6TH - MATHS - NUMBERS - BASIC CONCEPTS

Class 6 Mathematics

Complete Number Concepts – Part 1
Concepts 1–48 • Explanations • Worked examples • Revision
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How to study: Read each definition, follow the worked example, then solve the revision questions at the end.

Unit 1 – Fundamentals of Numbers

1. Meaning of Numbers

A number is used to count, measure, compare or identify quantities. Examples: 5 books, 12 students, ₹250 and 365 days.

2. Numerals and Number Names

A numeral is the symbol used to write a number; a number name writes it in words.

Numeral	Number name
7	Seven
25	Twenty-five
108	One hundred and eight
1,250	One thousand two hundred and fifty

3. Digits and Face Values

The ten digits are 0 to 9. Face value is the digit itself, whatever its position. In 5,482, the face values are 5, 4, 8 and 2.

4. Place Value

Place value depends on position. In 6,483: 6 = 6,000; 4 = 400; 8 = 80; 3 = 3. Thus 6,483 = 6,000 + 400 + 80 + 3.

5. Place Value Chart

For 4,56,782:

Lakhs	Ten thousands	Thousands	Hundreds	Tens	Ones
4	5	6	7	8	2

Read: four lakh fifty-six thousand seven hundred and eighty-two.

6. Expanded Form

73,526 = 70,000 + 3,000 + 500 + 20 + 64,08,215 = 4,00,000 + 8,000 + 200 + 10 + 5Expanded form adds the place values; zero contributes no value.

7. Standard Form

Write the number in usual numeral form. Example: 50,000 + 6,000 + 300 + 20 + 4 = 56,324.

8. Forming Numbers from Given Digits

Using 3, 5, 7, 9 without repetition, examples include 3,579 and 9,753. Each digit is used once.

9. Greatest Number

Arrange digits from greatest to smallest. Digits 2, 5, 7, 9 → 9,752.

10. Smallest Number

Arrange digits from smallest to greatest. Digits 2, 5, 7, 9 → 2,579.

Zero cannot be the first digit of a multi-digit number. From 0, 2, 4, 6, the smallest four-digit number is 2,046.

11. With and Without Repetition

Without repetition, a digit is used once: 123 from 1, 2, 3. With repetition, digits may repeat: 112.

12. Successor

The number immediately after a number. Successor = n + 1Example: successor of 999 = 1,000.

13. Predecessor

The number immediately before a number. Predecessor = n − 1Example: predecessor of 1,000 = 999.

14. Number Patterns

A pattern follows a rule: 2, 4, 6, 8 → next 10 (add 2); 5, 10, 20, 40 → next 80 (multiply by 2); 1, 4, 9, 16, 25 → next 36 (square numbers).

Unit 2 – Large Numbers

15. Five-Digit Numbers

Range: 10,000 to 99,999. Smallest = 10,000; greatest = 99,999.

16. Six-Digit Numbers

Indian system range: 1,00,000 to 9,99,999. Example: 5,67,890.

17. Seven-Digit Numbers

Range: 10,00,000 to 99,99,999. Example: 12,34,567.

18. Eight-Digit Numbers

Range: 1,00,00,000 to 9,99,99,999. Example: 4,25,67,890 = four crore twenty-five lakh sixty-seven thousand eight hundred and ninety.

19. Indian Place Value System

Place	Value
Ones	1
Tens	10
Hundreds	100
Thousands	1,000
Ten thousands	10,000
Lakhs	1,00,000
Ten lakhs	10,00,000
Crores	1,00,00,000

12,34,567 = twelve lakh thirty-four thousand five hundred and sixty-seven.

20. International Place Value System

Digits are grouped in threes from the right: thousands 1,000; hundred thousands 100,000; millions 1,000,000; ten millions 10,000,000. 1,234,567 is one million two hundred thirty-four thousand five hundred sixty-seven.

21. Reading Large Numbers

7,45,32,186 is read as seven crore forty-five lakh thirty-two thousand one hundred and eighty-six.

22. Writing Large Numbers in Words

3,08,015 = three lakh eight thousand and fifteen. “Forty-five lakh twenty thousand six hundred” = 45,20,600.

23. Commas in Numbers

Indian: 12345678 → 1,23,45,678. International: 12345678 → 12,345,678. Indian grouping: first 3 digits from right, then groups of 2; International: groups of 3.

24. Ones, Tens and Hundreds

In 583: 5 hundreds = 500, 8 tens = 80, 3 ones = 3. So 583 = 500 + 80 + 3.

