Question by Lê Quốc Trần Anh - Discuss with MathYouLike

Lê Quốc Trần Anh Coordinator

21/11/2017 at 13:57

What is the result when Ellen starts with the integer 123,456 and performs the following sequence of operations: subtract 6, divide by 10, subtract 5, divide by 10, subtract 4, divide by 10, subtract 3, divide by 10, subtract 2, divide by 10?

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Dao Trong Luan Coordinator 21/11/2017 at 17:59

123,456 is a integer. The answer must be:

\(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{123456-6}{10}-5}{10}-4}{10}-3}{10}-2}{10}=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{123450}{10}-5}{10}-4}{10}-3}{10}-2}{10}\)\(=\dfrac{\dfrac{\dfrac{\dfrac{12345-5}{10}-4}{10}-3}{10}-2}{10}=\dfrac{\dfrac{\dfrac{\dfrac{12340}{10}-4}{10}-3}{10}-2}{10}=\dfrac{\dfrac{\dfrac{1234-4}{10}-3}{10}-2}{10}=\dfrac{\dfrac{\dfrac{1230}{10}-3}{10}-2}{10}=\dfrac{\dfrac{123-3}{10}-2}{10}=\dfrac{\dfrac{120}{10}-2}{10}=\dfrac{12-2}{10}=\dfrac{10}{10}=1\)
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Nguyễn Hưng Phát 21/11/2017 at 17:26

Answer:\(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{123,456-6}{10}-5}{10}-4}{10}-3}{10}-2}{10}\)

=\(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{7341}{625}-5}{10}-4}{10}-3}{10}-2}{10}\)=\(\dfrac{\dfrac{\dfrac{\dfrac{2108}{3125}-4}{10}-3}{10}-2}{10}=\dfrac{\dfrac{\dfrac{-5196}{15625}-3}{10}-2}{10}\)

\(=\dfrac{-0,3332544-2}{10}=-0,223332544\)

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