🌈 Class 5 Maths Formulas – All Important Formulas, Rules and Examples
🎉 Welcome to Maths Wallah!
Hello, little mathematicians! Are you ready to make Maths fun? This colourful study guide brings together important Class 5 maths formulas, mathematical rules, solved examples and practice questions.
Explore large numbers, fractions, decimals, measurements, time, money, shapes and more. Open the interactive questions throughout the article to check your understanding.
Choose a topic to jump directly to that section.
🔢 1. Numbers and Place Value
Place value tells us the value of a digit according to its position in a number.
| Place | Value |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten Thousands | 10,000 |
| Lakhs | 1,00,000 |
| Ten Lakhs | 10,00,000 |
Expanded form = 7,00,000 + 50,000 + 4,000 + 300 + 20 + 6
Face value of 5 = 5
Place value of 5 = 50,000
- Successor = Number + 1
- Predecessor = Number − 1
- Smallest five-digit number = 10,000
- Greatest four-digit number = 9,999
🎯 Try It: What is the place value of 6 in 3,46,215?
➕ 2. Addition Formulas
Addition means combining two or more quantities.
12,345 + 23,456 = 35,801
45,678 + 12,345 = 58,023
25,000 + 15,000 = 40,000
Important Addition Rules
- 456 + 0 = 456
- 25 + 35 = 35 + 25 = 60
- Adding 1 gives the next number.
4,567 + 2,345 ------- 6,912
🎯 Try It: Calculate 34,567 + 12,456.
➖ 3. Subtraction Formulas
Subtraction finds the difference between two quantities.
8,765 − 3,245 = 5,520
10,000 − 4,567 = 5,433
25,000 − 12,500 = 12,500
Check: 5,433 + 4,567 = 10,000.
🎯 Try It: Calculate 50,000 − 27,845.
✖️ 4. Multiplication Formulas
Multiplication is a shortcut for repeated addition.
25 × 4 = 100
125 × 8 = 1,000
245 × 6 = 1,470
325 × 12 = 3,900
Important Multiplication Rules
- 456 × 1 = 456
- 456 × 0 = 0
- 12 × 8 = 8 × 12 = 96
- 345 × 10 = 3,450
🎯 Try It: There are 24 boxes with 6 pencils in each. How many pencils?
➗ 5. Division Formulas
Division means sharing equally or making equal groups.
144 ÷ 12 = 12
157 ÷ 12 = 13 remainder 1
Check: 12 × 13 + 1 = 157.
- 8 ÷ 8 = 1
- 0 ÷ 5 = 0
- Division by zero is undefined.
- The remainder must be smaller than the divisor.
🎯 Try It: Share 168 sweets equally among 12 children.
🧩 6. Factors, Multiples, HCF and LCM
A factor divides a number exactly. A multiple is obtained by multiplying a number by 1, 2, 3 and so on.
1, 2, 3, 4, 6, 8, 12, 24
First five positive multiples of 6:6, 12, 18, 24, 30
Highest Common Factor (HCF)
HCF is the greatest number that divides two or more numbers exactly.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 18: 1, 2, 3, 6, 9, 18.
Lowest Common Multiple (LCM)
LCM is the smallest positive number that is a multiple of two or more numbers.
🎯 Try It: Find the HCF of 8 and 12.
🎯 Try It: Find the LCM of 3 and 5.
HCF and LCM are useful extension topics and may vary by textbook edition.
↑ Back to contents🍕 7. Fractions
A fraction represents equal parts of a whole.
- Numerator: Number of parts being considered.
- Denominator: Total number of equal parts.
One-half = 1/2
One-third = 1/3
One-quarter = 1/4
Three-quarters = 3/4
Equivalent Fractions
Multiply or divide the numerator and denominator by the same non-zero number to obtain an equivalent fraction.
Simplifying Fractions
6/12 = 1/2, because both 6 and 12 can be divided by 6.
Addition with the Same Denominator
Example: 2/7 + 3/7 = 5/7.
Subtraction with the Same Denominator
Example: 5/8 − 2/8 = 3/8.
Adding Fractions with Different Denominators
First, find equivalent fractions with a common denominator.
Fraction of a Quantity
Half of 40 = 40 ÷ 2 = 20.
One-third of 30 = 30 ÷ 3 = 10.
One-quarter of 36 = 36 ÷ 4 = 9.
🎯 Try It: Calculate 3/8 + 2/8.
🎯 Try It: Find one-quarter of 48.
