When divided by 7, the number 661 leaves a remainder of 3, and 4779 leaves a remainder of 5. Without calculating Class 8

When divided by 7, the number 661 leaves a remainder of 3, and 4779 leaves a remainder of 5. Without calculating Class 8

Question 1.

When divided by 7, the number 661 leaves a remainder of 3, and 4779 leaves a remainder of 5. Without calculating, can you say what remainders the following expressions will leave when divided by 7? Show the solution both algebraically and visually. Class 8

(i) 4779 + 661

(ii) 4779 - 661

Solution:

(i) Remainder 1. (5 + 3 = 8 ÷ 7 leaves remainder 1)

(ii) Remainder will be 2 (5 - 3 = 2).

Algebraically:

(i) 4779 = 7p + 5 (Given)

and 661 = 7q + 3 (Given)

So, 4779 + 661 = 7p + 5 + 7q + 3

= 7 (p + q) + 8

= 7p + 7q + 7 + 1

= 7(p + q + 1) + 1

So, remainder is 1.

(ii) 4779 - 661 = 7p + 5 - (7q + 3)

= 7p - 7q + 5 - 3

= 7(p - q) + 2

So, remainder is 2.