Question

Find the product by suitable rearrangement: $2 \times 1768 \times 50$.

Answer 1

Hint: Here, we have to find the product of $2 \times 1768 \times 50$ by suitable arrangement. While arranging the term we should keep in mind that the multiplication became simple. we can easily multiply any number by a number ending with zero like $10$,$100$, $1000$. So firstly, find the product of $2$ and $50$ then their product is multiplied by $1768$ to get the required result.

Complete step-by-step answer:
Given, we have to find the product of $2 \times 1768 \times 50$.
We have to multiply $2$ and $50$ first so that we get a number ending with maximum zero.
Now, $2 \times 1768 \times 50$ can be written as $2 \times 50 \times 1768$.
$
   = 2 \times 50 \times 1768 \\
   = 100 \times 1768 \\
 $
We get a number ending with two zero, so its product becomes simple.
$ = 176800$

Thus, the product of $2 \times 1768 \times 50$ is $176800$.

Note:
This product can also be solved by using the distributive property over addition. For this method firstly, multiply $2$ and $1768$ then break the product in two parts so that one part gets maximum zero. Then apply the distributive law over addition and perform the necessary operation.
Now, $2 \times 1768 \times 50$
$ = 3536 \times 50$
Break $3536$ in to two parts as $3500$ and $36$.
$ = \left( {3500 + 36} \right) \times 50$
Using distributive law we can write,
$
   = 3500 \times 50 + 36 \times 50 \\
   = 175000 + 1800 \\
   = 176800 \\
 $
While solving the expression by rearrangement we have to use the various mathematical properties. Some of the properties are-
(1) commutative property of addition:
Suppose A and B are two numbers then $\left( {A + B} \right) = \left( {B + A} \right)$
(2) Associative property of addition:
Suppose A, B and c are three numbers then $A + \left( {B + C} \right) = \left( {A + B} \right) + C$
These two properties are also valid for the multiplication but not for the subtraction and division.
(3) Distributive property over addition or subtraction
Suppose A, B and C are three numbers then
$A \times \left( {B \pm c} \right) = {\rm A} \times B \pm A \times C$.