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NEW NCERT 2026–27 GANITA PRAKASH

Class 7 Maths Formulas

All 15 Chapters | Important Rules, Properties, Examples & Practice

Your chapter-wise mathematics revision guide from Maths Wallah.

Part IPart II Interactive Revision

Welcome to Maths Wallah! This special guide brings together important formulas, mathematical properties, rules and examples from the new NCERT Class 7 Mathematics books, Ganita Prakash Part I and Part II.

How to use this guide: Read the chapter summary, understand the worked examples, and then attempt the practice questions. The new NCERT approach emphasises mathematical thinking, patterns, reasoning and activities—not only memorising formulas.

Important: Some chapters have no single formula to memorise. Their key learning points are properties, constructions, logical rules or methods. Additional formulas are labelled as useful extensions where appropriate. Follow your school's prescribed textbook and teaching plan for examinations.

📚 Table of Contents

1. Part I — Chapter 1: Large Numbers Around Us
2. Part I — Chapter 2: Arithmetic Expressions
3. Part I — Chapter 3: A Peek Beyond the Point
4. Part I — Chapter 4: Expressions Using Letter-Numbers
5. Part I — Chapter 5: Parallel and Intersecting Lines
6. Part I — Chapter 6: Number Play
7. Part I — Chapter 7: A Tale of Three Intersecting Lines
8. Part I — Chapter 8: Working with Fractions
9. Part II — Chapter 1: Geometric Twins
10. Part II — Chapter 2: Operations with Integers
11. Part II — Chapter 3: Finding Common Ground
12. Part II — Chapter 4: Another Peek Beyond the Point
13. Part II — Chapter 5: Connecting the Dots...
14. Part II — Chapter 6: Constructions and Tilings
15. Part II — Chapter 7: Finding the Unknown
16. Quick Revision Table
17. Practice Questions
18. Frequently Asked Questions

1. Large Numbers Around Us

Large numbers are used to express populations, distances, money, quantities and measurements. Learn how to read, write, compare, estimate and round numbers.

Place Value

Place value = Digit × Value of its position Example: In 7,35,42,816, the digit 5 is in the lakh place, so its place value is 5,00,000.

Expanded Form

48,326 = 40,000 + 8,000 + 300 + 20 + 6 Write a number as the sum of the place values of its digits.

Indian Place-Value System

Common periods: ones, thousands, lakhs and crores.

Example: 1 lakh = 1,00,000 and 1 crore = 1,00,00,000.

Exact and Approximate Values

Rounding helps estimate quantities. To round to a place, inspect the digit immediately to its right: 5–9 means increase the retained digit by one; 0–4 means leave it unchanged.

Example: 4,768 rounded to the nearest hundred is 4,800.

Pattern in products: Explore how multiplying by 10, 100 or 1,000 changes place values. In the decimal system, multiplying a whole number by 10 shifts each digit one place to the left in the place-value chart.

2. Arithmetic Expressions

Arithmetic expressions combine numbers, operations and brackets. Correctly reading an expression is just as important as calculating it.

Order of Operations

Evaluate brackets first, then exponents where present, then multiplication and division from left to right, and finally addition and subtraction from left to right.

4 + 3 × 2 = 4 + 6 = 10 (4 + 3) × 2 = 7 × 2 = 14

Distributive Property

a × (b + c) = a × b + a × c a × (b − c) = a × b − a × c Example: 8 × 17 = 8 × (10 + 7) = 80 + 56 = 136.

Commutative and Associative Properties

a + b = b + a a × b = b × a (a + b) + c = a + (b + c) (a × b) × c = a × (b × c)

These properties allow terms to be reordered or regrouped in addition and multiplication. Subtraction and division are generally not commutative.

Brackets and Simplification

When a bracket is preceded by a plus sign, removing the bracket keeps the signs unchanged. When it is preceded by a minus sign, the signs inside change.

a + (b − c) = a + b − c a − (b − c) = a − b + c Example: 20 − (6 − 2) = 20 − 6 + 2 = 16.

