Bài 6: a. Tìm số đối của $-\dfrac{2}{3}$
b. So sánh hai số: $1\dfrac{1}{2}$ và $\dfrac{2}{3}$ và cho biết điểm $1\dfrac{1}{2}$ nằm trước hay sau điểm $\dfrac{2}{3}$ trên trục số
Bài 7: Thực hiện phép tính:
a. $\dfrac{3}{4} - \dfrac{1}{4} - \dfrac{1}{4}$; \hspace{0.5cm} b. $5, 3.45 - 44.5, 3$; \hspace{0.5cm} c. $0, 1. \sqrt{4} + 2 . \sqrt{16}$
Bài 8: Thực hiện phép tính
a. $-\dfrac{4}{12} + \dfrac{14}{21}$; \hspace{0.5cm} b. $-\dfrac{8}{3} - \dfrac{2}{11} - \dfrac{8}{9}$; \hspace{0.5cm} c. $0, 1.\sqrt{400} + 0, 2.\sqrt{1600}$
d. $\left( -\dfrac{1}{3} \right)^2 - \dfrac{3}{8} : (0,5)^3 - \dfrac{5}{2} . (-4) + 2026^0$
Bài 9: Tính hợp lý (nếu có thể):
a. $\dfrac{21}{11} - \dfrac{2}{11}$ \hspace{0.5cm} b. $0, 5.\sqrt{64} + 0, 5.\sqrt{4}$ \hspace{0.5cm} c. $-\dfrac{20}{11} \dfrac{5}{7} \dfrac{20}{11} \dfrac{12}{7}$
d. $\left( 1 - \dfrac{1}{3} \right)^{12} \left( \dfrac{2}{3} \right)^{10} - \dfrac{14}{9} - 202
Bài 13:
a: \(x-\frac34=2\frac17\)
=>\(x-\frac34=\frac{15}{7}\)
=>\(x=\frac{15}{7}+\frac34=\frac{60}{28}+\frac{21}{28}=\frac{81}{28}\)
b: \(\frac85+\frac25x=0,25\)
=>\(\frac25x=0,25-\frac85=\frac14-\frac85=\frac{5}{20}-\frac{32}{20}=-\frac{27}{20}\)
=>\(x=-\frac{27}{20}:\frac25=-\frac{27}{20}\cdot\frac52=\frac{-27}{8}\)
Bài 12:
a: \(25\%-x=1\frac56\)
=>\(\frac14-x=\frac{11}{6}\)
=>\(x=\frac14-\frac{11}{6}=\frac{3}{12}-\frac{22}{12}=-\frac{19}{12}\)
b: \(-\frac54+\frac23:x=0,75\)
=>\(\frac23:x=0,75+\frac54=0,75+1,25=2\)
=>\(x=\frac23:2=\frac13\)
Bài 11:
a: \(\frac76+\frac16\cdot\frac32=\frac76+\frac{3}{12}=\frac{14}{12}+\frac{3}{12}=\frac{17}{12}\)
b: \(\frac{11}{15}\cdot\frac{-19}{13}+\frac{-7}{13}\cdot\frac{11}{15}\)
\(=\frac{11}{15}\left(-\frac{19}{13}-\frac{7}{13}\right)=\frac{11}{15}\cdot\frac{-26}{13}=\frac{11}{15}\cdot\left(-2\right)=-\frac{22}{15}\)
c: \(\frac{2^3+2^4+2^5+2^6}{15^2}\)
\(=\frac{2^3\left(1+2+2^2+2^3\right)}{15^2}=\frac{2^3\cdot15}{15^2}=\frac{2^3}{15}=\frac{8}{15}\)
Bài 10:
a: \(\frac23:\frac{-6}{9}+\frac17=\frac23\cdot\frac{-9}{6}+\frac17=-1+\frac17=-\frac67\)
b: \(\frac{-3}{11}\cdot\frac59+\frac49\cdot\frac{-3}{11}\)
\(=-\frac{3}{11}\left(\frac59+\frac49\right)\)
\(=-\frac{3}{11}\cdot\frac99=-\frac{3}{11}\)
c: \(\frac{9^5\cdot8^2}{27^3\cdot16}=\frac{3^{10}\cdot2^6}{3^9\cdot2^4}=3\cdot2^2=12\)
Bài 9:
a: \(\frac{21}{11}-\frac{2}{11}=\frac{21-2}{11}=\frac{19}{11}\)
b: \(0,5\cdot\sqrt{64}+0,5\cdot\sqrt4\)
\(=0,5\cdot8+0,5\cdot2\)
\(=0,5\cdot\left(8+2\right)=0,5\cdot10=5\)
c: \(\frac{-20}{11}\cdot\frac57+\frac{20}{11}\cdot\frac{12}{7}\)
\(=\frac{20}{11}\left(-\frac57+\frac{12}{7}\right)\)
\(=\frac{20}{11}\cdot\frac77=\frac{20}{11}\)
d: \(\left(1-\frac13\right)^{12}:\left(\frac23\right)^{10}-1\frac49-2026^0\)
\(=\left(\frac23\right)^{12}:\left(\frac23\right)^{10}-\frac{13}{9}-1\)
\(=\frac49-\frac{13}{9}-1=-\frac99-1=-1-1=-2\)
Bài 8:
a: \(\frac{-4}{12}+\frac{14}{21}=-\frac13+\frac23=\frac13\)
b: \(-\frac83\cdot\frac{2}{11}-\frac83:\frac{11}{9}\)
\(=-\frac83\cdot\frac{2}{11}-\frac83\cdot\frac{9}{11}\)
\(=-\frac83\left(\frac{2}{11}+\frac{9}{11}\right)=-\frac83\)
c: \(0,1\cdot\sqrt{400}+0,2\cdot\sqrt{1600}\)
\(=0,1\cdot20+0,2\cdot40\)
=2+8
=10
d: \(\left(-\frac13\right)^2-\frac38:\left(0,5\right)^3-\frac52\cdot\left(-4\right)+2026^0\)
\(=\frac19-\frac38:\frac18+10+1\)
\(=\frac19-3+11=\frac19+8=\frac{73}{9}\)
Bài 7:
a: \(\frac34-\frac14-1\frac14=\frac24-1-\frac14=\frac14-1=-\frac34\)
b: \(5,3\cdot45-44\cdot5,3=5,3\cdot\left(45-44\right)=5,3\)
c: \(0,1\cdot\sqrt4+2\cdot\sqrt{16}=0,1\cdot2+2\cdot4=8+0,2=8,2\)
Bài 6:
a: Số đối của -2/3 là 2/3
b: \(1\frac12>1;\frac23<1\)
=>\(1\frac12>\frac23\)
=>\(1\frac12\) nằm sau 2/3 trên trục số
