Bài 10: Phép nhân phân số

b: \(\Leftrightarrow1-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{34}+...+\dfrac{1}{89}-\dfrac{1}{100}+x=\dfrac{5}{3}\)

=>x+99/100=5/3

=>x=5/3-99/100=203/300

c: \(\Leftrightarrow\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)-x+4+\dfrac{221}{231}=\dfrac{7}{3}\)

\(\Leftrightarrow\dfrac{10}{231}-x+4+\dfrac{221}{231}=\dfrac{7}{3}\)

=>5-x=7/3

hay x=8/3

\(a.-\dfrac{1}{5}.\dfrac{1}{2}\)

\(=\dfrac{-1.1}{5.2}\)

\(=\dfrac{-1}{10}.\)

\(b.-\dfrac{1}{8}.\dfrac{8}{9}\)

\(=\dfrac{-1.8}{8.9}\)

\(=\dfrac{-1}{9}.\)

\(c.-\dfrac{3}{7}.\dfrac{14}{15}\)

\(=\dfrac{-3.14}{7.15}\)

\(=\dfrac{-3.7.2}{7.3.5}\)

\(=\dfrac{-2}{5}.\)

\(d.-\dfrac{7}{5}.\dfrac{15}{21}\)

\(=\dfrac{-7.15}{5.21}\)

\(=\dfrac{-7.5.3}{5.7.3}\)

\(=-1.\)

\(e.-4.\dfrac{7}{24}\)

\(=\dfrac{-4.7}{24}\)

\(=\dfrac{-4.7}{4.6}\)

\(=\dfrac{-7}{6}.\)

\(f.-\dfrac{9}{13}.\dfrac{5}{18}\)

\(=\dfrac{-9.5}{13.18}\)

\(=\dfrac{-9.5}{13.9.2}\)

\(=\dfrac{-1.5}{13.2}\)

\(=\dfrac{-5}{26}.\)

Gọi hai số cần tìm là a,b

Theo đề, ta có: a+b=2 và ab=3

Do đó: a,b là hai nghiệm của phương trình \(x^2-2x+3=0\)

hay \(\left(a,b\right)\in\varnothing\)

Vì \(\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{a}{b}\cdot\dfrac{c}{d}\)

\(\Rightarrow\dfrac{ad-bc}{bd}=\dfrac{ac}{bd}\)

\(\Rightarrow ad-bc=ac\)

\(\Rightarrow ad=ac+bc\)

\(\Rightarrow ad=c\left(a+b\right)\)

\(\Rightarrow\dfrac{c}{d}=\dfrac{a}{a+b}\)

a/ \(\left|x+1\right|-5=0\)

\(\Leftrightarrow\left|x+1\right|=5\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=5\\x+1=-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-6\end{matrix}\right.\)

Vậy ..

b/ \(\dfrac{x}{3}=\dfrac{6}{-9}\)

\(\Leftrightarrow\dfrac{x}{3}=\dfrac{-2}{3}\)

\(\Leftrightarrow x=-2\)

Vậy ..

a) A \(=\dfrac{5}{x+2}\) là phân số \(\Leftrightarrow x+2\in Z\Leftrightarrow x\in Z\)

Vậy để A là phân số : x\(\in\) Z

b) A = \(\dfrac{-1}{2}\)\(\Leftrightarrow\dfrac{5}{x+2}=\dfrac{-1}{2}\)

\(\Leftrightarrow2.5=-1\left(x+2\right)\)

\(\Leftrightarrow10=-x-2\)

\(\Leftrightarrow10+2=-x\)

\(\Leftrightarrow12=-x\)

\(\Leftrightarrow x=-12\)

Vậy để \(A=\dfrac{-1}{2}\)thì x = -12

c) \(A\in Z\Leftrightarrow\dfrac{5}{x+2}\in Z\)

\(\Leftrightarrow x+2\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\Leftrightarrow x\in\left\{-7;-3;-1;3\right\}\)

Vậy để A là số nguyên thì \(x\in\left\{-7;-3;-1;3\right\}\)

a, Ta có :

\(\dfrac{1}{6}< \dfrac{1}{5}\)

\(\dfrac{1}{7}< \dfrac{1}{5}\)

.................

\(\dfrac{1}{9}< \dfrac{1}{5}\)

\(\dfrac{1}{10}=\dfrac{1}{10}\)

\(\dfrac{1}{11}< \dfrac{1}{10}\)

..................

\(\dfrac{1}{17}< \dfrac{1}{10}\)

\(\Leftrightarrow\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+......+\dfrac{1}{17}< \dfrac{1}{5}+\dfrac{1}{5}+....+\dfrac{1}{5}\)

\(\Leftrightarrow A< \dfrac{1}{5}.5+\dfrac{1}{10}.8\)

\(\Leftrightarrow A< 1+\dfrac{4}{5}=\dfrac{9}{5}< 2\)

\(\Leftrightarrow A< 2\left(đpcm\right)\)

b/ Ta có :

\(\dfrac{1}{11}>\dfrac{1}{30}\)

\(\dfrac{1}{12}>\dfrac{1}{30}\)

...............

\(\dfrac{1}{29}>\dfrac{1}{30}\)

\(\dfrac{1}{30}=\dfrac{1}{30}\)

\(\Leftrightarrow\dfrac{1}{11}+\dfrac{1}{12}+........+\dfrac{1}{30}>\dfrac{1}{30}+\dfrac{1}{30}+.......+\dfrac{1}{30}\)

\(\Leftrightarrow B>\dfrac{1}{30}.20=\dfrac{2}{3}\)

\(\Leftrightarrow B>\dfrac{2}{3}\left(đpcm\right)\)

ta có thể chuyển mẫu âm thành mẫu dương bằng cách nhân cả tử và mẫu với -1(tính nhẩm)

nếu phân số chưa tối giản ta có thể rút gọn để dễ thực hiện

chúc bạn học tốt!