3. A Peek Beyond the Point

This chapter develops understanding of decimals, smaller units, place value, measurement and comparing decimal numbers.

Decimal Place Value

0.1 = 1/10 0.01 = 1/100 0.001 = 1/1000

Decimal to Fraction

Write the decimal as a fraction with denominator 10, 100, 1,000, etc., then simplify.

0.75 = 75/100 = 3/4

Adding Decimals

Align decimal points and add corresponding place values.

3.45 + 2.7 = 3.45 + 2.70 = 6.15

Subtracting Decimals

Align decimal points and subtract.

5.20 − 1.75 = 3.45

Decimal Measurement Conversions

Conversion	Equivalent value
1 kilometre	1,000 metres
1 metre	100 centimetres
1 centimetre	10 millimetres
1 kilogram	1,000 grams
1 litre	1,000 millilitres

Comparing decimals: Compare whole-number parts first. If they are equal, compare tenths, then hundredths, then thousandths. Adding zeros to the end of a decimal does not change its value: 2.5 = 2.50 = 2.500.

4. Expressions Using Letter-Numbers

Letters can represent unknown or changing numbers. Expressions using letters help describe patterns and general rules.

Terms and Coefficients

In 5x + 3, the terms are 5x and 3. The coefficient of x is 5.

x + x = 2x 3a + 4a = 7a 7m − 2m = 5m

Only like terms can be combined by adding or subtracting their coefficients.

Evaluating Expressions

Substitute the given value for the letter and calculate.

If x = 4, then 3x + 2 = 3 × 4 + 2 = 14

Common Algebraic Rules

a + 0 = a a × 1 = a a × 0 = 0 a(b + c) = ab + ac

Example: 2(x + 5) = 2x + 10.

Do not confuse 3x with 3 + x. The expression 3x means 3 multiplied by x.

5. Parallel and Intersecting Lines

Lines can be parallel, intersecting or perpendicular. Angle relationships help us understand these geometric situations.

Essential Angle Facts

Angles on a straight line = 180° Angles around a point = 360° A right angle = 90°

Example: If two adjacent angles on a straight line are x and 65°, then x + 65° = 180°, so x = 115°.

When a Transversal Crosses Parallel Lines

• Corresponding angles are equal.
• Alternate interior angles are equal.
• Interior angles on the same side of the transversal add up to 180°.

Intersecting Lines

Vertically opposite angles are equal.

Adjacent angles forming a straight line add up to 180°.

A transversal is a line that crosses two or more lines. Draw and label the diagram before solving angle problems.

6. Number Play

This chapter explores number properties, parity, patterns and mathematical puzzles.

Even and Odd Numbers

Even + Even = Even Odd + Odd = Even Even + Odd = Odd Odd × Odd = Odd Even × Any Integer = Even

Consecutive Numbers

Consecutive integers differ by 1.

n, n + 1, n + 2

Example: 12, 13, 14.

Triangular Numbers

Tₙ = n(n + 1)/2

The first terms are 1, 3, 6, 10, 15, 21, ...

This rule describes the sum 1 + 2 + ... + n.

Square Numbers

n² = n × n

Examples: 1, 4, 9, 16, 25, 36, ...

Virahanka–Fibonacci Pattern

In the familiar Fibonacci-style sequence, each new term is the sum of the two previous terms.

1, 1, 2, 3, 5, 8, 13, 21, ... Next term = Previous term + Term before it

Example: After 8 and 13 comes 8 + 13 = 21.

Number puzzles: Check whether a sequence changes by addition, subtraction, multiplication, alternating rules or a combination of rules. Do not assume every sequence has the same pattern.

7. A Tale of Three Intersecting Lines

This chapter develops triangle properties, triangle construction and the relationship between given side lengths and possible triangles.

