NCERT Class 6 Solutions: Whole Numbers (Chapter 2) Exercise 2.3–Part 2

Q-4 Find using distributive property:

  1. Equation

  2. Equation

  3. Equation

  4. Equation

  5. Equation

Solution:

Equality of terms in distributive property

Understanding the Distributive Property

Equality of terms in distributive property

  1. Equation

    Equation

    Equation

    Equation

    Equation

  2. Equation

    Equation

    Equation

    Equation

    Equation

  3. Equation

    Equation

    Equation

    Equation

    Equation

    Equation

  4. Equation

    Equation

    Equation

    Equation

    Equation

  5. Equation

    Equation

    Equation

    Equation

    Equation

Q-5 Study the pattern:

Given the pattern
Given the pattern and find the next two steps

Equation

Equation

Equation

Equation

Equation

Write the next two steps. Can you say how the pattern works?

Solution:

The pattern works in such a way that in each step the digit added to the least significant digit is one less than previous digit. Therefore we can write the numbers as follows:

  • Equation

  • Equation

Let’s understand why such a pattern emerges with an example:

  • Equation , this is true for all numbers so we can generalize it Equation

  • Now subtract 1234 from our example we get, or number Equation . Applying the distributive property we get Equation . In general Equation

  • Now subtract 1234 again, we will get Equation . Now we can rewrite, 11110 – 1234 = (10000 + 1000 + 100 + 10) – (1000 + 200 + 30 + 4).

    Again using the distributive property we can write,

    Equation ,

    which we know would be Equation

    = Equation = 9000 + 800 + 70 + 6=9876. Therefore, Equation generalizing this argument we can write, Equation .

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