 = 6 + (−9) = −3.
5. Fractions
A fraction represents part of a whole. In a/b, a is the numerator and b is the denominator; b cannot be zero.
Equivalent Fractions
a/b = (a × n)/(b × n) Multiply numerator and denominator by the same non-zero number.Example: 2/3 = 4/6 = 6/9.
Addition and Subtraction
For the same denominator:
a/c + b/c = (a + b)/c a/c − b/c = (a − b)/cExample: 2/7 + 3/7 = 5/7.
For different denominators, convert the fractions to equivalent fractions with a common denominator first.
Multiplication and Division
a/b × c/d = ac/bd a/b ÷ c/d = a/b × d/cDivision is defined when the divisor fraction is not zero.
Example: 1/2 × 3/4 = 3/8.
6. Decimals
Decimals use a decimal point to represent tenths, hundredths, thousandths and more.
Place Values
0.1 = one tenth = 1/10 0.01 = one hundredth = 1/100 0.001 = one thousandth = 1/1000Operations with Decimals
- Addition and subtraction: line up decimal points.
- Multiplication: multiply as whole numbers, then place the decimal point using the total number of decimal places in the factors.
- Division: if needed, multiply both dividend and divisor by the same power of 10 to make the divisor a whole number.
Example: 2.5 + 1.25 = 3.75.
Example: 0.4 × 0.3 = 0.12.
7. Ratio and Proportion
Ratio
Ratio of a to b = a : b = a/b A ratio compares quantities in the same units.Example: 2 red balls and 3 blue balls give a red-to-blue ratio of 2 : 3.
Equivalent Ratios
a : b = (a × n) : (b × n)Example: 2 : 3 = 4 : 6 = 6 : 9.
Proportion
If a/b = c/d, where the denominators are non-zero: a × d = b × cExample: 2/3 = 4/6 because 2 × 6 = 3 × 4 = 12.
8. Patterns and Introductory Algebra
Patterns follow a rule. Algebra uses letters or symbols to represent numbers.
Number Patterns
2, 4, 6, 8, 10, … Rule: add 2 each time.Square Numbers
n² = n × n Examples: 1, 4, 9, 16, 25, 36, …Triangular Numbers
Tₙ = n(n + 1)/2 Examples: 1, 3, 6, 10, 15, …This formula describes the sum 1 + 2 + … + n.
Simple Expressions
x + x = 2x x + 3 means a number plus 3 If x = 5, then x + 3 = 8.9. Lines, Angles and Shapes
Basic Geometry
- Point: an exact position.
- Line segment: part of a line with two endpoints.
- Line: extends endlessly in both directions.
- Ray: has one endpoint and extends endlessly in one direction.
- Parallel lines: lines in a plane that do not meet.
- Perpendicular lines: lines meeting at a right angle of 90°.
Types of Angles
Acute: less than 90° Right: exactly 90° Obtuse: greater than 90° and less than 180° Straight: exactly 180° Reflex: greater than 180° and less than 360°Angle Facts
Angles on a straight line = 180° Angles around a point = 360° A right angle = 90°Example: If one angle on a straight line is 120°, the other is 180° − 120° = 60°.
10. Triangles and Quadrilaterals
Triangles
Sum of interior angles of a triangle = 180°Example: If two angles are 50° and 60°, the third angle is 180° − 110° = 70°.
- Equilateral triangle: all three sides equal; each angle is 60°.
- Isosceles triangle: two sides equal.
- Scalene triangle: all sides have different lengths.
- Right triangle: one angle is 90°.
Quadrilaterals
Sum of interior angles of a quadrilateral = 360°Examples include squares, rectangles, parallelograms, rhombuses and trapeziums.
- Square: four equal sides and four right angles.
- Rectangle: opposite sides equal and four right angles.
- Rhombus: four equal sides.
- Parallelogram: opposite sides parallel and equal.
11. Symmetry
A shape has line symmetry when it can be folded along a line so that its two halves match exactly.
Square
4 lines of symmetryRectangle
2 lines of symmetryEquilateral Triangle
3 lines of symmetryCircle
Infinitely many lines of symmetryRotational symmetry: a shape has rotational symmetry if it looks unchanged after a rotation of less than one complete turn. The order is the number of times it matches itself during a full 360° turn.