Triangle Angle Sum

A + B + C = 180°

Example: If two angles are 50° and 60°, the third is 180° − 110° = 70°.

Equilateral Triangle

All three sides are equal. Each interior angle = 60°

If each side is 6 cm, the perimeter is 6 + 6 + 6 = 18 cm.

Triangle Inequality

The sum of any two side lengths of a triangle must be greater than the third side.

a + b > c; a + c > b; b + c > a

Example: 3 cm, 4 cm and 5 cm can form a triangle. But 2 cm, 3 cm and 6 cm cannot.

Types of Triangles by Sides

• Equilateral: three equal sides.
• Isosceles: at least two equal sides.
• Scalene: all sides unequal.

By angles, a triangle may be acute-angled, right-angled or obtuse-angled.

Construction tasks require a ruler, compass and protractor where instructed. A diagram should be made accurately, with given lengths and angles clearly marked.

8. Working with Fractions

Fractions represent parts of a whole. The denominator cannot be zero.

Equivalent Fractions

a/b = (a × n)/(b × n), for non-zero n

Example: 2/3 = 4/6 = 6/9.

Addition and Subtraction

When denominators are equal:

a/c + b/c = (a + b)/c a/c − b/c = (a − b)/c

For different denominators, first express the fractions with a common denominator.

Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Multiplication of Fractions

a/b × c/d = (a × c)/(b × d)

Example: 2/3 × 3/5 = 6/15 = 2/5.

Cancel common factors before multiplying when possible.

Division of Fractions

a/b ÷ c/d = a/b × d/c

The divisor fraction must not be zero. Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

Fraction of a Quantity

a/b of N = (a × N)/b

Example: 3/4 of 20 = (3 × 20)/4 = 15.

9. Geometric Twins

Congruent shapes have exactly the same shape and size. They can be placed on top of one another so that corresponding points match.

Congruence of Line Segments

AB = CD means the segments have equal lengths.

Equal length alone is enough to show that two line segments are congruent.

Congruence of Angles

∠A = ∠B means the angles have equal measures.

When shapes are congruent, their corresponding sides and corresponding angles are equal.

Triangle Congruence Criteria

• SSS: three corresponding sides are equal.
• SAS: two corresponding sides and the included angle are equal.
• ASA: two corresponding angles and the included side are equal.
• RHS: for right triangles, the hypotenuse and one corresponding side are equal.

Remember: Similar shapes have the same shape but may have different sizes. Congruent shapes have both the same shape and the same size.

10. Operations with Integers

Integers include negative whole numbers, zero and positive whole numbers.

Addition and Subtraction

a − b = a + (−b)

Example: 5 + (−8) = −3.

Example: −4 − (−7) = −4 + 7 = 3.

Multiplication Sign Rules

Positive × Positive = Positive Negative × Negative = Positive Positive × Negative = Negative Negative × Positive = Negative

Example: (−6) × (−3) = 18; (−6) × 3 = −18.

Division Sign Rules

Same signs → Positive quotient Different signs → Negative quotient

Examples: (−20) ÷ (−5) = 4; 20 ÷ (−5) = −4.

Division by zero is undefined.

Distributive Property with Integers

a(b + c) = ab + ac

Example: (−3)(4 + 2) = (−3)(4) + (−3)(2) = −18.

11. Finding Common Ground

This chapter focuses on common factors and multiples, prime factorisation and using common denominators.

Factors and Multiples

A factor divides a number exactly. A multiple is obtained by multiplying a number by an integer.

Factors of 12: 1, 2, 3, 4, 6, 12.

Positive multiples of 5: 5, 10, 15, 20, ...

HCF and LCM

HCF = Highest common factor LCM = Least common positive multiple

Example: HCF of 12 and 18 is 6; LCM is 36.

For two positive integers: HCF × LCM = Product of the two integers

Prime Factorisation

Write a number as a product of prime numbers.

60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

For HCF, use the prime factors common to both numbers with the smallest powers. For LCM, use all prime factors needed with the greatest powers.

