Verified Answer :

  • Start the division by analyzing the dividend 1,658 from the left.
  • Compare the leading digits to the divisor 25.
  • Identify 165 as the smallest prefix of 1,658 that is greater than or equal to 25.
  • Conclude that the division starts by dividing 25 into 165, resulting in \(\boxed{25}\) and \(\boxed{165}\).

Explanation

  1. Problem Analysis

The division process \(1658 \div 25\) involves a dividend of \(1658\) and a divisor of \(25\). In long division, we approach the dividend by examining its digits from left to right to find the smallest substring that is greater than or equal to the divisor. This allows us to start the division process effectively.

  1. Determining the First Division Step

We examine the digits of the dividend \(1658\) starting from the left:

  1. First, we look at the digit \(1\). Since \(1 < 25\), we cannot divide \(25\) into \(1\).
  2. Next, we include the second digit to form the number \(16\). Since \(16 < 25\), we still cannot divide \(25\) into \(16\).
  3. Then, we include the third digit to form the number \(165\). Since \(165 \geq 25\), we can successfully perform the first step of the division by dividing \(25\) into \(165\).
  1. Final Answer

Based on our step-by-step examination of the digits, we conclude that the division begins by dividing the divisor \(25\) into the prefix \(165\). Therefore, we fill the boxes as follows: "start by dividing \(\boxed{25}\) into \(\boxed{165}\)".

Examples

Imagine you have 1,658 stickers to distribute equally among 25 students in your class. To figure out how many each student gets, you perform long division. Starting the division by determining how many times 25 goes into the first three digits, 165, helps you begin the process systematically. Once you know 25 fits into 165, you can proceed to calculate the remainder and bring down the next digit (8) to continue the distribution until all stickers are accounted for.

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