Question

When a child divided a positive integer a by 9, he obtained the quotient and remainder

as q and 13 .Is the division complete? If no, complete the division and find the actual

quotient and remainder​

Answer 1

SOLUTION

GIVEN

When a child divided a positive integer a by 9, he obtained the quotient and remainder as q and 13 .

TO CHECK

Is the division complete? If no, complete the division and find the actual quotient and remainder

EVALUATION

By division algorithm if we divide number a by the number b where quotient is q and remainder is r then

a = bq + r

Where

$\sf{0 \leqslant r < b}$

Here it is given that when a child divided a positive integer a by 9, he obtained the quotient and remainder as q and 13

Thus a = 9q + 13

So b = 9 , r = 13

Since 13 > 9

So it contradicts Division algorithm property

Hence the division is incomplete

Again a = 9q + 13

Which can be rewritten as

$\sf{ a = 9q+9+4}$

$\sf{ \implies \: a = 9(q+1)+4}$

Actual quotient = q + 1 and remainder = 4

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