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NL
Nguyễn Lê Phước Thịnh
CTVHS
12 tháng 9 2025
Bài 1:
a: \(M=\frac13xy\left(-\frac12xy^2z^3\right)^2\cdot x^3y\)
\(=\frac13x^4y^2\cdot\frac14x^2y^4z^6\)
\(=\left(\frac13\cdot\frac14\right)\cdot\left(x^4\cdot x^2\right)\cdot\left(y^4\cdot y^2\right)\cdot z^6=\frac{1}{12}x^6y^6z^6\)
Bậc là 6+6+6=18
Hệ số là 1/12
Phần biến là \(x^6;y^6;z^6\)
b: \(M=\frac{1}{12}x^6y^6z^6=\frac{1}{12}\cdot\left(xyz\right)^6\)
Thay x=-4;y=0,5;z=-0,5 vào M, ta được:
\(M=\frac{1}{12}\cdot\left\lbrack-4\cdot0,5\cdot\left(-0,5\right)\right\rbrack^6=\frac{1}{12}\cdot\left(2\cdot0,5\right)^6=\frac{1}{12}\)
Bài 2:
a: \(\left(xy^2-6x^2y\right)-\left(-2xy^2-5x^2y\right)+\left(x^2y-6xy^2\right)\)
\(=xy^2-6x^2y+2xy^2+5x^2y+x^2y-6xy^2=-3xy^2\)
b: \(N=\left(15x^5y^4-20x^3y^2+5x^2y^3\right):5x^2y\)
\(=\frac{15x^5y^4}{5x^2y}-\frac{20x^3y^2}{5x^2y}+\frac{5x^2y^3}{5x^2y}=3x^3y^3-4xy+y^2\)
Thay x=1;y=1 vào N, ta được:
\(N=3\cdot1^3\cdot1^3-4\cdot1\cdot1+1^2\)
=3-4+1
=0
c: \(\left(3x^2-x-3\right)-2x\left(x+2\right)-\left(x+4\right)\left(x-5\right)=1\)
=>\(3x^2-x-3-2x^2-4x-\left(x^2-x-20\right)=1\)
=>\(x^2-5x-3-x^2+x+20=1\)
=>-4x+17=1
=>-4x=-16
=>x=4
BÀi 3:
a: \(\left(-\frac72\right)\cdot\left(-\frac{11}{21}\right)=\frac72\cdot\frac{11}{21}=\frac{7}{21}\cdot\frac{11}{2}=\frac{11}{2}\cdot\frac13=\frac{11}{6}\)
b: \(\left(-\frac{10}{3}\right)\cdot\left(-2.5\right)=\frac{10}{3}\cdot\frac52=\frac{50}{6}=\frac{25}{3}\)
c: \(1\frac35\cdot\frac{-3}{4}=\frac85\cdot\frac{-3}{4}=\frac{-6}{5}\)
d: \(2\frac13\cdot1\frac{1}{14}\)
\(=\frac73\cdot\frac{15}{14}=\frac{15}{3}\cdot\frac{7}{14}=\frac52\)
Bài 1:
a: \(\frac{1}{12}+\frac{-3}{12}=\frac{1-3}{12}=-\frac{2}{12}=-\frac16\)
b: \(\frac78-\frac54=\frac78-\frac{10}{8}=-\frac38\)
c: \(1\frac25+3\frac35=1+\frac25+3+\frac35=4+1=5\)
d: \(\frac{-14}{20}+0,6=-\frac{14}{20}+\frac{12}{20}=\frac{-2}{20}=-\frac{1}{10}\)
Bài 1: C
Câu 2: A
Câu 3: A
Câu 4: D
Câu 5: B
Câu 6: A
Câu 7: A
I. Trắc nghiệm
Bài 1: C
Bài 2: A
Bài 3: A
Bài 4: A
Bài 5: D
Bài 6: A
Bài 7: A
II. Các Dạng Bài Tập
Bài 1:
a) \(\frac{1}{12}+\frac{-3}{12}\) = \(\frac{1+\left(-3\right)}{12}=-\frac{2}{12}=-\frac16\)
b) \(\frac78-\frac54=\frac78-\frac{10}{8}=-\frac38\)
c) \(1\frac25+3\frac35=\frac75+\frac{18}{5}=\frac{25}{5}=5\)
d) \(\frac{-14}{20}+0,6=\frac{-14}{20}+\frac{6}{10}=\frac{-14}{20}+\frac{12}{20}=-\frac{2}{20}=-0,1\)
Bài 2:
a) \(\frac{-3}{14}+\frac{8}{35}=\frac{-3\times5}{70}+\frac{8\times2}{70}=\frac{-15+16}{70}=\frac{1}{70}\)
b) \(\frac{4}{25}+\frac{-2}{15}=\frac{4\times3}{75}-\frac{2\times5}{75}=\frac{12-10}{75}=\frac{2}{75}\)
c) \(\frac{-1}{21}+\frac{-1}{14}=\frac{-1\times2}{42}+\frac{-1\times3}{42}=\frac{-2+\left(-3\right)}{42}=\frac{-5}{42}\)
d) \(\frac{-14}{20}+0,6=-0,1\)
Bài 3:
a) \(\left(-\frac72\right)\left(-\frac{11}{21}\right)=\frac{77}{42}=\frac{11}{6}\)
