8. Finding remainder without long division

When divided by 8, the number 754 leaves a remainder of 2, and 5463 leaves a remainder of 7. Without calculating, can you say what remainders the following expressions will leave when divided by 8? Show the solution algebraically.

 

(i) \(5463 + 754\)

 

(ii) \(5463 - 754\)

 

Ans:

 

Let $5463=8p+i$ and $754=8q+i$

 

(i) \(5463 + 754\) \(=\) $8\left(i+q+i\right)+i$

 

Remainder \(=\) $i$