Đề bài

Sắp xếp các số sau theo thứ tự tăng dần: a) \(3\frac{2}{{11}};2\frac{1}{{12}};\frac{{15}}{{21}};\frac{{17}}{{21}}\); b) – 5,12; 0,534; – 23; 123; 0; 0,543.

Lời giải chi tiết

a)  \(3\dfrac{2}{{11}};{\rm{ }}2\dfrac{1}{{12}};{\rm{ }}\dfrac{{15}}{{21}};{\rm{ }}\dfrac{{17}}{{21}}\).Cách 1: Ta có:Vì 15 < 17 nên \(\dfrac{{15}}{{21}}{\rm{  <  }}\dfrac{{17}}{{21}}\).\(2\dfrac{1}{{12}} = \dfrac{{25}}{{12}} = \dfrac{{175}}{{84}};{\rm{ }}\dfrac{{17}}{{21}} = \dfrac{{68}}{{84}}\). Do \(\dfrac{{175}}{{84}}{\rm{  > }}\,{\rm{ }}\dfrac{{68}}{{84}}\) nên \(2\dfrac{1}{{12}} > \dfrac{{17}}{{21}}\).\(3\dfrac{2}{{11}} = \dfrac{{35}}{{11}} = \dfrac{{420}}{{132}};{\rm{ 2}}\dfrac{1}{{12}} = \dfrac{{25}}{{12}} = \dfrac{{275}}{{132}}\)Do \(\dfrac{{420}}{{132}}{\rm{  >  }}\dfrac{{275}}{{132}}\) nên \(3\dfrac{2}{{11}}{\rm{  >  2}}\dfrac{1}{{12}}\).Suy ra: \(\dfrac{{15}}{{21}}{\rm{  <  }}\dfrac{{17}}{{21}}{\rm{  <  }}2\dfrac{1}{{12}}{\rm{  <  }}3\dfrac{2}{{11}}\).Các số theo thứ tự tăng dần: \(\dfrac{{15}}{{21}}{\rm{; }}\dfrac{{17}}{{21}}{\rm{; }}2\dfrac{1}{{12}}{\rm{; }}3\dfrac{2}{{11}}\).Cách 2:Vì 15 < 17 nên \(\dfrac{{15}}{{21}}{\rm{  <  }}\dfrac{{17}}{{21}}\).Ta có: \(\dfrac{{15}}{{21}}{\rm{  <  }}\dfrac{{17}}{{21}}<1<2\dfrac{1}{{12}}<3<3\dfrac{2}{{11}}\) Ta được: \(\dfrac{{15}}{{21}}{\rm{  <  }}\dfrac{{17}}{{21}}{\rm{  <  }}2\dfrac{1}{{12}}{\rm{  <  }}3\dfrac{2}{{11}}\).Các số theo thứ tự tăng dần: \(\dfrac{{15}}{{21}}{\rm{; }}\dfrac{{17}}{{21}}{\rm{; }}2\dfrac{1}{{12}}{\rm{; }}3\dfrac{2}{{11}}\).b) – 5,12; 0,534; – 23; 123; 0; 0,543.Ta có: \(-{\rm{ }}5,12;{\rm{ }}-23 < {\rm{ }}0{\rm{ }} < {\rm{ 0,534; 123; 0,543}}\).Do: \(-{\rm{ }}5,12{\rm{  > }}-23;{\rm{ 0,534  <  0,543  <  123}}\).Nên \(-23 <  - 5,12 < 0 < {\rm{0,534  <  0,543  < }}\,{\rm{123}}\)Các số theo thứ tự tăng dần: \(-23; - 5,12;{\rm{ }}0;{\rm{ 0,534; 0,543; 123}}\).