Find using distributive property:
(a) $ 728 \times 101 $
(b) $5437 \times 1001$
(c) $824 \times 25$
(d) $4275 \times 125$
(e) $504 \times 35$

To do:

We have to find the values of the given expressions by using distributive property.

Solution:

Distributive property of multiplication over addition can be written as:

$a\times (b+c) = a\times b + a\times c$

(a) 101 can be written as $100+1$.

Therefore,

$728 \times 101 =728 \times (100+1)$

$= 728\times100 + 728\times1$

$= 72800 + 728$

$=73528$

So, the value of $728 \times101$ is $73528$ .

(b) 1001 can be written as $1000+1$.

Therefore,

$5437 \times 1001 =5437 \times (1000+1)$

$= 5437\times1000 + 5437\times1$

$= 5437000 + 5437$

$=5442437$

So, the value of $5437 \times1001$ is $5442437$ . 

(c) 824 can be written as $800+24=800+(25-1)$.

Therefore,

$824 \times 25 =[800+(25-1)] \times 25$

$= 800\times25 + 25\times25-1\times25$

$= 20000 + 625-25$

$=20600$

So, the value of $824 \times25$ is $20600$ . 

(d) 4275 can be written as $4000+200+75=4000+200+(100-25)=4000+300-25$.

Therefore,

$4275 \times 125 =(4000+300-25) \times 125$

$= 4000\times125 + 300\times125-25\times125$

$= 500000 + 37500-3125$

$=534375$

So, the value of $4275 \times125$ is $534375$ . 

(e) 504 can be written as $500+4$.

Therefore,

$504 \times 35 =(500+4) \times 35$

$= 500\times35 + 4\times35$

$= 17500 + 140$

$=17640$

So, the value of $504 \times35$ is $17640$ . 

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Updated on: 10-Oct-2022

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