Find the product by suitable rearrangement:
(a) $ 2 \times 1768 \times 50 $
(b) $4 \times 166 \times 25$
(c) $8 \times 291 \times 125$
(d) $625 \times 279 \times 16$
(e) $285 \times 5 \times 60$
(f) $125 \times 40 \times 8 \times 25$

To do: 

We have to find the values of the given expressions by suitable rearrangement.

Solution:

Rearrangement is done to make calculations easy.

(a) In this case, it is difficult to calculate the product of 2 and 1768 and then again multiply that value with 50 to get the final answer.

$2\ \times\ 1768\ \times 50$

Now, we know that product of 2 and 50 is easy to calculate. So, rearranging the digits:

$=\ 1768\ \times\ (2\ \times\ 50)$

$=\ 1768\ \times \ 100$

It is easier to calculate the final value now:

$=\ \mathbf{176800}$

So, the value of the given expression is 176800. 

(b) In this case, it is difficult to calculate the product of 4 and 166 and then again multiply that value with 25 to get the final answer.

$4\ \times\ 166\ \times 25$

Now, we know that product of 4 and 25 is easy to calculate. So, rearranging the digits:

$=\ 166\ \times\ (4\ \times\ 25)$

$=\ 166\ \times \ 100$

It is easier to calculate the final value now:

$=\ \mathbf{16600}$

So, the value of the given expression is 16600. 

(c) In this case, it is difficult to calculate the product of 8 and 291 and then again multiply that value with 125 to get the final answer.

$8\ \times\ 291\ \times 125$

Now, we know that product of 8 and 125 is easy to calculate. So, rearranging the digits:

$=\ 291\ \times\ (8\ \times\ 125)$

$=\ 291\ \times \ 1000$

It is easier to calculate the final value now:

$=\ \mathbf{291000}$

So, the value of the given expression is 291000. 

(d) In this case, it is difficult to calculate the product of 625 and 279 and then again multiply that value with 16 to get the final answer.

$625\ \times\ 279\ \times 16$

Now, we know that product of 625 and 16 is easy to calculate. So, rearranging the digits:

$=\ 279\ \times\ (625\ \times\ 16)$

$=\ 279\ \times \ 10000$

It is easier to calculate the final value now:

$=\ \mathbf{2790000}$

So, the value of the given expression is 2790000. 

(e) Here, the product of 5 and 60 is easy to calculate. So:

$\ 285\ \times\ (5\ \times\ 60)$

$=\ 285\ \times \ 300$

$=85500$

So, the value of the given expression is 85500. 

(f) In this case, it is difficult to calculate the product of 125 and 40 and then again multiply that value with 8 and then with 25 to get the final answer.

\( 125 \times 40 \times 8 \times 25 \)

Now, we know that product of 125 and 8 is easy to calculate and the product of 40 and 25 is easy to calculate. So, rearranging the digits:

$=(125\times8)\times(40\times25)$

$=\ 1000\ \times \ 1000$

It is easier to calculate the final value now:

$=\ \mathbf{1000000}$

So, the value of the given expression is 1000000. 

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Updated on: 10-Oct-2022

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