a) \(\left(-12\right).8\) với \(\left(-19\right).3\)

Ta có:

\(\left(-12\right).8=\left(-96\right)\)

\(\left(-19\right).3=\left(-57\right)\)

Mà \(\left(-96\right)< \left(-57\right)\) nên \(\left(-12\right).8< \left(-19\right).3\)

b) \(11.\left(-2\right)\) với \(\left(-3\right).10\)

Ta có:

\(11.\left(-2\right)=\left(-22\right)\)

\(\left(-3\right).10=\left(-30\right)\)

Mà \(\left(-22\right)>\left(-30\right)\) nên \(11.\left(-2\right)>\left(-3\right).10\)

Hai hình đồng dạng em nhé!

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

 A = 9 + 99 + 999 + ... + 999..99 (2019 chữ số 9)

Tổng tất cả các chữ số của A là:

  B = 9 + 9 x 2 + 9 x 3 + 9 x 2019

B = 9 x (1 + 2 + 3+ ... + 2019)

B = 9 x (2019 + 1)x[(2019 - 1) : 1 + 1] : 2

B = 18352710

Lời giải:
$T = \frac{1}{7^2}+\frac{2}{7^3}+\frac{3}{7^4}+....+\frac{99}{7^{100}}$
$7T = \frac{1}{7}+\frac{2}{7^2}+\frac{3}{7^3}+....+\frac{99}{7^{99}}$

$\Rightarrow 6T=7T-T = \frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{99}}-\frac{99}{7^{100}}$
$42T = 1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{98}}-\frac{99}{7^{99}}$

$\Rightarrow 42T-6T = 1-\frac{100}{7^{99}}+\frac{99}{7^{100}}$

$\Rightarrow 36T = 1-\frac{601}{7^{100}}< 1$

$\Rightarrow T< \frac{1}{36}$

1\(\dfrac{ }{ }\)3/5

Hỗn số 1 và 3/5 là:

\(1\dfrac{3}{5}\)

\(a,-\dfrac{9}{4}< 0;\dfrac{1}{3}>0.Nên:-\dfrac{9}{4}< \dfrac{1}{3}\\ b,-\dfrac{8}{3}< -2;\dfrac{4}{-7}>-1.Nên:-\dfrac{8}{3}< -2< -1< \dfrac{4}{-7}\\ Vậy:-\dfrac{8}{3}< \dfrac{4}{-7}\\ c,\dfrac{9}{-5}< -1;\dfrac{7}{-10}>-1.Nên:\dfrac{9}{-5}< -1< \dfrac{7}{-10}.Vậy:\dfrac{9}{-5}< \dfrac{7}{-10}\\ d,\dfrac{3}{14}>0;-\dfrac{6}{14}< 0.Nên:\dfrac{3}{14}>0>-\dfrac{6}{14}.Vậy:\dfrac{3}{14}>-\dfrac{6}{14}\\ e,\dfrac{7}{-12}=\dfrac{7.3}{-12.3}=\dfrac{21}{-36};\dfrac{11}{-18}=\dfrac{11.2}{-18.2}=\dfrac{22}{-36}\\ Vì:\dfrac{21}{-36}>\dfrac{22}{-36}.Nên:\dfrac{7}{-12}>\dfrac{11}{-18}\)

\(f,-\dfrac{4}{7}< -\dfrac{1}{2};-\dfrac{4}{10}>\dfrac{-1}{2}.Nên:-\dfrac{4}{7}< -\dfrac{1}{2}< -\dfrac{4}{10}.Vậy:-\dfrac{4}{7}< -\dfrac{4}{10}\\ g,-\dfrac{8}{15}< -\dfrac{1}{2};\dfrac{5}{-24}>-\dfrac{1}{2}.Nên:-\dfrac{8}{15}< -\dfrac{1}{2}< \dfrac{5}{-24}.Vậy:-\dfrac{8}{15}< \dfrac{5}{-24}\\ h,\dfrac{69}{-230}=\dfrac{69:23}{-230:23}=\dfrac{3}{-10};\dfrac{-39}{143}=\dfrac{-39:13}{143:13}=\dfrac{-3}{11}\\ Vì:\dfrac{-3}{10}< -\dfrac{3}{11}.Vậy:\dfrac{69}{-230}< \dfrac{-39}{143}\\ i,\dfrac{7}{41}=1-\dfrac{34}{41};\dfrac{13}{47}=1-\dfrac{34}{47}\\ Vì:\dfrac{34}{41}>\dfrac{34}{47}.Nên:1-\dfrac{34}{41}< 1-\dfrac{34}{47}.Vậy:\dfrac{7}{41}< \dfrac{13}{47}\)

