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a. \(\left(2-\frac{3}{4}\right)^2:\frac{11}{16}=\frac{5}{4}^2.\frac{11}{16}=\frac{25}{16}.\frac{16}{11}=\frac{25}{11}\)
b. \(2^3.\frac{7}{20}+\frac{7}{10}=8.\frac{7}{20}+\frac{7}{10}=\frac{14}{5}+\frac{7}{10}=\frac{7}{2}\)
c. \(\sqrt{3^2+4^2}-\sqrt{1^3+2^3+3^3}=\sqrt{9+16}-\sqrt{1+8+27}\)
\(=\sqrt{25}-\sqrt{36}=5-6=-1\)
d. \(21^3:\left(-7\right)^3=\left(21:\left(-7\right)\right)^3=-3^3=-27\)
a) \(\left(2-\frac{3}{4}\right)^2\div\frac{11}{16}=\left(\frac{5}{4}\right)^2.\frac{16}{11}=\frac{25}{16}.\frac{16}{11}=\frac{25}{11}\)
b) \(2^3.\frac{7}{20}+\frac{7}{10}=8.\frac{7}{20}+\frac{7}{10}=\frac{14}{5}+\frac{7}{10}=\frac{7}{2}\)
c) \(\sqrt{3^2+4^2}-\sqrt{1^3+2^3+3^3}=\sqrt{9+16}-\sqrt{1+8+27}\)
\(=\sqrt{25}-\sqrt{36}=5-6=-1\)
d) \(\frac{21^3}{\left(-7\right)^3}=\frac{9261}{-343}=-27\)
a) Ta có: \(\frac{-1}{12}-\left(2\frac{5}{8}-\frac{1}{3}\right)\)
\(=-\frac{1}{12}-\frac{21}{8}+\frac{1}{3}\)
\(=\frac{-6}{72}-\frac{189}{72}+\frac{24}{72}\)
\(=-\frac{19}{8}\)
b) Ta có: \(-1,75-\left(\frac{-1}{9}-2\frac{1}{18}\right)\)
\(=\frac{-7}{4}+\frac{1}{9}+\frac{37}{18}\)
\(=\frac{-63}{36}+\frac{4}{36}+\frac{74}{36}\)
\(=\frac{5}{12}\)
c) Ta có: \(\frac{2}{5}+\frac{-4}{3}+\frac{-1}{2}\)
\(=\frac{12}{30}+\frac{-40}{30}+\frac{-15}{30}\)
\(=-\frac{43}{30}\)
d) Ta có: \(\frac{3}{12}-\left(\frac{6}{15}-\frac{3}{10}\right)\)
\(=\frac{3}{12}-\frac{6}{15}+\frac{3}{10}\)
\(=\frac{15}{60}-\frac{24}{60}+\frac{18}{60}\)
\(=\frac{3}{20}\)
e) Ta có: \(\left(8\frac{5}{11}+3\frac{5}{8}\right)-3\frac{5}{11}\)
\(=\frac{93}{11}+\frac{29}{8}-\frac{38}{11}\)
\(=5+\frac{29}{8}=\frac{40}{8}+\frac{29}{8}=\frac{69}{8}\)
f) Ta có: \(\frac{4}{9}:\left(-\frac{1}{7}\right)+6\frac{5}{9}:\left(-\frac{1}{7}\right)\)
\(=\frac{4}{9}\cdot\left(-7\right)+\frac{59}{9}\cdot\left(-7\right)\)
\(=\left(-7\right)\cdot\left(\frac{4}{9}+\frac{59}{9}\right)=\left(-7\right)\cdot7=-49\)
g) Ta có: \(\frac{-1}{4}\cdot13\frac{9}{11}-0,25\cdot6\frac{2}{11}\)
\(=\frac{-1}{4}\cdot\frac{152}{11}+\frac{-1}{4}\cdot\frac{68}{11}\)
\(=\frac{-1}{4}\cdot\left(\frac{152}{11}+\frac{68}{11}\right)=-\frac{1}{4}\cdot20=-5\)
h) Ta có: \(5\frac{27}{5}+\frac{27}{23}+0,5-\frac{5}{27}+\frac{16}{23}\)
\(=\frac{52}{5}+\frac{27}{23}+\frac{1}{2}-\frac{5}{27}+\frac{16}{23}\)