12. Perimeter and Area
Perimeter measures the total distance around a closed shape. Area measures the surface enclosed by a flat shape.
Square
Perimeter = 4 × side Area = side × side = side² Example: Side = 5 cm; perimeter = 20 cm and area = 25 cm².Rectangle
Perimeter = 2 × (length + breadth) Area = length × breadth Example: Length = 8 cm, breadth = 3 cm; perimeter = 22 cm and area = 24 cm².Triangle
Perimeter = a + b + cFor a triangle with sides 3 cm, 4 cm and 5 cm, perimeter = 12 cm.
The general area formula, often taught in later or extension lessons, is:
Area = ½ × base × perpendicular heightGeneral Polygon
Perimeter = Sum of all side lengthsAlways use the same unit for every side before adding.
13. Volume and Measurement
Volume measures the space occupied by a three-dimensional object. This is useful revision material, but coverage may vary by Class 6 textbook edition.
Cube
Volume = side × side × side = side³ Example: A cube with side 3 cm has volume 27 cm³.Cuboid
Volume = length × breadth × height Example: 4 cm × 3 cm × 2 cm = 24 cm³.Useful Unit Conversions
| Measurement | Conversion |
|---|---|
| Length | 1 km = 1,000 m |
| Length | 1 m = 100 cm |
| Length | 1 cm = 10 mm |
| Mass | 1 kg = 1,000 g |
| Capacity | 1 L = 1,000 mL |
| Area | 1 m² = 10,000 cm² |
| Volume | 1 cm³ = 1,000 mm³ |
Remember that conversions for area and volume use squared and cubed conversion factors respectively.
14. Data Handling
Data handling means collecting, organising, representing and interpreting information.
Frequency
Frequency = Number of times a value occurs Example: In 2, 3, 3, 4, 3, the frequency of 3 is 3.Mean (Average)
Mean = Sum of observations ÷ Number of observations Example: Mean of 4, 6 and 8 = (4 + 6 + 8) ÷ 3 = 6.Range
Range = Largest value − Smallest value Example: For 3, 5, 9, 10, range = 10 − 3 = 7.Charts: Bar graphs compare categories using bars. Pictographs represent quantities using pictures or symbols. Always check the scale and key before interpreting a graph.
15. Prime Numbers and Number Play
Prime Number
A whole number greater than 1 with exactly two positive factors: 1 and itself.Examples: 2, 3, 5, 7, 11.
Composite Number
A whole number greater than 1 with more than two positive factors.Examples: 4, 6, 8, 9, 10.
Special Facts
1 is neither prime nor composite. 2 is the only even prime number.Divisibility Rules
- Divisible by 2: last digit is 0, 2, 4, 6 or 8.
- Divisible by 3: sum of digits is divisible by 3.
- Divisible by 5: last digit is 0 or 5.
- Divisible by 10: last digit is 0.
- Divisible by 9: sum of digits is divisible by 9.
16. Zero and Number Properties
Rules to Remember
a + 0 = a a × 0 = 0 a × 1 = a a − a = 0Division by zero is undefined. Zero divided by a non-zero number is zero.
Even and Odd Numbers
Even numbers are divisible by 2. Odd numbers are not divisible by 2.
Even + Even = Even Odd + Odd = Even Even + Odd = Odd Odd × Odd = Odd Even × Any Integer = EvenFor number-line questions, numbers farther to the right are greater than numbers to the left. This rule also helps compare negative integers: −2 is greater than −5.
17. Solved Examples
Example 1: Find the HCF of 18 and 24
Factors of 18: 1, 2, 3, 6, 9, 18.Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Greatest common factor = 6.
Example 2: Add 3/8 and 2/8
The denominators are equal, so add the numerators.3/8 + 2/8 = (3 + 2)/8 = 5/8.
Example 3: Find the perimeter of a square with side 9 cm
Perimeter = 4 × side = 4 × 9 = 36 cm.Example 4: Find the area of a rectangle of length 7 cm and breadth 4 cm
Area = length × breadth = 7 × 4 = 28 cm².Example 5: Find the missing angle on a straight line if one angle is 65°
Angles on a straight line add up to 180°.Missing angle = 180° − 65° = 115°.
Example 6: Find the mean of 5, 7, 9 and 11
Sum = 5 + 7 + 9 + 11 = 32.Number of observations = 4.
Mean = 32 ÷ 4 = 8.
Example 7: Convert 3.5 metres into centimetres
1 metre = 100 centimetres.3.5 × 100 = 350 cm.
Example 8: Find the next number: 5, 10, 15, 20, ...
Each term increases by 5.The next number is 25.
18. Interactive Practice Questions
Try each question before opening its answer. This is a quick way to check your understanding.
Q1. What is the place value of 6 in 4,682?
Answer: 600.Q2. Calculate 375 + 248.
Answer: 623.Q3. Find the HCF of 16 and 20.
Answer: 4.Q4. Calculate 4/9 + 2/9.
Answer: 6/9 = 2/3 in simplest form.Q5. Calculate 4.6 + 2.35.
Answer: 6.95.Q6. A rectangle is 12 cm long and 5 cm wide. Find its perimeter.
Answer: 2 × (12 + 5) = 34 cm.Q7. Find the area of a square with side 8 cm.
Answer: 8 × 8 = 64 cm².Q8. Two angles of a triangle are 45° and 75°. Find the third angle.
Answer: 180° − (45° + 75°) = 60°.Q9. Is 29 prime or composite?
Answer: Prime. Its only positive factors are 1 and 29.Q10. Find the range of 6, 12, 4, 15 and 9.
Answer: 15 − 4 = 11.19. Frequently Asked Questions (FAQs)
1. What are the most important Class 6 Maths formulas?
Important revision formulas include perimeter of a square and rectangle, area of a square and rectangle, fraction operations, angle facts, unit conversions and basic data-handling formulas. Your exact examinable list depends on the textbook edition used by your school.2. Does the Class 6 NCERT Maths book contain all these topics?
Not necessarily. NCERT has a newer Class 6 book called Ganita Prakash, while older editions cover a different chapter sequence. This article combines common concepts and additional revision topics. Use your prescribed edition as the final syllabus guide.3. What is the formula for the perimeter of a rectangle?
Perimeter = 2 × (length + breadth).4. What is the formula for the area of a square?
Area = side × side = side².5. How do I add fractions with different denominators?
Convert the fractions to equivalent fractions with a common denominator. Then add the numerators and simplify the answer if possible.6. What is the difference between perimeter and area?
Perimeter is the distance around a shape, while area is the surface enclosed by the shape. Perimeter uses linear units and area uses square units.7. How can I remember formulas easily?
Understand what each formula measures, draw a diagram, solve two or three examples, and revise regularly instead of memorising formulas without practice.8. Is this article useful for school exams?
Yes, it can be used for revision and practice. Match the topics to your teacher's syllabus and textbook, and also complete the textbook exercises.9. Are HCF and LCM important in Class 6?
They are useful number concepts and appear in many school mathematics resources. Confirm their coverage and depth in your current NCERT edition.10. Can I use this page for quick revision before an exam?
Yes. Review the relevant formula cards, read the worked examples, and attempt the practice questions before checking the answers.20. Quick Formula Revision Table
| Topic | Formula or Rule |
|---|---|
| Division | Dividend = Divisor × Quotient + Remainder |
| Equivalent fraction | a/b = an/bn, for non-zero n |
| Fraction addition, same denominator | a/c + b/c = (a + b)/c |
| Ratio | a : b = a/b |
| Triangle angles | Sum = 180° |
| Quadrilateral angles | Sum = 360° |
| Straight angle | 180° |
| Angles around a point | 360° |
| Square perimeter | 4 × side |
| Square area | side² |
| Rectangle perimeter | 2 × (length + breadth) |
| Rectangle area | length × breadth |
| Mean | Sum of observations ÷ Number of observations |
| Range | Largest value − Smallest value |
| Triangular number | n(n + 1)/2 |
| Cube volume | side³ |
| Cuboid volume | length × breadth × height |
