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.
4779 + 661
The remainder when (4779 + 661) is divided by 7 is 1. Algebraically: Remainder of 4779 + Remainder of 661 = 5 + 3 = 8. Since 8 > 7, the actual remainder is 8 - 7 = 1.
4779 - 661
The remainder when (4779 - 661) is divided by 7 is 2. Algebraically: Remainder of 4779 - Remainder of 661 = 5 - 3 = 2.
Explanation
(i) The chapter shows that when adding two numbers, the remainder of the sum equals the sum of remainders (modulo the divisor). 4779 = + 5 and 661 = + 3. So 4779 + 661 leaves remainder 5 + 3 = 8, which is equivalent to remainder 1 when divided by 7. (ii) The chapter demonstrates that when subtracting, the remainder of the difference equals the difference of remainders (when positive). 4779 - 661 leaves remainder 5 - 3 = 2 when divided by 7.