Đề bài:So sánh 2 p/s hữu tỉ(toán 7)
a) So sánh x=-2/3 và y=0
Ta có: \(-\dfrac{2}{3}< 0\\ =>x< y\)
b) So sánh x=2017/2018 và y=7/3
Ta có: \(\dfrac{2017}{2018}< 1\\ \dfrac{7}{6}>1\\ =>\dfrac{2017}{2018}< \dfrac{7}{6}\\ =>x< y\)
c) So sánh x=-33/37 và y=-34/35
Ta có: \(-\dfrac{33}{37}=-1+\dfrac{4}{37}\\ -\dfrac{34}{35}=-1+\dfrac{1}{35}\\ Vì:\dfrac{4}{37}>\dfrac{1}{35}\\ =>-1+\dfrac{4}{37}>-1+\dfrac{1}{35}\\ < =>-\dfrac{33}{37}>-\dfrac{34}{35}\)
d,+) Nếu \(a\le b\Rightarrow an\le bn\Rightarrow ab+an\le ab+bn\)
\(\Rightarrow a\left(b+n\right)\le b\left(a+n\right)\Rightarrow\dfrac{a}{b}\le\dfrac{a+n}{b+n}\)
+) Nếu \(a>b\Rightarrow an>bn\Rightarrow ab+an>ab+bn\)
\(\Rightarrow a.\left(b+n\right)>b.\left(a+n\right)\Rightarrow\dfrac{a}{b}>\dfrac{a+n}{b+n}\)
Vậy nếu \(a\le b\) thì \(\dfrac{a}{b}\le\dfrac{a+n}{b+n}\); nếu \(a>b\Rightarrow\dfrac{a}{b}>\dfrac{a+n}{b+n}\)