Question

Find using distributive property \[504\times 35\] .

Answer 1

Hint: Questions like these are very common to see and these types are quite straightforward and simple to solve. We need to have some basic idea of number systems as well as distributive property and how to apply them in our problem. The first thing that we need to do when we have multiplications of two large numbers is to break the two numbers in such a way that one part is a multiple of \[10\] . This is done because multiples of \[10\] are quite easy to multiply with any other number.

Complete step by step solution:
Now we start off with the solution to the given problem by breaking both the numbers in multiples of \[10\] . We do it as,
\[\left( 500+4 \right)\times \left( 30+5 \right)\]
Now here we apply the distributive property and then simplify the problem by removing the brackets. We do it as,
\[=\left( 500\times 30 \right)+\left( 500\times 5 \right)+\left( 4\times 30 \right)+\left( 4\times 5 \right)\]
Now our problem is almost done. We simply need to multiply the required parts and then add them individually to find out our required answer. We first multiply the parts inside the bracket to get,
\[=15000+2500+120+20\]
Now we need to add them up to find the desired answer,
\[\begin{align}
  & =15000+2500+120+20 \\
 & =17640 \\
\end{align}\]
So our required answer to the problem is \[17640\] .

Note: Such problems require a thorough understanding of distributive property as well as its implications. However if the question wouldn’t have been bound to distributive property, then we could have done a simple multiplication of the two numbers to find out the answer to the problem. Distributive theorem is very helpful especially in algebra as well as when we are given multiplications of very large numbers which may consume a lot of time.