1/7 < ... / 17 < 2/7
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\(\dfrac{12}{17}.\dfrac{5}{7}-\left(-\dfrac{12}{17}\right).\dfrac{1}{7}+\dfrac{1}{17+7}\)
\(=\dfrac{12}{17}.\dfrac{5}{7}+\dfrac{12}{17}.\dfrac{1}{7}+\dfrac{1}{24}\)
\(=\dfrac{12}{17}\left(\dfrac{5}{7}+\dfrac{1}{7}\right)+\dfrac{1}{24}\)
\(=\dfrac{12}{17}.\dfrac{6}{7}+\dfrac{1}{24}\)
\(=\dfrac{72}{119}+\dfrac{1}{24}=\dfrac{1847}{2856}\)
a: =(5/7+2/7)+(4/3+5/3)=3+1=4
b: =(17/12+7/12)+(29/7-8/7)
=2+3=5
c: =(2/5+3/5)+(6/9+1/3)+(7/4+1/4)
=1+2+1
=4
d: =(1/3+2/3)+(13/17+4/17)+(29/11+4/11)
=1+1+3=5
Phương pháp giải:
- Tính giá trị của mỗi vế
- So sánh rồi điền dấu thích hợp vào chỗ trống.
Lời giải chi tiết:
19 + 7 < 19 + 9 17 + 7 < 17 + 9
17 + 9 = 19 + 7 37 + 15 < 55 − 1
38 − 8 = 23 + 7 28 − 3 > 17 + 6
d) Ta có: \(32\%-0.25:x=-\dfrac{17}{5}\)
\(\Leftrightarrow0.25:x=\dfrac{8}{25}+\dfrac{17}{5}=\dfrac{93}{25}\)
hay \(x=\dfrac{25}{372}\)
Vậy: \(x=\dfrac{25}{372}\)
e) Ta có: \(\left(x+\dfrac{1}{5}\right)^2+\dfrac{17}{25}=\dfrac{26}{25}\)
\(\Leftrightarrow\left(x+\dfrac{1}{5}\right)^2=\dfrac{9}{25}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{5}=\dfrac{3}{5}\\x+\dfrac{1}{5}=-\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
Vậy: \(x\in\left\{\dfrac{2}{5};-\dfrac{4}{5}\right\}\)
f) Ta có: \(-\dfrac{32}{27}-\left(3x-\dfrac{7}{9}\right)^3=-\dfrac{24}{27}\)
\(\Leftrightarrow\left(3x-\dfrac{7}{9}\right)^3=\dfrac{-8}{27}\)
\(\Leftrightarrow3x-\dfrac{7}{9}=-\dfrac{2}{3}\)
\(\Leftrightarrow3x=\dfrac{1}{9}\)
hay \(x=\dfrac{1}{27}\)
g) Ta có: \(60\%\cdot x+0.4x+x:3=2\)
\(\Leftrightarrow\dfrac{4}{3}x=2\)
hay \(x=\dfrac{3}{2}\)
Vậy: \(x=\dfrac{3}{2}\)
h) PT \(\Leftrightarrow\left|\dfrac{20}{9}-x\right|=\dfrac{2}{9}\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{20}{9}-x=\dfrac{2}{9}\\x-\dfrac{20}{9}=\dfrac{2}{9}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{22}{9}\end{matrix}\right.\)
Vậy ...
i) PT \(\Leftrightarrow\dfrac{8}{5}+\dfrac{2}{5}x=\dfrac{16}{5}\) \(\Leftrightarrow\dfrac{2}{5}x=\dfrac{8}{5}\) \(\Leftrightarrow x=4\)
Vậy ...
a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)
= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)
= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)
= 1 - 1 - \(\dfrac{11}{25}\)
= - \(\dfrac{11}{25}\)
b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)
= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))
= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)
= - \(\dfrac{499}{35}\)
\(A=\frac{2}{7}+\frac{-3}{8}+\frac{11}{7}+\frac{1}{3}+\frac{1}{7}+\frac{5}{-8}\)
\(A=\left(\frac{2}{7}+\frac{11}{7}+\frac{1}{7}\right)+\left(\frac{-3}{8}+\frac{5}{-8}\right)+\frac{1}{3}\)
\(A=2-1+\frac{1}{3}\)
\(A=\frac{4}{3}\)
\(B=\frac{3}{17}+\frac{-5}{13}+\frac{-18}{35}+\frac{14}{17}+17\)
\(B=\left(\frac{3}{17}+\frac{14}{17}\right)+\frac{-5}{13}+\frac{-18}{35}+17\)
\(B=1+\frac{-5}{13}+\frac{-18}{35}+17\)
\(B=18+\frac{-5}{13}+\frac{-18}{35}\)
\(B=\frac{7781}{455}\)
\(\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+\frac{7}{13.17}+\frac{7}{17.21}\)
\(=\frac{7}{1}-\frac{7}{5}+\frac{7}{5}-\frac{7}{9}+\frac{7}{9}-\frac{7}{13}+\frac{7}{13}-\frac{7}{17}+\frac{7}{17}-\frac{7}{21}\)
\(=7.\frac{1}{4}.\left(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+......+\frac{1}{17}-\frac{1}{21}\right)\)
\(=7.\frac{1}{4}.\left(1-\frac{1}{21}\right)\)
\(=7.\frac{1}{4}.\frac{20}{21}\)
\(=\frac{5}{3}\)
Dấu chấm là dấu x đấy nha..
\(\dfrac{1}{7}\) < \(\dfrac{◻}{17}\) < \(\dfrac{2}{7}\)
Gọi số thích hợp cần điền vào chỗ \(◻\) là \(x\) thì \(x\) là số tự nhiên.
Ta có: \(\dfrac{1}{7}\) < \(\dfrac{x}{17}\) < \(\dfrac{2}{7}\)
\(\dfrac{1\times17}{7\times17}\) < \(\dfrac{x\times7}{17\times7}\) < \(\dfrac{2\times17}{7\times17}\)
\(\dfrac{17}{119}\) < \(\dfrac{x\times7}{119}\) < \(\dfrac{34}{119}\)
17 < \(x\) \(\times\) 7 < 34
17:7 < \(x\) < 34:7
2,4 < \(x\) < 4,8
vì \(x\) là số tự nhiên nên \(x\) = 3; 4
Vậy số thích hợp điền vào chỗ \(◻\) là 3; 4