Show that 954 – 459 is exactly divisible by 99.

1.	Show that 954 – 459 is exactly divisible by 99.
Answer» To show : 954 – 459 is exactly divisible by 3 99, where a = 9, b = 5, c = 4 abc = 100a + 10b + c => 954 = 100 x 9 + 10 x 5 + 4 => 954 = 900 + 50 + 4 ………(i) and 459 = 100 x 4+ 10 x 5 + 9 => 459 = 400 + 50 + 9 ……..(ii) Subtracting (ii) from (i), we get 954 – 459 = 900 + 50 + 4 – 400 – 50 – 9 => 954 – 459 = 500 – 5 => 954 – 459 = 495 => 954 – 459 = 99 x 5 Hence, 954 – 459 is exactly divisible by 99 Hence proved.

Answer»

To show : 954 – 459 is exactly divisible by 3 99, where a = 9, b = 5, c = 4 abc = 100a + 10b + c

=> 954 = 100 x 9 + 10 x 5 + 4

=> 954 = 900 + 50 + 4 ………(i)

and 459 = 100 x 4+ 10 x 5 + 9

=> 459 = 400 + 50 + 9 ……..(ii)

Subtracting (ii) from (i), we get

954 – 459 = 900 + 50 + 4 – 400 – 50 – 9

=> 954 – 459 = 500 – 5

=> 954 – 459 = 495

=> 954 – 459 = 99 x 5

Hence, 954 – 459 is exactly divisible by 99

Hence proved.

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