\(=\frac{52}{5}+\frac{43}{23}+\frac{1}{2}-\frac{5}{27}\)
\(=\frac{64584}{6210}+\frac{11610}{6210}+\frac{3105}{6210}-\frac{1150}{6210}\)
\(=\frac{78149}{6210}\)
i) Ta có: \(\frac{3}{8}\cdot27\frac{1}{5}-51\frac{1}{5}\cdot\frac{3}{8}+19\)
\(=\frac{3}{8}\cdot\frac{136}{5}-\frac{3}{8}\cdot\frac{206}{5}+\frac{3}{8}\cdot\frac{152}{3}\)
\(=\frac{3}{8}\cdot\left(\frac{136}{5}-\frac{206}{5}+\frac{152}{3}\right)=\frac{3}{8}\cdot\frac{110}{3}\)
\(=\frac{55}{4}\)
\(C=(\frac{2}{3}-\frac{1}{4}+\frac{5}{11}):(\frac{5}{12}+1-\frac{7}{11})\)
\(=\left(\frac{88}{132}-\frac{33}{132}+\frac{60}{132}\right):\left(\frac{55}{132}+\frac{132}{132}-\frac{84}{132}\right)=\left(\frac{115}{132}\right):\frac{103}{132}=\frac{115}{132}.\frac{132}{103}=\frac{115}{103}\)
\(D=1\frac{1}{3}+\frac{1}{8}:\left(0,75-\frac{1}{2}\right)-\frac{25}{100}.\frac{1}{2}=\frac{1}{3}+\frac{1}{8}:\frac{1}{4}-\frac{1}{8}=\frac{1}{3}+\frac{1}{2}-\frac{1}{8}=\frac{8+12-3}{24}=\frac{17}{24}\)
\(E=\left(-\frac{1}{2}\right)^2-\left(-2\right)^2-5^0=\frac{1}{4}-4-1=\frac{1-16-4}{4}=\frac{-19}{4}\)
a. \(\left(\frac{2}{3}\right)^3-\left(\frac{3}{4}\right)^2.\left(-1\right)^5=\frac{8}{27}-\frac{9}{16}.\left(-1\right)=\frac{8}{27}+\frac{9}{16}=\frac{371}{432}\)
b. \(12:\left(\frac{3}{4}-\frac{5}{6}\right)^2=12:\left(-\frac{1}{12}\right)^2=12:\frac{1}{144}=12.144=1728\)
c. \(\frac{7}{22}:\frac{3}{11}+\frac{7}{22}:\frac{4}{11}=\frac{7}{22}.\frac{11}{3}+\frac{7}{22}.\frac{11}{4}=\frac{7}{22}\left(\frac{11}{3}+\frac{11}{4}\right)\)
\(=\frac{7}{22}.\frac{77}{12}=\frac{49}{24}\)
d. \(\frac{12}{35}\left(\frac{7}{4}+\frac{13}{4}\right)-\frac{1}{3}=\frac{12}{35}.5-\frac{1}{3}=\frac{12}{7}-\frac{1}{3}=\frac{29}{21}\)
Bài 2: Mỗi xe ô tô có 4 bánh xe . Hỏi 5 xe ô tô như thế có bao nhiêu bánh xe ?
Bài giải
5 xe ô tô như thế có số bánh xe là :
4 x 5= 20 (bánh xe )
Đáp số : 20 bánh xe
a) \(\frac{-6}{21}.\frac{3}{2}=-\frac{3}{7}\) b) \(\left(-3\right).\left(\frac{-7}{12}\right)=\frac{21}{12}=\frac{7}{4}\)
c) \(\left(\frac{11}{12}:\frac{33}{16}\right).\frac{3}{5}=\frac{11}{12}.\frac{16}{33}.\frac{3}{5}=\frac{4}{15}\)
d) \(\sqrt{\left(-7\right)^2}+\sqrt{\frac{2}{16}}=7+\sqrt{\frac{1}{8}}\)
c) \(\frac{1}{2}.\sqrt{100}-\sqrt{\frac{1}{16}}+\left(\frac{1}{3}\right)^0=\frac{1}{2}.10-\frac{1}{4}+1=5\frac{3}{4}\)