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Find the value of the product by suitable rearrangement.
A) $125 \times 40 \times 8 \times 25$
B) $285 \times 5 \times 60$

Answer Verified Verified
Hint: In order to find the product, we have to use the basic property of rearrangement which involves trying your best to get the multiples of 5 and 10 because we are all aware of the ease of solving questions with the multiples of these numbers especially 10. This basic property will help you a lot in other questions too which involves bigger multiplications so it is suggested to always get the multiples of 5 and 10 to make the task easier and give suitable one suitable time. One should also know that the multiples of 10 are better to deal with in bigger calculations so always try your best to go for them.

Complete step-by-step answer:
Since, $25 \times 4$= 100 ends with 0 and,
$125 \times 8 = 1000$ also ends with 0
So, in order to find out the solution, multiply them –
$
   = {\text{ }}\left( {125 \times 8} \right) \times \left( {40 \times 25} \right) \\
   = {\text{ }}\left( {125 \times 8} \right) \times \left( {4 \times 10 \times 25} \right) \\
   = {\text{ }}\left( {125 \times 8} \right) \times \left( {4 \times 25 \times 10} \right) \\
   = {\text{ 1000}} \times \left( {100 \times 10} \right) \\
   = {\text{ 1000}} \times {\text{1000}} \\
  {\text{ = 1000000}} \\
    \\
 $
$\therefore $ The solution is 1000000
(b) For the rearrangement of $285 \times 5 \times 60$ the solution will be-
$
   = {\text{ 285}} \times {\text{300}} \\
   = {\text{ 285}} \times {\text{100}} \times {\text{3}} \\
  {\text{ = 285}} \times {\text{3}} \times {\text{100}} \\
  {\text{ = 855}} \times {\text{100}} \\
  {\text{ = 85500}} \\
 $
$\therefore $ The solution is 85500

Note: Whenever we face such type of problems, the key concept is that we have to arrange the numbers in such a way that our multiplication becomes easier and as we know that multiplication becomes easier when we get numbers in the multiples of 5 and 10 as you can see it has been done in the question that way but first we must know that there are numerous ways of arranging these numbers so, it is always feasible as well as recommended that one must go for the arrangement in such a way we get the multiples of 10. This same procedure has been used in the question above.
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