Bài 2. Thực hiện phép tính:
1. \(\frac{5}{15} + \frac{14}{25} - \frac{12}{9} + \frac{2}{7} + \frac{11}{25}\)
2. \(\frac{5}{8} \cdot \frac{17}{3} - 41 \cdot \frac{1}{3} + \frac{5}{8} + 21\)
3. \(\left( \frac{2}{7} \right) \cdot .343 - .2023 + \left( -\frac{64}{2023} \right)^3\)
4. \(\frac{3}{2} - \left( \frac{5}{8} \right)^0 \cdot \left( -\frac{1}{2} \right)^2 + \sqrt{4}\)
5. \(\left( \frac{1}{3} \right)^2 + \frac{16}{\sqrt{49}} \cdot \frac{7}{36}\)
6. \(\frac{9^{14}}{3^{12} \cdot 27^6}\)
Bài 3. Tính giá trị các biểu thức sau:
1. \(A = \frac{-27}{59} + \frac{27}{59} + \frac{13}{7} \cdot \frac{32}{59}\)
2. \(B = \left( -0,5 - \frac{3}{5} \right) \cdot (-3) + \frac{1}{3} \cdot \left( -\frac{1}{6} \right) \cdot (-2)\)
3. \(C = \left( \frac{16}{9} \right)^{\frac{1}{4}} \cdot \left( \frac{25}{16} \right)^{\frac{1}{4}} \cdot 100^{\frac{1}{3}} \cdot \frac{3}{5}\)
Bài 4: Tính giá trị của các biểu thức sau
3: \(\sqrt{\frac49}-\frac12:\left|-\frac23\right|\)
\(=\frac23-\frac12:\frac23\)
\(=\frac23-\frac34=\frac{8}{12}-\frac{9}{12}=-\frac{1}{12}\)
13: \(\sqrt{64}+2\cdot\sqrt{\left(-3\right)^2}-7\cdot\sqrt{1,69}+3\cdot\sqrt{\frac{25}{16}}\)
\(=8+2\cdot6-7\cdot1,3+3\cdot\frac54\)
=8+12-9,1+3,75=14,65
4: \(\left(40\%-1\frac23\right):\frac{-3}{2}+\left(-\frac12\right)^2\)
\(=\left(\frac25-\frac53\right)\cdot\frac{-2}{3}+\frac14\)
\(=\left(\frac{6}{15}-\frac{25}{15}\right)\cdot\frac{-2}{3}+\frac14=\frac{-19}{15}\cdot\frac{-2}{3}+\frac14=\frac{38}{45}+\frac14\)
\(=\frac{152}{180}+\frac{45}{180}=\frac{197}{180}\)
14: \(\left\lbrack-\sqrt{2,25}+4\cdot\sqrt{\left(-2,15\right)^2}-\left(3\sqrt{\frac76}\right)^2\right\rbrack\cdot\sqrt{1\frac{9}{16}}\)
\(=\left\lbrack-1,5+4\cdot2,15-9\cdot\frac76\right\rbrack\cdot\sqrt{\frac{25}{16}}\)
\(=\left\lbrack-1,5+8,6-10,5\right\rbrack\cdot\frac54=-3,4\cdot\frac54=-4,25\)
5: \(\frac{5}{14}-3,7-\frac{19}{14}+\frac89-6,3\)
\(=\left(\frac{5}{14}-\frac{19}{14}\right)+\left(-3,7-6,3\right)+\frac89\)
\(=-\frac{14}{14}-10+\frac89=-11+\frac89=-\frac{99}{9}+\frac89=-\frac{91}{9}\)
15: \(-\left(\frac89+\frac75-\frac{2}{11}\right)+\left(-\frac25+\frac{17}{9}-\frac{13}{11}\right)\)
\(=-\frac89-\frac75+\frac{2}{11}-\frac25+\frac{17}{9}-\frac{13}{11}\)
\(=\left(-\frac89+\frac{17}{9}\right)+\left(-\frac75-\frac25\right)+\left(\frac{2}{11}-\frac{13}{11}\right)\)