suy ra: 20 x 21 = 12 x ( 41- x)

           420 = 492 -12x

            12x= 492-420

            12x= 72

               x= 72 ;12

              x = 6
 vậy x=6

\(\dfrac{20}{41-x}=\dfrac{12}{21}\)

\(41-x=20:\dfrac{12}{21}\)

\(41-x=20\times\dfrac{21}{12}\)

\(41-x=\dfrac{420}{12}\)

\(41-x=35\)

\(x=41-35\)

\(x=6\)

Vậy \(=6\)

25 x 4 + 25 x 7 + 25

= 25 x 4 + 25 x 7 + 25 x 1

= 25 x (4 + 7 + 1)

= 25 x 12

= 300

25x4+25x7+25

=25x4+25x7+25x1

=25x(4+7+1)

=25x12

=300

Tổng số tuổi 2 chị em Quyên:

40 : 2 = 20 (tuổi)

Khi mẹ 49 tuổi thì hai chị em Quyên tổng tuổi là:

(49 - 40) x 2 + 20 = 38 (tuổi)

Khi mẹ 49 tuổi thì Quyên:

(38 - 6):2= 16 (tuổi)

Khi mẹ 49 tuổi thì chị của Quyên:

16 + 6 = 22 (tuổi)

Đ.số::............

Bài 4:

a; \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) = \(\dfrac{5}{20}\) - \(\dfrac{4}{20}\) = \(\dfrac{1}{20}\)

b; \(\dfrac{3}{5}\) - \(\dfrac{-1}{2}\) = \(\dfrac{6}{10}\) + \(\dfrac{5}{10}\) = \(\dfrac{11}{10}\)

c; \(\dfrac{3}{5}\) - \(\dfrac{-1}{3}\) = \(\dfrac{9}{15}\) + \(\dfrac{5}{15}\) = \(\dfrac{14}{15}\)

d; \(\dfrac{-5}{7}\) - \(\dfrac{1}{3}\)= \(\dfrac{-15}{21}\) - \(\dfrac{7}{21}\)= \(\dfrac{-22}{21}\)

Bài 5

a; 1 + \(\dfrac{3}{4}\) = \(\dfrac{4}{4}\) + \(\dfrac{3}{4}\) = \(\dfrac{7}{4}\)       b; 1 - \(\dfrac{1}{2}\) = \(\dfrac{2}{2}\) - \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\)

c; \(\dfrac{1}{5}\) - 2 = \(\dfrac{1}{5}\) - \(\dfrac{10}{5}\) = \(\dfrac{-9}{5}\)     d; -5 - \(\dfrac{1}{6}\) = \(\dfrac{-30}{6}\) - \(\dfrac{1}{6}\) = \(\dfrac{-31}{6}\)

e; - 3 - \(\dfrac{2}{7}\)= \(\dfrac{-21}{7}\) - \(\dfrac{2}{7}\)= \(\dfrac{-23}{7}\)     f; - 3 + \(\dfrac{2}{5}\) = \(\dfrac{-15}{5}\) + \(\dfrac{2}{5}\)= - \(\dfrac{13}{5}\)

g; - 3 - \(\dfrac{2}{3}\) = \(\dfrac{-9}{3}\) - \(\dfrac{2}{3}\) = \(\dfrac{-11}{3}\)     h; - 4 - \(\dfrac{-5}{7}\) = \(\dfrac{-28}{7}\)+ \(\dfrac{5}{7}\) = - \(\dfrac{23}{7}\)