🔢 8. Decimals
Decimals represent numbers with fractional parts.
| Place | Value |
|---|---|
| Ones | 1 |
| Tenths | 0.1 |
| Hundredths | 0.01 |
| Thousandths | 0.001 |
Adding Decimals
Align the decimal points and add.
Subtracting Decimals
Align the decimal points and subtract.
Multiplying and Dividing by 10 and 100
3.45 × 10 = 34.5
3.45 × 100 = 345
45.6 ÷ 10 = 4.56
45.6 ÷ 100 = 0.456
🎯 Try It: Calculate 12.75 + 4.50.
💯 9. Percentage: An Introduction
Percentage means “out of 100.” This is a useful introductory topic and may be covered in more detail in later classes.
Percentage = (40 ÷ 50) × 100 = 80%.
50% = 1/2
25% = 1/4
75% = 3/4
10% = 1/10
🎯 Try It: Find 25% of 80.
📏 10. Measurement Formulas
Length and Distance
1 m = 100 cm
1 km = 1,000 m
Examples: 5 m = 500 cm; 3 km = 3,000 m.
Weight
Examples: 4 kg = 4,000 g; 2 kg 500 g = 2,500 g.
Capacity
Examples: 3 L = 3,000 mL; 2 L 250 mL = 2,250 mL.
🎯 Try It: Convert 7 metres into centimetres.
🎯 Try It: Convert 3.5 litres into millilitres.
🕒 11. Time Formulas
| Time Unit | Relationship |
|---|---|
| Minute | 1 minute = 60 seconds |
| Hour | 1 hour = 60 minutes |
| Day | 1 day = 24 hours |
| Week | 1 week = 7 days |
| Year | 1 year = 12 months |
| Ordinary year | 365 days |
| Leap year | 366 days |
4 hours = 4 × 60 = 240 minutes.
3 minutes = 3 × 60 = 180 seconds.
2 days = 2 × 24 = 48 hours.
Elapsed Time
Elapsed time is the time between a starting point and an ending point.
Elapsed time = 1 hour 45 minutes.
🎯 Try It: How many minutes are there in 5 hours?
💰 12. Money Formulas
₹125 + ₹250 = ₹375
₹500 − ₹275 = ₹225
Cost of a school bag = ₹650
Money paid = ₹1,000
Change = ₹1,000 − ₹650 = ₹350.
🎯 Try It: A book costs ₹375. You pay ₹500. Find your change.
📐 13. Geometry: Lines, Angles and Shapes
Lines
- A line extends endlessly in both directions.
- A line segment has two endpoints.
- A ray has one endpoint and extends in one direction.
Types of Angles
| Angle | Measurement |
|---|---|
| Acute | Less than 90° |
| Right | Exactly 90° |
| Obtuse | Greater than 90° but less than 180° |
| Straight | Exactly 180° |
Basic Shapes
| Shape | Property |
|---|---|
| Triangle | 3 sides |
| Square | 4 equal sides |
| Rectangle | Opposite sides equal |
| Circle | Round shape |
| Cube | 6 square faces |
| Cuboid | 6 rectangular faces |
| Sphere | Ball-shaped |
| Cylinder | Two circular ends and a curved surface |
| Cone | One circular base and a pointed top |
Symmetry
A shape has line symmetry when it can be divided into matching halves by a line.
- A square has 4 lines of symmetry.
- A rectangle has 2 lines of symmetry.
- An equilateral triangle has 3 lines of symmetry.
- A circle has infinitely many lines of symmetry.
🎯 Try It: What is the measurement of a right angle?
📏 14. Perimeter Formulas
Perimeter is the total distance around the boundary of a closed shape.
Perimeter = 4 × 8 = 32 cm.
Perimeter = 2 × (10 + 5) = 30 cm.
Perimeter = 5 + 6 + 7 = 18 cm.
🎯 Try It: A square has a side of 9 cm. Find its perimeter.
🟦 15. Area Formulas
Area is the amount of surface covered by a flat shape.
Area = 8 × 4 = 32 cm².
Area = 6 × 6 = 36 cm².
🎯 Try It: A rectangle is 9 cm long and 4 cm wide. Find its area.
Area formulas may extend beyond the exact topics in some Class 5 textbook editions.
↑ Back to contents📦 16. Volume: Basic Concept
Volume tells us how much space a three-dimensional object occupies.
Volume = 4 × 3 × 2 = 24 cm³.
Volume may be introduced in later classes depending on the syllabus.
↑ Back to contents🔢 17. Patterns and Number Sequences
Count by 5: 5, 10, 15, 20, 25, ...