\(=\frac99-\frac95-\frac{11}{11}=-\frac95\)
6: \(-3-\frac{16}{23}-\sqrt{\frac{4}{49}}-\frac{7}{23}+\frac{\left(-3\right)^2}{7}\)
\(=-3-\left(\frac{16}{23}+\frac{7}{23}\right)-\frac27+\frac97=-3+1-\frac{23}{23}=-2-1=-3\)
16: \(\frac17\cdot\frac38+\frac17\cdot\frac58+\frac{\left(-1\right)^{2019}}{7}\)
\(=\frac17\left(\frac38+\frac58\right)-\frac17\)
\(=\frac17-\frac17\)
=0
7: \(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
\(=\left(\frac{11}{24}+\frac{13}{24}\right)+\left(-\frac{5}{41}-\frac{36}{41}\right)+0,5\)
=1-1+0,5
=0,5
17: \(\frac45\cdot\frac37-\frac{-4}{7}:\sqrt{\frac{25}{16}}-\left|-1\right|\)
\(=\frac45\cdot\frac37+\frac47:\frac54-1\)
\(=\frac45\left(\frac37+\frac47\right)-1=\frac45-1=-\frac15\)
8: \(-12:\left(\frac34-\frac56\right)^2=-12:\left(\frac{9}{12}-\frac{10}{12}\right)^2\)
\(=-12:\left(-\frac{1}{12}\right)^2=-12:\frac{1}{144}=-12\cdot144=-1728\)
18: \(\left|1,37\right|\cdot\frac29-7,37\cdot\left|-\frac29\right|\)
\(=1,37\cdot\frac29-7,37\cdot\frac29\)
\(=\frac29\left(1,37-7.37\right)=\frac29\cdot\left(-6\right)=-\frac{12}{9}=-\frac43\)
9: \(\left(2^2:\frac43-\frac12\right)\cdot\frac65-17\)
\(=\left(4\cdot\frac34-\frac12\right)\cdot\frac65-17=\frac52\cdot\frac65-17\)
=3-17
=-14
19: \(\left(-\frac23\right)^2\cdot\frac{5}{13}-\frac{8}{13}:\frac{-9}{4}-\frac12\)
\(=\frac49\cdot\frac{5}{13}+\frac{8}{13}\cdot\frac49-\frac12\)
\(=\frac49\left(\frac{5}{13}+\frac{8}{13}\right)-\frac12\)
\(=\frac49-\frac12=-\frac{1}{18}\)
20: \(\left(\frac49\right)^{11}\cdot\left(\frac23\right)^{12}:\left(\frac{8}{27}\right)^{10}\)
\(=\left(\frac23\right)^{22}\cdot\left(\frac23\right)^{12}:\left(\frac23\right)^{30}\)
\(=\left(\frac23\right)^{22+12-30}=\left(\frac23\right)^4=\frac{16}{81}\)
10: \(\frac{2\cdot6^9-2^5\cdot18^4}{2^2\cdot6^8}\)
\(=\frac{2\cdot2^9\cdot3^9-2^5\cdot2^4\cdot3^8}{2^2\cdot2^8\cdot3^8}=\frac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{10}\cdot3^8}\)
\(=\frac{2^9\cdot3^8\left(2\cdot3-1\right)}{2^{10}\cdot3^8}=\frac12\cdot5=\frac52\)
21: \(\left(\frac14\right)^5\cdot\left(\frac18\right)^6:\left(\frac12\right)^{26}\)
\(=\left(\frac12\right)^{10}\cdot\left(\frac12\right)^{18}:\left(\frac12\right)^{26}\)
\(=\left(\frac12\right)^{10+18-26}=\left(\frac12\right)^2=\frac14\)
11: \(\left(-\frac{5}{11}:\frac{13}{8}-\frac{5}{11}:\frac{13}{5}\right)+\frac{-1}{33}\)