25. Thousands and Ten Thousands

In 46,725: 4 ten-thousands = 40,000; 6 thousands = 6,000; 7 hundreds = 700; 2 tens = 20; 5 ones = 5.

26. Lakhs and Ten Lakhs

In 35,42,000: 3 ten-lakhs = 30,00,000; 5 lakhs = 5,00,000; 4 ten-thousands = 40,000; 2 thousands = 2,000.

27. Crores and Ten Crores

6,25,00,000 = six crore twenty-five lakh. The place value of 6 is 6,00,00,000.

28. Indian and International Systems

Indian	International
1,00,000 (one lakh)	100,000 (one hundred thousand)
10,00,000 (ten lakh)	1,000,000 (one million)
1,00,00,000 (one crore)	10,000,000 (ten million)

Unit 3 – Comparison and Ordering

29. Comparing Two Numbers

First compare digit count; more digits means a greater number. Example: 12,345 > 8,765. If digit counts match, compare from the leftmost digit.

30. Greater Than (>)

The symbol > means greater than. Example: 25 > 18.

31. Less Than (<)

The symbol < means less than. Example: 12 < 20.

32. Equal To (=)

Both sides have the same value. Example: 25 + 5 = 20 + 10 = 30.

33. Ascending Order

Smallest to greatest. 45, 12, 89, 23 → 12, 23, 45, 89.

34. Descending Order

Greatest to smallest. 45, 12, 89, 23 → 89, 45, 23, 12.

35. Ordering by Place Value

Ascending order of 4,532; 4,235; 4,523 is 4,235 < 4,523 < 4,532. Compare hundreds, then tens if needed.

36. Greatest and Smallest

Among 567, 765, 657 and 576: greatest = 765; smallest = 567.

37. Real-Life Comparison

School A has 1,250 students; School B has 1,475. Difference = 1,475 − 1,250 = 225. School B has 225 more students.

Unit 4 – Four Fundamental Operations

38. Addition

Addition combines quantities. 245 + 378: ones 5 + 8 = 13 (write 3, carry 1); tens 4 + 7 + 1 = 12 (write 2, carry 1); hundreds 2 + 3 + 1 = 6. Answer: 623.

39. Subtraction

Subtraction finds a difference. 725 − 348: borrow as needed; ones 15 − 8 = 7; tens 11 − 4 = 7; hundreds 6 − 3 = 3. Answer: 377.

40. Multiplication

Multiplication is repeated addition. 24 × 3 = 24 + 24 + 24 = 72.

41. Division

Division shares equally or makes equal groups. 48 ÷ 6 = 8. Dividend 48, divisor 6, quotient 8, remainder 0.

42. Addition Word Problem

A library has 1,250 Tamil books and 1,875 English books. Total = 1,250 + 1,875 = 3,125 books.

43. Subtraction Word Problem

A shop had 5,000 notebooks and sold 2,375. Remaining = 5,000 − 2,375 = 2,625 notebooks.

44. Multiplication Word Problem

One box holds 24 pencils. For 35 boxes: 24 × 35 = 24 × (30 + 5) = 720 + 120 = 840 pencils.

45. Division Word Problem

360 notebooks are shared equally among 12 students. 360 ÷ 12 = 30 notebooks each.

46. Combined Operations

Use the correct order of operations. 20 + 5 × 4: multiply first, so 20 + 20 = 40.

47. Missing-Number Problems

25 + □ = 60 → □ = 60 − 25 = 358 × □ = 72 → □ = 72 ÷ 8 = 9Use the inverse operation to find the missing value.

48. Verification of Operations

Check addition with subtraction: 245 + 378 = 623; 623 − 378 = 245. For division: Dividend = Divisor × Quotient + RemainderExample: 47 ÷ 5 = 9 remainder 2; check 5 × 9 + 2 = 47.

Quick Revision – Try These

1. Write 58,306 in expanded form.
2. Find the successor of 99,999.
3. Arrange 3,450; 3,405; 3,540 in ascending order.
4. Calculate 125 × 8.
5. Find the missing number: 7 × □ = 91.

Tap to show answers

1. 50,000 + 8,000 + 300 + 6
2. 1,00,000
3. 3,405; 3,450; 3,540
4. 1,000
5. 13

End of Part 1 – Concepts 1 to 48
Next: Properties, BODMAS, Estimation, Even/Odd, Factors, Multiples, Divisibility, Primes, HCF, LCM, Fractions and Integers.