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\(1,\frac{2}{3}+\frac{4}{9}+\frac{1}{5}+\frac{2}{15}+\frac{3}{2}-\frac{17}{18}\)
\(< =>\frac{4}{9}+\frac{3}{2}+\left(\frac{2}{3}+\frac{1}{5}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{8}{18}+\frac{27}{18}+\left(\frac{10}{15}+\frac{3}{15}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{35}{18}+1-\frac{17}{18}\)
\(< =>\frac{53}{18}-\frac{17}{18}\)
\(< =>2\)
\(2,\frac{13}{28}\cdot\frac{5}{12}-\frac{5}{28}\cdot\frac{1}{12}\)
\(< =>\left(\frac{13}{28}-\frac{5}{28}\right)\cdot\left(\frac{5}{12}-\frac{1}{12}\right)\)
\(< =>\frac{2}{7}\cdot\frac{1}{3}\)
\(< =>\frac{2}{21}\)
\(3,\frac{19}{4}\cdot\frac{15}{23}-\frac{15}{4}\cdot\frac{7}{23}+\frac{15}{4}\cdot\frac{11}{23}\)
\(< =>\frac{285}{92}-\frac{105}{92}+\frac{165}{92}\)
\(< =>\frac{15}{4}\)
\(\dfrac{8}{9}\) : ( 2 - 3 \(\times\) y) = \(\dfrac{5}{3}\)
2 - 3 \(\times\) y = \(\dfrac{8}{9}\) : \(\dfrac{5}{3}\)
2 - 3 \(\times\) y = \(\dfrac{8}{15}\)
3 \(\times\) y = 2 - \(\dfrac{8}{15}\)
3 \(\times\) y = \(\dfrac{22}{15}\)
y = \(\dfrac{22}{15}\) : 3
y = \(\dfrac{22}{45}\)
b: =>x(8-7)=-33
=>x=-33
c: =>-12x+60+21-7x=5
=>-19x=-76
hay x=4
d: =>-2x-2-x+5+2x=0
=>3-x=0
hay x=3
a, 48.84
= (22)8.(23)4
= 216.212
= 228
b, 415.515
= (4.5)15
= 2015
c, 210.15 + 210.85
= 210.(15 + 85)
= 210.100
=210.(2.5)2
= 212.52
d, 33.92
= 33 . (32)2
= 33.34
= 37
e, 512.7 - 511.10
= 511.(5.7 - 10)
= 511.25
=511.52
=513
f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)
= \(x^{1+2+3+...+100}\)
= \(x^{\left(1+100\right).100:2}\)
= \(x^{5050}\)
a: x*3/4=1/5
=>x=1/5:3/4=1/5*4/3=4/15
b: x*3/7=2/5
=>x=2/5:3/7=2/5*7/3=14/15
c: 1/3+2/9=2/12x
=>1/6x=3/9+2/9=5/9
=>x=5/9*6=30/9=10/3
d: 4/15*x-2/3=1/5
=>4/15*x=2/3+1/5=10/15+3/15=13/15
=>4x=13
=>x=13/4
e: x:1/7=2/3
=>x=2/3*1/7=2/21
f: 1/9:x=7/3
=>x=1/9:7/3=1/9*3/7=3/63=1/21
j: 1/4+5/12=8/3:x
=>8/3:x=3/12+5/12=8/12=2/3
=>x=4
h: =>7/4:x=1/5+1/2=7/10
=>x=7/4:7/10=10/4=5/2
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1) \(\frac{4}{5}.x=\frac{8}{35}\Rightarrow x=\frac{8}{25}:\frac{4}{5}\Rightarrow x=\frac{2}{5}\)
\(\frac{2}{3}.x+\frac{1}{4}=\frac{7}{12}\Rightarrow\frac{2}{3}.x=\frac{7}{12}-\frac{1}{4}\)
\(\Rightarrow\frac{2}{3}.x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{3}:\frac{2}{3}\)
\(x=\frac{1}{2}\)
\(\frac{x}{10}=\frac{3}{10}\Rightarrow x=\frac{10.3}{10}\Rightarrow x=3\)
a) Ta có: \(\frac{-6}{12}< \frac{x}{12}< \frac{-4}{12}\Rightarrow-6< x< -4\Rightarrow x=-5\)
b) \(\frac{-6}{5}+\frac{13}{15}< \frac{x}{15}< \frac{-2}{5}+\frac{1}{3}\)
\(\Rightarrow\frac{-1}{3}< \frac{x}{15}< \frac{-1}{15}\)
\(\Rightarrow\frac{-5}{15}< \frac{x}{15}< \frac{-1}{15}\)
\(\Rightarrow-5< x< -1\)
\(\Rightarrow x=\left\{-4;-3;-2\right\}\)
Ta có :1.2+2.4+3.6+4.8+5.10/3.4+6.8+9.12+12.16+15.20=[1.2(1+4+9+...+25)]/[3.4(1+4+9+16)]
=(1.2)/(3.4)=2/12=1/6
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\(\left[4.\left(2x-5\right)+12\right]:2=15\\ \Rightarrow4.\left(2x-5\right)+12=30\\ \Rightarrow4.\left(2x-5\right)=18\\ \Rightarrow2x-5=\dfrac{18}{4}\\ \Rightarrow2x=\dfrac{19}{2}\\ \Rightarrow x=\dfrac{19}{4}.\)
[4.(2.\(x\) -5) + 12]:2 = 15
4.(2\(x\) - 5) + 12 = 30
8\(x\) - 20 = 30 - 12
8\(x\) = 18
8\(x\) = 38
\(x\) = \(\dfrac{19}{4}\)