\(=\left(-\frac{5}{11}\cdot\frac{8}{13}-\frac{5}{11}\cdot\frac{5}{13}\right)+\frac{-1}{33}\)
\(=-\frac{5}{11}-\frac{1}{33}=-\frac{16}{33}\)
22: \(\frac{\frac27+\frac25+\frac{2}{17}-\frac{2}{25}}{\frac{3}{14}+\frac{3}{10}+\frac{3}{34}-\frac{3}{50}}\)
\(=\frac{2\left(\frac15+\frac17+\frac{1}{17}-\frac{1}{25}\right)}{\frac32\left(\frac15+\frac17+\frac{1}{17}-\frac{1}{25}\right)}\)
\(=2:\frac32=\frac43\)
Bài 2:
1: \(\frac{5}{15}+\frac{14}{25}-\frac{12}{9}+\frac27+\frac{11}{25}\)
\(=\left(\frac13-\frac43\right)+\left(\frac{14}{25}+\frac{11}{25}\right)+\frac27\)
\(=-1+1+\frac27=\frac27\)
2: \(\frac58\cdot17\frac13-41\frac13\cdot\frac58+21\)
\(=\frac58\left(17+\frac13-41-\frac13\right)+21\)
\(=\frac58\cdot\left(-24\right)+21=21-15=6\)
3: \(\left(-\frac27\right)^2\cdot343-\left(-\frac{2022}{2023}\right)^0+64\cdot\left(\frac12\right)^3\)
\(=\frac{4}{49}\cdot343-1+64\cdot\frac18\)
=28-1+8
=36-1
=35
4: \(\frac32-\left(\frac58\right)^0:\left(-\frac12\right)^2+\sqrt4=\frac32-1:\frac14+2\)
\(=\frac72-4=-\frac12\)
5: \(\left(\frac13-\frac12\right)^2+\left(\sqrt{\frac{16}{49}}-3\right)^0-\frac{7}{36}\)
\(=\left(\frac26-\frac36\right)^2+1-\frac{7}{36}\)
\(=\frac{1}{36}+1-\frac{7}{36}=1-\frac{6}{36}=1-\frac16=\frac56\)
6: \(\frac{9^{14}}{3^{12}\cdot27^6}=\frac{3^{28}}{3^{12}\cdot3^{18}}=\frac{3^{28}}{3^{30}}=\frac{1}{3^2}=\frac19\)
Bài 3:
1: \(A=-\frac{27}{59}\cdot\frac57+\frac{27}{59}\cdot\frac{13}{7}+1\frac17\cdot\frac{32}{59}\)
\(=\frac{27}{59}\left(\frac{13}{7}-\frac57\right)+\frac87\cdot\frac{32}{59}\)
\(=\frac{27}{59}\cdot\frac87+\frac87\cdot\frac{32}{59}\)
\(=\frac87\left(\frac{27}{59}+\frac{32}{59}\right)=\frac87\)
2: \(B=\left(-0,5-\frac35\right):\left(-3\right)+\frac13-\left(-\frac16\right):\left(-2\right)\)
\(=\left(-\frac12-\frac35\right):\left(-3\right)+\frac13-\frac16:2\)
\(=\left(-\frac{5}{10}-\frac{6}{10}\right):\left(-3\right)+\frac13-\frac{1}{12}\)
\(=\frac{11}{30}+\frac13-\frac{1}{12}=\frac{22}{60}+\frac{20}{60}-\frac{5}{60}=\frac{37}{60}\)
3: \(C=\left(\sqrt{\frac{16}{9}}+1\right)^2-\left(\sqrt{\frac{25}{16}}-\frac14\right)^{100}+\frac13:\frac35\)
\(=\left(\frac43+1\right)^2-\left(\frac54-\frac14\right)^{100}+\frac13\cdot\frac53\)
\(=\left(\frac73\right)^2+\frac59-1=\frac{49}{9}+\frac59-1=\frac{54}{9}-1\)
=6-1
=5