Common Denominators

The LCM of the denominators can be used to find a common denominator for adding or subtracting fractions.

1/4 + 1/6 = 3/12 + 2/12 = 5/12

12. Another Peek Beyond the Point

This chapter extends decimal and fraction understanding, including operations and practical applications.

Multiplying Decimals

Multiply as whole numbers, then position the decimal point using the total number of decimal places in the factors.

0.4 × 0.3 = 0.12 2.5 × 1.2 = 3.00 = 3

Dividing Decimals

Move the decimal point in both dividend and divisor the same number of places until the divisor is a whole number.

4.8 ÷ 0.6 = 48 ÷ 6 = 8

Fractions and Decimals

1/2 = 0.5 1/4 = 0.25 3/4 = 0.75 1/5 = 0.2

To convert a fraction to a decimal, divide its numerator by its denominator.

Percentage and Ratio — Useful Extension

Percentage = (Part ÷ Whole) × 100% Percentage of a quantity = (Percentage ÷ 100) × Quantity Ratio a : b = a/b

Example: 25% of 80 = 25/100 × 80 = 20.

Percentage and ratio formulas are useful extensions and may be covered differently depending on the prescribed course plan. Prioritise the exact methods taught in your current NCERT chapter.

13. Connecting the Dots...

This chapter connects numerical information with points, graphs, patterns and relationships.

Coordinates

A point on a coordinate grid is described by an ordered pair (x, y). The first number tells the horizontal position and the second tells the vertical position.

(3, 2) means 3 units horizontally and 2 units vertically from the origin, following the grid's positive directions.

Do not reverse the order: (3, 2) and (2, 3) usually represent different points.

Reading Graphs

• Read the title and labels on both axes.
• Check the scale before comparing values.
• For a point on a graph, read the horizontal coordinate first, then the vertical coordinate.

Patterns and Relationships

If a sequence increases by a constant amount, compare consecutive terms to identify the step.

5, 8, 11, 14, ... → add 3 each time

A simple rule for the nth term of this sequence is 3n + 2, starting at n = 1.

Use the coordinate grid and graphing conventions shown in your textbook. Some graphing or algebraic rules here are explanatory tools rather than formulas that must be memorised.

14. Constructions and Tilings

Geometric constructions use accurate drawings to make lines, angles and shapes. Tilings cover a flat surface without gaps or overlaps.

Construction Essentials

• Use a ruler to draw straight line segments.
• Use a compass to transfer distances and draw arcs.
• Use a protractor when an angle measurement is required.
• Mark equal lengths and angles clearly.

Angle Relationships for Constructions

Straight angle = 180° Right angle = 90° Angles around a point = 360°

To construct an angle bisector, draw an arc from the vertex, then use equal-radius arcs from the two points where it crosses the arms. Join the vertex to the arcs' intersection.

Tilings

A tiling covers a surface without leaving gaps or overlapping shapes. At a point where polygon corners meet, their interior angles must add up to 360° for a complete flat tiling around that point.

Angles around a tiling vertex = 360°

Example: Three regular hexagons can meet at one point because 120° + 120° + 120° = 360°.

15. Finding the Unknown

Equations express that two quantities are equal. Solve an equation by performing the same valid operation on both sides.

Simple Equations

x + a = b → x = b − a x − a = b → x = b + a ax = b → x = b/a, when a ≠ 0 x/a = b → x = ab, when a ≠ 0

Example: x + 7 = 19, so x = 19 − 7 = 12.

Equations with Two Steps

2x + 3 = 13

Subtract 3 from both sides: 2x = 10.

Divide both sides by 2: x = 5.

Checking a Solution

Substitute the answer into the original equation.

For x + 7 = 19, substituting x = 12 gives 12 + 7 = 19, which is true.

Golden rule: Whatever operation you apply to one side of an equation, apply the same operation to the other side to preserve equality.

