Question 6 of 19intermediate🔧 ApplyNumerical4 marks
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.
(i)
4779 + 661
Answer
Remainder is 1 when 4779 + 661 is divided by 7.
(ii)
4779 - 661
Answer
Remainder is 2 when 4779 - 661 is divided by 7.
Explanation
(i) 4779 ≡ 5 (mod 7) and 661 ≡ 3 (mod 7). So 4779 + 661 ≡ 5 + 3 = 8 ≡ 1 (mod 7). The remainder is 1. (ii) 4779 ≡ 5 (mod 7) and 661 ≡ 3 (mod 7). So 4779 - 661 ≡ 5 - 3 = 2 (mod 7). The remainder is 2.