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Find the product of the given number by suitable rearrangement.
$125 \times 40 \times 8 \times 25$

Answer
VerifiedVerified
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Hint: For solving such type of questions, it will be easier if somehow we make a pair whose product will be multiple of \[10,100,1000, - - - \] OR we can start with multiplying two terms which gives \[0\] which simplifies further calculations.

Given that $125 \times 40 \times 8 \times 25$
First we will make the pair and proceed further
\[
   = 125 \times 40 \times 8 \times 25 \\
   = \left( {125 \times 8} \right) \times \left( {40 \times 25} \right) \\
 \]
Now simplifying the terms inside each bracket by breaking in parts
\[
   = \left( {125 \times \left( {4 \times 2} \right)} \right) \times \left( {\left( {10 \times 4} \right) \times 25} \right)\left[ {\because 8 = 4 \times 2\& 40 = 10 \times 4} \right] \\
   = \left( {\left( {125 \times 4} \right) \times 2} \right) \times \left( {10 \times \left( {4 \times 25} \right)} \right)\left[ {\because \left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)} \right] \\
   = \left( {\left( {500} \right) \times 2} \right) \times \left( {10 \times \left( {100} \right)} \right) \\
   = \left( {1000} \right) \times \left( {1000} \right) \\
   = 1000000 \\
 \]
Hence, the product of the given number is $1000000$

Note: The following question can also be solved by continuous multiplication of each number step by step. But that process will take a lot of time and will be difficult. In order to solve such types of questions containing large calculations, always try to make some pair in order to fetch some numbers in the multiple of 10. That makes the calculation easier.