Question

Ученица нашла НОК (33,198) и получила 99. Не проверяя вычислений, учитель определил, что была допущена ошибка. Как он это сделал?

Answer 1

НОК - это делитель чисел, в данном случае 33 и 198

99 меньше, чем 198 и не может делится на него

Answer 2

Identifying the Error Without Calculating

The teacher was able to identify the error without performing the calculations. This suggests that the teacher used a method that did not involve actually computing the result.

Method Used by the Teacher

The teacher likely used a method that involves divisibility rules or other mathematical shortcuts to quickly determine if the result is correct without performing the actual calculation.

Divisibility Rules

Divisibility rules are shortcuts to determine if a number is divisible by another number without actually performing the division. For example, the rule for divisibility by 3 states that if the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3.

Application of Divisibility Rules

In this case, the teacher might have quickly checked the sum of the digits of the given number to see if it is divisible by 3, 9, or any other relevant number to verify the correctness of the result.

Conclusion

By using mathematical shortcuts such as divisibility rules, the teacher was able to identify the error without performing the actual calculations, thus determining that a mistake had been made.