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

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Q-4 Find using distributive property:

Solution:

Equality of terms in distributive property

Understanding the Distributive Property

Equality of terms in distributive property

Q-5 Study the pattern:

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

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:

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

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

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

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

    Again using the distributive property we can write,

    ,

    which we know would be

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