Find the smallest number to be added to 1000 so that 45 divides the sum exactly.

### Concept & Formula When finding the smallest number to add to a dividend so it is exactly divisible by a divisor, the required number is the difference between the divisor and the remainder. $$ \text{Number to add} = \text{Divisor} - \text{Remainder} $$ ### Step-by-Step Solution - **Given:** Dividend = 1000, Divisor = 45. - **Calculation / Deduction:** Divide 1000 by 45 to find the remainder. - $1000 \div 45$ gives a quotient of 22 and a remainder of 10. - The remainder 10 represents the excess above the previous multiple of 45. - To reach the next multiple of 45, we must bridge the gap between the remainder and the divisor. - Required number = $45 - 10 = 35$. ### Exam Strategy & Shortcut Execute the division quickly focusing only on the remainder. Once you see a remainder of 10, mentally subtract it from 45. There's no need to calculate the exact quotient or the final divisible number (1035) unless explicitly asked. ### Common Pitfall The most common error is selecting the remainder (10) as the answer. Subtracting 10 makes the number divisible, but the question asks what must be *added*. Always apply the divisor minus remainder logic for addition questions. ### Final Answer Therefore, the correct answer is 35.