Answer

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**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

$A \times \left( {B \pm c} \right) = {\rm A} \times B \pm A \times C$.

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