\(\frac{3}{1.4}+\frac{6}{4.10}+\frac{9}{10.19}+\frac{12}{19.31}+\frac{15}{31.46}+\frac{18}{46.64}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{10}+\frac{1}{10}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}+\frac{1}{31}-\frac{1}{46}+\frac{1}{46}-\frac{1}{64}\)

\(=1-\frac{1}{64}=\frac{63}{64}\)

Bạn ko hiểu chỗ nào là phải hỏi mình ngay nhé!

1/3 + 1/6 + 1/9 + 1/18

= 6/18 + 3/18 + 2/18 + 1/18

= 12/18

= 2/3

b)  42/24 - 10/8 - 2/4

= 42/24 - 30/24 - 12/24

= 0

=1/2x3 + 1/3x4 + 1/ 4x5 +.............+1/9x10

=3-2/2x3 + 4-3/3x4 + 5-4/4x5 + ..........+ 10-9/9x10

=3/2x3 - 2/3x2 + 4/3x4 - 3/4x3 + 5/4x5 - 4/4x5 + .............+10/9x10 - 9 /10x9

=1/2-1/3+1/3-1/4+1/4-1/5+.........................+1/9-1/10

=1/2-1/10

=2/5

\(\frac{1}{9}+\frac{8}{9}=\frac{1+8}{9}=\frac{9}{9}=1\)

\(\frac{1}{12}+\frac{2}{12}+\frac{6}{12}+\frac{3}{12}=\frac{1+2+6+3}{12}=\frac{12}{12}=1\)

Chúc bạn học tốt !!

\(\frac{1}{9}\)+\(\frac{8}{9}\)=\(\frac{1+8}{9}\)=\(\frac{9}{9}\)=\(1\)

\(\frac{1}{12}\)+\(\frac{2}{12}\)+\(\frac{6}{12}\)+\(\frac{3}{12}\)=\(\frac{1+2+6+3}{12}\)=\(\frac{12}{12}\)=\(1\)

a)\(\left(17\frac{13}{15}-3\frac37\right)-\left(2\frac{12}{15}-4\right)\)

=\(17\frac{13}{15}-3\frac37-2\frac{12}{15}+4\)

=\(\left(17-2-3+4\right)+\left(\frac{13}{15}-\frac{12}{15}-\frac37\right)\)

=\(16+\left(\frac{1}{15}-\frac37\right)\)

=\(16+\left(\frac{7}{105}-\frac{45}{105}\right)\)

=\(16-\frac{38}{105}\)

=\(\frac{1680}{105}-\frac{38}{105}\)

=\(\frac{1642}{105}\)

b)\(\left(3\frac29\times\frac{15}{23}\times1\frac{7}{29}\right):\frac{5}{23}\)

=\(\left(\frac{29}{9}\times\frac{15}{23}\times\frac{36}{29}\right)\times\frac{23}{5}\)

=\(\left(\frac{29}{9}\times\frac{36}{29}\right)\times\left(\frac{15}{23}\times\frac{23}{5}\right)\)

=4x3

=12

\(2\frac{17}{20}-1\frac{11}{5}+6\frac{9}{20}:3\)

=\(\frac{57}{20}-\frac{16}{5}+\frac{129}{20}:3\)

=\(\frac{57}{20}-\frac{16}{5}+\frac{129}{20}\times\frac13\)

=\(\frac{57}{20}-\frac{16}{5}+\frac{129}{60}\)

=\(\frac{225}{60}-\frac{192}{60}+\frac{129}{60}\)

=\(\frac{159}{60}\)

\(a)x+30\%x=-1,31\)

\(\Leftrightarrow x+\frac{3x}{10}=-1,31\)

\(\Leftrightarrow10x+3x=-13,1\)

\(\Leftrightarrow13x=-13,1\Leftrightarrow x=-\frac{131}{130}\)

\(b)\left(x-\frac{1}{2}\right):\frac{1}{3}+\frac{5}{7}=9\frac{5}{7}\)

\(\Leftrightarrow\frac{2x-1}{2}.3+\frac{5}{7}=\frac{68}{7}\)

\(\Leftrightarrow\frac{6x-3}{2}=\frac{63}{7}\)

\(\Leftrightarrow\frac{6x-3}{2}=9\)

\(\Leftrightarrow6x-3=18\)

\(\Leftrightarrow x=\frac{7}{2}\)

\(c)\frac{1}{2}x-\frac{3}{4}=\frac{14}{9}.\frac{3}{7}\)

\(\Leftrightarrow\frac{x}{2}-\frac{3}{4}=\frac{2}{3}\)

\(\Leftrightarrow\frac{x}{2}=\frac{17}{12}\)

\(\Leftrightarrow12x=34\Leftrightarrow x=\frac{17}{6}\)

1)

a)

\(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)

\(\frac{-1}{1}.\frac{20}{5}< x< \frac{-1}{5}.\frac{3}{2}\)

\(\frac{-20}{5}< x< \frac{-3}{10}\)

\(\frac{-40}{10}< x< \frac{-3}{10}\)

\(\Rightarrow Z\in\left\{-4;-5;-6;-7;-8;-9;-10;...;-39\right\}\)

\(\left(\frac{-5}{3}\right)^3< x< \frac{-24}{35}.\frac{-5}{6}\)

\(\frac{25}{3}< x< \frac{-4}{7}.\frac{1}{1}\)

\(\frac{-25}{3}< x< \frac{-4}{7}\)

\(\frac{-175}{21}< x< \frac{-12}{21}\)

\(\Rightarrow Z\in\left\{-13;-14;-15;-16;...;-174\right\}\)

2)

a)

\(\left(\frac{9}{10}-\frac{15}{16}\right).\left(\frac{5}{12}-\frac{11}{15}-\frac{7}{20}\right)\)

\(=\left(\frac{72}{80}-\frac{75}{80}\right).\left(\frac{25}{60}-\frac{44}{60}-\frac{21}{60}\right)\)

\(=\frac{-3}{80}.\frac{-40}{60}\)

\(=\frac{-1}{-2}.\frac{-1}{-20}\)

\(=\frac{1}{40}\)