b) \(\left(\frac{-10}{3}\right)\left(-2,5\right)=\left(\frac{-10}{3}\right)\left(\frac{-5}{2}\right)=\frac{50}{6}=\frac{25}{3}\)
\(c)1\frac35\cdot\frac{-3}{4}=\frac85\cdot\frac{-3}{4}=\frac{-24}{20}=\frac{-6}{5}\)
d) \(2\frac13\cdot1\frac{1}{14}=\frac73\cdot\frac{15}{14}=\frac52=2,5\)
Bài 4:
a) \(\frac{-15}{4}:\frac{21}{-10}=\frac{-15}{4}\cdot\frac{-10}{21}=\frac{25}{14}\)
b) \(\frac{-7}{15}:\left(-0,14\right)=\frac{-7}{15}\cdot\frac{-100}{14}=\frac{10}{3}\)
c) \(\left(-\frac{11}{15}\right):1\frac{1}{10}=-\frac{11}{15}:\frac{11}{10}=-\frac{11}{15}\cdot\frac{10}{11}=-\frac23\)
d) \(2\frac17:1\frac{1}{14}=\frac{15}{7}:\frac{15}{14}=\frac{15}{7}\cdot\frac{14}{15}=2\)
Bài 5:
a) \(\frac{-4}{12}-\left(\frac{-13}{39}-0,25\right)+0,75\)
= \(\left(\frac{-4}{12}-\frac{-13}{39}\right)+\left(0,25+0,75\right)\)
\(=\left(\frac{-12}{39}+\frac{13}{39}\right)+1\)
\(=\frac{1}{39}+1\)
= \(\frac{40}{39}\)
b) \(\frac25-\left(\frac43+\frac45\right)-\left(-\frac19-0,4\right)+\frac{11}{9}\)
\(=\left(\frac25-\frac45+0,4\right)+\left(-\frac43+\frac19+\frac{11}{9}\right)\)
\(=\left(-\frac25+\frac25\right)+\left(-\frac{12}{9}+\frac19+\frac{11}{9}\right)\)
= 0+0
=0
Bài 6:
A= \(\left(-\frac{24}{11}\right)+\left(-\frac{19}{13}\right)+\frac{2}{11}+\left(-\frac{20}{13}\right)\)
= \(\left(-\frac{24}{11}+\frac{2}{11}\right)+\left(-\frac{19}{13}-\frac{20}{13}\right)\)
= \(\left(-\frac{22}{11}\right)+\left(-\frac{39}{13}\right)\)
\(=-2+\left(-3\right)\)
= -5
Bài 7:
a) \(\left(-\frac{25}{13}\right)+\left(-\frac{9}{17}\right)+\frac{12}{13}+\left(-\frac{25}{17}\right)\)
= \(\left(-\frac{25}{13}+\frac{12}{13}\right)+\left(-\frac{9}{17}-\frac{25}{17}\right)\)
= \(\left(-\frac{13}{13}\right)+\left(-\frac{34}{17}\right)\)
= -1+(-2)
=-3
b) \(\frac23+\frac{-1}{-4}+\frac{1}{21}+\frac{1}{12}\)
= \(\left(\frac{14}{21}+\frac{1}{21}\right)+\left(\frac{3}{12}+\frac{1}{12}\right)\)
\(=\frac{15}{21}+\frac13\)
\(=\frac{15}{21}+\frac{7}{21}\)
\(=\frac{21}{21}=1\)
Bài 8:
a) \(\left(\frac{-5}{11}\right)\cdot\frac{7}{15}\cdot\left(\frac{11}{-5}\right)\cdot-30\)
= \(\left(\frac{-5}{11}\cdot\frac{11}{-5}\right)\cdot\left(\frac{7}{15}\cdot-30\right)\)
\(=1\cdot-14\)
= -14
b) \(\left(\frac{-1}{3}\right)\left(\frac{-15}{19}\right)\cdot\frac{38}{45}\)
\(=\frac{5}{19}\cdot\frac{38}{45}\)
= \(\frac29\)
c) \(\left(-\frac59\right)\cdot\frac{3}{11}+\left(-\frac{13}{18}\right)\cdot\frac{3}{11}\)
= \(\frac{3}{11}\left(-\frac{13}{18}-\frac59\right)\)
\(=\frac{3}{11}\cdot\left(-\frac{13}{18}-\frac{10}{18}\right)\)
= \(\frac{3}{11}\cdot-\frac{23}{18}\)
= \(-\frac{23}{66}\)
d) \(\left(2\frac{2}{15}\cdot\frac{9}{17}\cdot\frac{3}{32}\right):\left(-\frac{3}{17}\right)\)
= \(\left(\frac{32}{15}\cdot\frac{3}{32}\cdot\frac{9}{17}\right):\left(-\frac{3}{17}\right)\)
= \(\left(\frac15\cdot\frac{9}{17}\right)\cdot-\frac{17}{3}\)
= \(\frac{9}{5\cdot17}\cdot-\frac{17}{3}\)
= \(-\frac35\)
bài 8: