Class 6 Maths All Formulas: The Complete CBSE Formula Sheet (2026)

Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. Whether you searched for a maths class 6 worksheet or a worksheet math class 6 resource, you have landed in the right place. SparkEd's Class 6 maths practice covers the full CBSE syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

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Each maths worksheet for class 6 includes a mix of short-answer, long-answer, and maths questions and answers for class 6 in MCQ format. You get a complete maths worksheet for class 6 with answers, making self-study easy. The content is suitable as a maths worksheet for class 6 cbse as well as a maths worksheet for class 6 ncert resource — both boards follow the same core syllabus. Looking for a simpler label? It is the same math worksheet for class 6 you need.

For revision before exams, try the maths worksheet for class 6th with answers alongside our maths mcq for class 6 with answers sets. Teachers can use the class 6 maths mcq question paper bank for quick classroom tests. Browse all class 6 maths worksheets cbse topics on the All Class 6 worksheets page, or start with the popular Number Play worksheet. Ready to practise? Head to SparkEd home and pick your chapter.

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Why This Formula Sheet Helps

Looking for a class 6 math worksheet or maths worksheet for class 6 with answers? This comprehensive resource covers everything you need. Class 6 is where Maths transitions from basic arithmetic to more structured concepts. You meet integers for the first time, learn about HCF and LCM, start working with fractions and decimals properly, and begin formal geometry.

This page puts every important formula and key fact in one place. It is designed for quick revision before tests and exams. Each formula includes a short explanation so you understand when to use it.

Beyond this worksheet, SparkEd offers interactive online practice for Knowing Our Numbers with step-by-step solutions and progress tracking — perfect for daily revision.

Number System and Place Value

Understanding place value is the foundation for all number work.

Place Value System

Indian place value system:

International place value system:

Conversions:

$$1 \text{ Crore} = 10{,}000{,}000 = 10 \text{ Million}$$

$$1 \text{ Million} = 10 \text{ Lakhs}$$

$$1 \text{ Billion} = 100 \text{ Crores}$$

Estimation and rounding:
- Round to the nearest $10$: look at the ones digit. If $\ge 5$, round up.
- Round to the nearest $100$: look at the tens digit.
- Round to the nearest $1000$: look at the hundreds digit.

Roman numerals key values:
$I = 1$, $V = 5$, $X = 10$, $L = 50$, $C = 100$, $D = 500$, $M = 1000$

Memory tip: In the Indian system, commas are placed after the hundreds, then every two digits (e.g., 1,23,45,678). In the international system, commas are placed every three digits (e.g., 12,345,678).

Whole Numbers

Whole numbers: $0, 1, 2, 3, 4, 5, \ldots$

Properties of Whole Numbers

Successor: $n + 1$ (the next number)
Predecessor: $n - 1$ (the previous number)

Closure property:

Whole numbers are closed under addition and multiplication.

Commutative property:

Associative property:

$$(a \times b) \times c = a \times (b \times c)$$

Distributive property:

$$a \times (b - c) = a \times b - a \times c$$

Identity elements:
- Additive identity: $a + 0 = a$
- Multiplicative identity: $a \times 1 = a$

Multiplication by zero: $a \times 0 = 0$

Division by zero: Not defined.

Memory tip: The distributive property is your best friend for mental maths. Use it to break hard multiplications: $7 \times 98 = 7 \times (100 - 2) = 700 - 14 = 686$.

HCF and LCM

HCF and LCM are used throughout mathematics for simplifying fractions, finding common denominators, and solving word problems.

HCF and LCM Formulas

Factors: Numbers that divide a given number exactly (remainder $0$).

Multiples: Products of a number with whole numbers.

Prime number: A number greater than $1$ with exactly two factors ($1$ and itself).

Composite number: A number greater than $1$ with more than two factors.

Note: $1$ is neither prime nor composite.

Prime factorisation: Every composite number can be expressed as a product of primes.

Example: $60 = 2^2 \times 3 \times 5$

HCF (Highest Common Factor): The largest factor common to two or more numbers.

LCM (Lowest Common Multiple): The smallest multiple common to two or more numbers.

Key relationship:

Example: Find HCF and LCM of $12$ and $18$.
$12 = 2^2 \times 3$ and $18 = 2 \times 3^2$
$\text{HCF} = 2^1 \times 3^1 = 6$
$\text{LCM} = 2^2 \times 3^2 = 36$
Check: $6 \times 36 = 216 = 12 \times 18$. Correct.

Divisibility rules:
- By $2$: last digit is even ($0, 2, 4, 6, 8$)
- By $3$: sum of digits is divisible by $3$
- By $4$: last two digits form a number divisible by $4$
- By $5$: last digit is $0$ or $5$
- By $6$: divisible by both $2$ and $3$
- By $9$: sum of digits is divisible by $9$
- By $10$: last digit is $0$
- By $11$: difference of sums of alternate digits is $0$ or divisible by $11$

Integers

Integers extend whole numbers to include negative numbers.

