Question

Find the product of largest 4-digit number and smallest 3-digit number.
[Hint: Use distributive law.]​

Answer 1

Answer:

Largest 4-digit number is 9999 and smallest 3-digit number is 100 and product is 10000.

Answer 2

Concept:

Distributive Law of multiplication:

Suppose we have three numbers a, b and c. Using distributive law, we have

a × (b + c) = (a×b) + (a×c)           --------------------------  (i)

Find:

The product of the largest 4-digit number and the smallest 3-digit number.

Answer:

Product of largest 4-digit number and smallest 3-digit number = 999900.

Solution:

Largest 4-digit number, L = 9999

Smallest 3-digit number, S = 100

The product of the largest 4-digit number and the smallest 3-digit number is given by,

Product = L×S

             = 100 × 9999

We can write 9999 as (9000 + 900 + 90 + 9).

∴ Product = 100 × (9000 + 900 + 90 + 9)

Using distributive law, we have

Product = (100 × 9000) + (100 × 900) + (100 × 90) + (100 × 9)

             = 900000 + 90000 + 9000 + 900

             = 999900

Hence the product of largest 4-digit number and smallest 3-digit number is 999900.

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