Question

the remainder on dividing gives integers a and b by 7 are respectively 5and 4 what is the remainder when ab is divided by 7...
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Answer 1

Answer:

The answer for your qn is 6

Answer 2

Answer:

Required reminder is 6.

Step-by-step explanation:

The basic identity of a division is :

Dividend (number being divided) = Divisor x Quotient + Remainder

So by given informations,

$A=7p + 4$

and

$B = 7q + 5$

Here p and q are the respective quotients (non-negative integer values).

Clearly,

$A – B \\ = 7p + 4 – 7q – 5 \\ = 7(p – q) – 1$

Now on using the basic identity of a division, this equation implies that when (A – B) is divided by 7, the quotient is (p – q) and the remainder is -1.

However, the remainder (when dividing by 7) can only be integer values from 0 to 6. This means we need to make the remainder positive!

So we rewrite the above equation as:

$A – B \\ = 7(p – q – 1 + 1) – 1$

i.e.

$A – B \\ = 7(p – q – 1) + 7 – 1$

Hence,

$A – B \\ = 7(p – q – 1) + 6$

Again using the basic identity of a division, this means that when (A – B) is divided by 7, the quotient is (p – q – 1) and the remainder is 6