Class 6 · Mathematics

NCERT Solutions: Whole Numbers (Class 6 Maths)

Properties of whole numbers, the number line, and worked practice problems for the Whole Numbers chapter in Class 6 Maths (Ganita Prakash).

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Chapter overview

Whole numbers are the set of natural numbers (1, 2, 3, …) together with zero: 0, 1, 2, 3, and so on. This chapter covers their properties on the number line and the rules that govern addition, subtraction, multiplication, and division within this set.

Key properties

  • Closure property: the sum and product of two whole numbers is always a whole number. Subtraction and division are not always closed (e.g. 3 - 5 is not a whole number).
  • Commutative property: a + b = b + a and a × b = b × a
  • Associative property: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
  • Distributive property: a × (b + c) = a × b + a × c
  • Identity elements: 0 is the additive identity (a + 0 = a); 1 is the multiplicative identity (a × 1 = a).
  • Every whole number has a successor (add 1) except none is missing one, and every whole number except 0 has a predecessor (subtract 1).

Worked practice problem 1 — Using the distributive property

Question: Use the distributive property to calculate 47 × 102 mentally.

Solution:

47 × 102 = 47 × (100 + 2)
         = 47 × 100 + 47 × 2
         = 4700 + 94
         = 4794

Answer: 47 × 102 = 4794

Worked practice problem 2 — Number line representation

Question: Represent the addition 3 + 4 on the number line.

Solution: Start at 0, move 3 units to the right to reach 3, then move 4 more units to the right. You land on 7.

Answer: 3 + 4 = 7, shown as two forward jumps on the number line ending at 7.

Worked practice problem 3 — Identifying properties

Question: Which property justifies the statement 25 × (4 + 6) = 25 × 4 + 25 × 6?

Solution: The left side multiplies a sum by 25; the right side distributes that multiplication across each term of the sum before adding. This matches the definition of the distributive property of multiplication over addition.

Answer: Distributive property.

Common mistakes to avoid

  • Assuming subtraction and division of whole numbers always give a whole number - they don’t.
  • Forgetting that 0 has no predecessor.
  • Mixing up the additive identity (0) with the multiplicative identity (1).

Looking for the official textbook PDF for this chapter? Visit our Class 6 NCERT Books page for the direct download link.