Count backwards by 10: 100, 90, 80, 70, ...
Double each time: 2, 4, 8, 16, 32, ...
Example: 125, 150, 175, 200, __
🎯 Reveal the next number
🏛️ 18. Roman Numerals
| Roman Numeral | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
II = 2
IV = 4
IX = 9
XII = 12
XX = 20
XL = 40
🎯 Try It: What number is represented by XIV?
⭐ 19. All Important Class 5 Maths Formulas
| Topic | Formula or Rule |
|---|---|
| Place Value | Digit × Value of Its Place |
| Expanded Form | Sum of Place Values |
| Successor | Number + 1 |
| Predecessor | Number − 1 |
| Addition | Addend + Addend = Sum |
| Subtraction | Minuend − Subtrahend = Difference |
| Checking Subtraction | Difference + Subtrahend = Minuend |
| Multiplication | Groups × Objects per Group |
| Division | Dividend ÷ Divisor = Quotient |
| Division with Remainder | Dividend = Divisor × Quotient + Remainder |
| Fraction of a Quantity | Quantity ÷ Denominator for a Unit Fraction |
| Equivalent Fractions | Multiply or Divide Both Terms by the Same Non-Zero Number |
| Percentage | (Part ÷ Whole) × 100 |
| Length | 1 m = 100 cm |
| Distance | 1 km = 1,000 m |
| Weight | 1 kg = 1,000 g |
| Capacity | 1 L = 1,000 mL |
| Time | 1 hour = 60 minutes |
| Money | ₹1 = 100 paise |
| Change | Money Paid − Cost |
| Square Perimeter | 4 × Side |
| Rectangle Perimeter | 2 × (Length + Breadth) |
| Triangle Perimeter | Sum of All Three Sides |
| Square Area | Side × Side |
| Rectangle Area | Length × Breadth |
| Cuboid Volume | Length × Breadth × Height |
📝 20. Class 5 Maths Practice Questions
Try these questions before revealing the answers. Challenge yourself to solve them without help!
- Write 8,45,672 in expanded form.
- Find the place value of 6 in 3,46,215.
- Calculate 45,678 + 23,456.
- Calculate 80,000 − 35,675.
- Calculate 345 × 24.
- Calculate 1,728 ÷ 12.
- Find the HCF of 12 and 18.
- Find the LCM of 4 and 6.
- Simplify 6/12.
- Calculate 2/7 + 3/7.
- Calculate 3/4 − 1/4.
- Calculate 12.50 + 3.25.
- Convert 7 metres into centimetres.
- Convert 6 kilograms into grams.
- How many minutes are there in 5 hours?
- A book costs ₹375. You pay ₹500. Find the change.
- A square has a side of 9 cm. Find its perimeter.
- A rectangle is 12 cm long and 5 cm wide. Find its perimeter.
- A rectangle is 8 cm long and 4 cm wide. Find its area.
- Find 25% of 80.
- Find the volume of a cuboid measuring 5 cm × 3 cm × 2 cm.
- Complete: 150, 175, 200, 225, __.
🏆 Click Here to Reveal All 22 Answers
- 8,00,000 + 40,000 + 5,000 + 600 + 70 + 2
- 6,000
- 69,134
- 44,325
- 8,280
- 144
- 6
- 12
- 1/2
- 5/7
- 2/4 = 1/2
- 15.75
- 700 cm
- 6,000 g
- 300 minutes
- ₹125
- 36 cm
- 34 cm
- 32 cm²
- 20
- 30 cm³
- 250
❓ Frequently Asked Questions (FAQ)
1. What are the most important Class 5 Maths formulas?
2. Where can I find all Class 5 Maths formulas in one place?
3. What is the formula for finding the perimeter of a square?
4. What is the formula for the area of a rectangle?
5. How do I find a fraction of a number?
6. How many centimetres are there in one metre?
7. How many grams are there in one kilogram?
8. How can children learn Class 5 Maths formulas easily?
9. Are all these formulas included in every NCERT Class 5 Maths textbook?
10. Is this Class 5 Maths formula article suitable for revision?
🎉 Conclusion
Congratulations, little mathematicians! 🌟 You have explored important Class 5 Maths formulas, rules, examples and practice questions.
Remember: understand the idea, practise regularly and learn from your mistakes. Mathematics becomes easier when you take one step at a time.
📚 Maths Wallah
Learn • Practise • Improve
By BK Pawar
Educational note: This is an NCERT-level revision resource, not a verbatim reproduction of an NCERT textbook. The exact topics and depth may vary by textbook edition and school syllabus.