📌 Quick Revision Table

Topic	Rule or Formula
Place value	Digit × Position value
Order of operations	Brackets, powers if present, multiplication/division, addition/subtraction
Distributive property	a(b + c) = ab + ac
Decimal fraction	0.1 = 1/10; 0.01 = 1/100
Like terms	3x + 4x = 7x
Straight angle	180°
Angles around a point	360°
Triangle angle sum	A + B + C = 180°
Triangle inequality	Sum of any two sides > third side
Triangular number	n(n + 1)/2
Square number	n² = n × n
Fraction multiplication	a/b × c/d = ac/bd
Fraction division	a/b ÷ c/d = a/b × d/c
HCF and LCM	For two positive integers: HCF × LCM = product
Integer subtraction	a − b = a + (−b)
Percentage	(Part ÷ Whole) × 100% — extension/revision
Equation	Perform the same valid operation on both sides

🧠 Interactive Practice Questions

Try to solve each question before expanding the answer.

Q1. Round 48,763 to the nearest thousand.

Answer: 49,000.

Q2. Calculate 5 + 4 × 3.

Answer: 5 + 12 = 17.

Q3. Calculate 4.65 + 2.8.

Answer: 4.65 + 2.80 = 7.45.

Q4. Simplify 5x + 3x.

Answer: 8x.

Q5. One angle on a straight line is 72°. Find the other angle.

Answer: 180° − 72° = 108°.

Q6. Find the next term: 2, 5, 8, 11, ...

Answer: 14. Add 3 each time.

Q7. Calculate 2/3 × 3/8.

Answer: 6/24 = 1/4.

Q8. Calculate (−7) + 12.

Answer: 5.

Q9. Find the HCF of 18 and 30.

Answer: 6.

Q10. Solve x + 9 = 24.

Answer: x = 24 − 9 = 15.

Q11. Can 2 cm, 4 cm and 7 cm form a triangle?

Answer: No. 2 + 4 is not greater than 7.

Q12. Find 20% of 150.

Answer: 20/100 × 150 = 30. This is an extension/revision question.

❓ Frequently Asked Questions

1. What is the new NCERT Class 7 Maths book called?

The new NCERT Class 7 Mathematics series is called Ganita Prakash and is available in Part I and Part II.

2. How many chapters are there in the new Class 7 Maths books?

The chapter list used in this guide contains 8 chapters in Part I and 7 chapters in Part II, making 15 chapters altogether.

3. Does every chapter have a formula?

No. Some chapters focus on reasoning, number patterns, geometric constructions, congruence or interpreting graphs. Understanding their rules and methods is more important than memorising a formula.

4. What are the most important geometry rules?

Remember that angles on a straight line total 180°, angles around a point total 360°, and the interior angles of a triangle total 180°. Learn the parallel-line angle relationships and triangle congruence criteria as taught in your textbook.

5. What are the main fraction formulas?

For multiplication, multiply the numerators and denominators. For division, multiply by the reciprocal of the divisor. For addition and subtraction, use a common denominator.

6. How do I solve a simple equation?

Perform the same valid operation on both sides to isolate the unknown, then substitute the answer back into the original equation to check it.

7. Is this guide enough for my Class 7 exam?

Use it as a revision companion, but also read the complete textbook, complete activities and exercises, and follow the chapters included by your teacher or school.

8. Are percentages and ratio part of every new Class 7 chapter plan?

Coverage and emphasis can vary by prescribed book and school plan. In this guide, percentage and ratio are identified as useful extension/revision material rather than being presented as guaranteed standalone chapters.

9. How can I memorise maths formulas more effectively?

Understand the meaning of each rule, draw a diagram where possible, solve examples yourself and revise mistakes regularly. Practising a formula in context is more useful than memorising it alone.

10. Where can I find the official NCERT books?

Visit the official NCERT textbook portal and select the relevant Class 7 Mathematics book and chapter.

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