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4/3 + 3/3 = 7/3
5/2 x 4 = 10
2 - 7/8 = 16/8 - 7/8 = 9/8
5 x 7/5 = 7
5/6 x 7/2= 35/12
4/3 + 3/3 = 7/3
5/2 x 4 = 10
2 - 7/8 = 16/8 - 7/8 = 9/8
5 x 7/5 = 7
5/6 x 7/2= 35/12
a.
\(\frac{6}{7}+\frac{5}{8}\div5-\frac{3}{16}\times\left(-2\right)^2=\frac{6}{7}+\frac{5}{8}\times\frac{1}{5}-\frac{3}{16}\times4=\frac{6}{7}+\frac{1}{8}-\frac{3}{4}=\frac{48}{56}+\frac{7}{56}-\frac{42}{56}=\frac{13}{56}\)
b.
\(\frac{2}{3}+\frac{1}{3}\times\left(-\frac{4}{9}+\frac{5}{6}\right)\div\frac{7}{12}=\frac{2}{3}+\frac{1}{3}\times\left(-\frac{8}{18}+\frac{15}{18}\right)\times\frac{12}{7}=\frac{2}{3}+\frac{7}{18}\times\frac{4}{7}=\frac{2}{3}+\frac{2}{9}=\frac{6}{9}+\frac{2}{9}=\frac{8}{9}\)
c.
\(\left[6+\left(\frac{1}{3}\right)^3-\left|-2\right|\right]\div\frac{3}{2}=\left(6+\frac{1^3}{3^3}-2\right)\times\frac{2}{3}=\left(4+\frac{1}{27}\right)\times\frac{2}{3}=\left(\frac{108}{27}+\frac{1}{27}\right)\times\frac{2}{3}=\frac{109}{27}\times\frac{2}{3}=\frac{218}{81}\)
d.
\(\left(-2\right)^3\times\left(-\frac{1}{24}\right)+\left(\frac{4}{3}-\frac{11}{6}\right)\div\frac{5}{12}\)\(=\left(-8\right)\times\left(-\frac{1}{24}\right)+\left(\frac{8}{6}-\frac{11}{6}\right)\times\frac{12}{5}=\frac{1}{3}+\left(-\frac{3}{6}\right)\times\frac{12}{5}=\frac{1}{3}-\frac{6}{5}=\frac{5}{15}-\frac{18}{15}\)\(=-\frac{13}{15}\)
Câu 1,2 bạn đã đăng và có lời giải rồi
Câu 3:
\(=\frac{(\sqrt{3})^2+(2\sqrt{5})^2-2.\sqrt{3}.2\sqrt{5}}{\sqrt{2}(\sqrt{3}-2\sqrt{5})}=\frac{(\sqrt{3}-2\sqrt{5})^2}{\sqrt{2}(\sqrt{3}-2\sqrt{5})}=\frac{\sqrt{3}-2\sqrt{5}}{\sqrt{2}}\)
1)\(\dfrac{2}{9}+\dfrac{-3}{4}+\dfrac{5}{30}\)
\(=\dfrac{2.20}{9.20}+\dfrac{-3.45}{4.45}+\dfrac{5.6}{30.6}\)
\(=\dfrac{40}{180}+\dfrac{-135}{180}+\dfrac{30}{180}\)
\(=\dfrac{40+\left(-135\right)+30}{180}\)
\(=\dfrac{-65}{180}\)
\(=\dfrac{-13}{36}\)
2)\(\dfrac{-7}{12}-\dfrac{11}{18}\)
\(=\dfrac{-7.3}{12.3}-\dfrac{11.2}{18.2}\)
\(=\dfrac{-21}{36}-\dfrac{22}{36}\)
\(=\dfrac{-21-22}{36}\)
\(=\dfrac{-43}{36}\)
3)\(\dfrac{7}{8}-\dfrac{-5}{16}\)
\(=\dfrac{7.2}{8.2}-\dfrac{-5}{16}\)
\(=\dfrac{14}{16}-\dfrac{-5}{16}\)
\(=\dfrac{14-\left(-5\right)}{16}\)
\(=\dfrac{19}{16}\)
4)\(\dfrac{3}{8}-\dfrac{-9}{10}-\dfrac{5}{16}\)
\(=\dfrac{3.10}{8.10}-\dfrac{-9.8}{10.8}-\dfrac{5.5}{16.5}\)
\(=\dfrac{30}{80}-\dfrac{-72}{80}-\dfrac{25}{80}\)
\(=\dfrac{30-\left(-72\right)-25}{80}\)
\(=\dfrac{77}{80}\)
\(\dfrac{9}{54}=\dfrac{1}{6}=\dfrac{4}{24}< \dfrac{7}{24}\)
\(\dfrac{7}{24}< \dfrac{12}{24}< \dfrac{16}{24}=\dfrac{2}{3}\)
\(\dfrac{2}{3}< \dfrac{2+1}{3+1}=\dfrac{3}{4}\)
\(\dfrac{3}{4}< \dfrac{3+2}{4+2}=\dfrac{5}{6}\)
\(\dfrac{5}{6}< \dfrac{5+2}{6+2}=\dfrac{7}{8}\)
\(\dfrac{7}{8}< \dfrac{7+9}{8+9}=\dfrac{16}{17}\)
Vậy \(\dfrac{9}{54}< \dfrac{7}{24}< \dfrac{2}{3}< \dfrac{3}{4}< \dfrac{5}{6}< \dfrac{7}{8}< \dfrac{16}{17}\)
\(A=\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10+6\cdot12}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20+18\cdot24}\)
\(A=\frac{2\cdot3\left[1\cdot2\right]+2\cdot3\left[2\cdot4\right]+2\cdot3\left[3\cdot6\right]+2\cdot3\left[4\cdot8\right]+2\cdot3\left[5\cdot10\right]}{3\cdot4\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}\)
\(A=\frac{\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}{2\cdot3\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}=\frac{1}{2\cdot3}=\frac{1}{6}\)
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