Question

the remainder on dividing given integers 'a' and 'b' by 7 are respectively 5 and 4. what is the remainder when 'ab' is divided by 7?​

Answer 1

Answer:

The basic identity of a division is :

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

So, A = 7p + 3 and B = 7q + 5

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

Clearly, A - B = 7p + 3 - 7q - 5 = 7(p - q) - 2

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 -2.

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) - 2

i.e. A - B = 7(p - q - 1) + 7 - 2

Hence, A - B = 7(p - q - 1) + 5

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 5

Step-by-step explanation:

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