Integer Operations

Integers: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$

Absolute value: $|a|$ is the distance of $a$ from $0$ on the number line.

Addition rules:
- Same sign: Add absolute values, keep the common sign.

- Different signs: Subtract the smaller absolute value from the larger, take the sign of the larger.

$$(-7) + 4 = -(7 - 4) = -3$$

Subtraction: Add the additive inverse.

$$5 - (-3) = 5 + 3 = 8$$

Ordering: On the number line, a number to the right is always greater.

Memory tip: Subtracting a negative is the same as adding a positive. "Minus a minus is a plus."

Fractions and Decimals

Fractions and decimals represent parts of a whole.

Fraction Formulas

Types of fractions:
- Proper: numerator $<$ denominator (value $< 1$)
- Improper: numerator $\ge$ denominator (value $\ge 1$)
- Mixed: whole number + proper fraction

Converting mixed to improper:

Equivalent fractions:

Simplest form: Divide numerator and denominator by their HCF.

Adding/subtracting like fractions:

Adding/subtracting unlike fractions: Find LCM of denominators, convert, then add.

Comparing fractions: Cross multiply or convert to common denominator.

Decimal to fraction:

Fraction to decimal: Divide numerator by denominator.

Adding/subtracting decimals: Line up decimal points, then add or subtract.

Memory tip: To add unlike fractions, find the LCM of denominators first. To compare fractions, cross-multiplication is the fastest method.

Basic Geometry

Geometry in Class 6 introduces the basic building blocks.

Key Geometry Facts

Point: A location with no size.
Line segment: Definite length, two endpoints.
Ray: One endpoint, extends infinitely in one direction.
Line: No endpoints, extends infinitely in both directions.

Types of angles:
- Acute: $0° < \theta < 90°$
- Right: $\theta = 90°$
- Obtuse: $90° < \theta < 180°$
- Straight: $\theta = 180°$
- Reflex: $180° < \theta < 360°$

Angle sum in a triangle:

Angle sum in a quadrilateral:

Sum of interior angles of a polygon with $n$ sides:

Circle terms:
- Radius $r$, Diameter $d = 2r$
- Chord (line segment with endpoints on circle)
- Diameter is the longest chord

Memory tip: The angle sum formula $(n-2) \times 180°$ works for any polygon. Triangle: $(3-2) \times 180° = 180°$. Quadrilateral: $(4-2) \times 180° = 360°$.

Mensuration: Perimeter and Area

Perimeter is the boundary length. Area is the space enclosed.

Perimeter and Area Formulas

Rectangle (length $l$, breadth $b$):

$$\text{Area} = l \times b$$

Square (side $a$):

$$\text{Area} = a^2$$

Triangle (base $b$, height $h$):

Perimeter of a triangle: Sum of all three sides.

Circle (radius $r$):

$$\text{Area} = \pi r^2$$

(Use $\pi \approx \frac{22}{7}$ or $3.14$)

Memory tip: Perimeter is always a length (measured in cm, m, etc.). Area is always in square units (cm$^2$, m$^2$, etc.). Never mix them up.

Ratio and Proportion

Ratios and proportions compare quantities and solve real-world problems.

Ratio and Proportion Formulas

Ratio: A comparison of two quantities of the same unit.

Always express in simplest form by dividing by HCF.
Example: $12 : 18 = 2 : 3$ (divide both by $6$).

Equivalent ratios: Multiply or divide both terms by the same number.

Proportion: Four numbers $a, b, c, d$ are in proportion if:

The numbers $a$ and $d$ are called extremes, and $b$ and $c$ are called means.

Product of extremes = Product of means:

Unitary method: Find the value of one unit, then multiply for the required number of units.

Example: If $5$ pens cost Rs. $30$, what do $8$ pens cost?
Cost of $1$ pen $= \frac{30}{5} = 6$
Cost of $8$ pens $= 6 \times 8 = 48$

Memory tip: In a proportion $a : b :: c : d$, cross-multiply to check: $a \times d$ should equal $b \times c$.

Symmetry

Symmetry is about balanced, identical halves.

Lines of Symmetry

Line of symmetry: A line that divides a figure into two identical halves that are mirror images of each other.

Lines of symmetry in common shapes:

| Shape | Lines of symmetry |
|-------|-------------------|
| Equilateral triangle | 3 |
| Isosceles triangle | 1 |
| Scalene triangle | 0 |
| Square | 4 |
| Rectangle | 2 |
| Circle | Infinite |
| Regular hexagon | 6 |
| Regular pentagon | 5 |

General rule: A regular polygon with $n$ sides has $n$ lines of symmetry.

Memory tip: The more symmetric a shape is, the more lines of symmetry it has. A circle is the most symmetric shape (infinite lines).

Quick Revision Strategy