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1) A = \(\frac{-15}{19}.\frac{23}{37}+\frac{14}{37}.\frac{15}{19}=\frac{15}{19}.\frac{-23}{37}+\frac{14}{37}.\frac{15}{19}=\frac{15}{19}.\left(\frac{-23}{37}+\frac{14}{37}\right)=\frac{15}{19}.\frac{-9}{37}=\frac{-135}{703}\)
\(a,2\frac{x}{7}=\frac{75}{35}\)
\(\frac{75}{35}=2\frac{5}{35}=2\frac{1}{7}\)
\(\Rightarrow x=1\)
\(b,47:4=...\left(+3\right)\)
\(\Rightarrow\left(47-3\right):4=11\)
\(\Rightarrow x=11\)
\(c,\frac{112}{5}=\frac{336}{15}=22\left(+6\right)\)
\(\Rightarrow x=22\frac{x=6}{15}\)
\(d,7,5x=\frac{75x}{100}:\left(9-6\frac{13}{21}\right)=2\frac{13}{25}\)
\(\frac{75x}{100}:\left(9-\frac{139}{21}\right)=\frac{63}{25}\)
\(\frac{75x}{100}:\frac{50}{21}=\frac{63}{25}\)
\(\Rightarrow\frac{63^3}{25^{\left(1\right)}}\cdot\frac{50^{\left(2\right)}}{21^1}=6=\frac{6}{1}\)
\(\Rightarrow\frac{6}{1}=\frac{600}{100}\)
Con d sai đề
\(1)\)
Để \(\frac{13}{a-1}\) là số nguyên thì \(13⋮\left(a-1\right)\)\(\Rightarrow\)\(\left(a-1\right)\inƯ\left(13\right)\)
Mà \(Ư\left(13\right)=\left\{1;-1;13;-13\right\}\)
Suy ra :
| \(a-1\) | \(1\) | \(-1\) | \(13\) | \(-13\) |
| \(a\) | \(2\) | \(0\) | \(14\) | \(-12\) |
Vậy \(a\in\left\{2;0;14;-12\right\}\)
\(2)\)
Ta có :
\(\frac{x}{5}=\frac{y}{3}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{5}=\frac{y}{3}=\frac{x+y}{5+3}=\frac{16}{8}=2\)
Do đó :
\(\frac{x}{5}=2\Rightarrow x=2.5=10\)
\(\frac{y}{3}=2\Rightarrow y=2.3=6\)
Vậy x=10 và y=6
a,\(\frac{-2}{3}+\frac{1}{5}=\frac{-2.5}{3.5}+\frac{3.1}{3.5}=-\frac{10}{15}+\frac{3}{15}=-\frac{7}{15}\)
b,\(3\frac{11}{13}-5\frac{11}{3}=3+\frac{11}{13}-(5+\frac{11}{13})=\left(3-5\right)+\left(\frac{11}{13}-\frac{11}{13}\right)=-2+0=-2\)
c,\(1\frac{2}{3}:(-\frac{5}{3})=\frac{5}{3}:\left(-\frac{5}{3}\right)=\frac{5.3}{3.\left(-5\right)}=\frac{15}{-15}=-1\)
d,\(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{14}{17}=\left(\frac{31}{17}-\frac{14}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)=1+\left(-1\right)=0\)
Tìm x:
a,x+12=8
x=8-12
x=-4
b,\(\frac{2}{3}x+\frac{1}{2}=\frac{1}{10}\)
\(\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}\)
\(\frac{2}{3}x=\frac{1}{10}-\frac{5}{10}\)
\(\frac{2}{3}x=\frac{2}{5}\)
\(x=\frac{2}{5}:\frac{2}{3}\)
\(x=\frac{6}{10}\)
\(x=\frac{3}{5}\)
a) \(\frac{-2}{3}+\frac{1}{5}=\frac{-10}{15}+\frac{3}{15}=\frac{-10+3}{15}=\frac{-7}{15}\)
b) \(3\frac{11}{13}-5\frac{11}{13}=\frac{50}{13}-\frac{76}{13}=\frac{50-76}{13}=\frac{-26}{13}=-2\)
c) \(1\frac{2}{3}:\frac{-5}{3}=\frac{5}{3}:\frac{-5}{3}=\frac{5}{3}\times\frac{3}{-5}=\frac{15}{-15}=-1\)
d) \(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{14}{17}\)
\(=\left(\frac{31}{17}-\frac{14}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)\)
\(=\left(\frac{31-14}{17}\right)+\left(\frac{-5-8}{13}\right)\)
\(=\frac{17}{17}+\frac{-13}{13}\)
\(=1+\left(-1\right)\)
\(=0\)
TÌM x
a) \(x+12=8\)
\(\Leftrightarrow x=8-12\)
\(\Leftrightarrow x=-4\)
b) \(\frac{2}{3}x+\frac{1}{2}=\frac{1}{10}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}=\frac{1}{10}-\frac{5}{10}=\frac{1-5}{10}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{-4}{10}=\frac{-2}{5}\)
\(\Leftrightarrow x=\frac{-2}{5}:\frac{2}{3}=\frac{-2}{5}\times\frac{3}{2}\)
\(\Leftrightarrow x=\frac{-6}{10}=\frac{-3}{5}\)