Bài 1:

\(\frac{3}{5}+\frac{4}{15}=\frac{9}{15}+\frac{4}{15}=\frac{13}{15}\)

\(\frac{5}{6}:\frac{-7}{12}=\frac{5}{6}.\frac{-12}{7}=\frac{-60}{42}=\frac{-10}{7}\)

\(\frac{-21}{24}:\frac{-14}{8}=\frac{-21}{24}.\frac{-8}{14}=\frac{168}{336}=\frac{1}{2}\)

\(\frac{4}{5}:\frac{-8}{15}=\frac{4}{5}.\frac{-15}{8}=\frac{-60}{40}=\frac{-3}{2}\)

\(\frac{5}{12}-\frac{-7}{6}=\frac{5}{12}+\frac{7}{6}=\frac{5}{12}+\frac{14}{12}=\frac{19}{12}\)

\(\frac{-15}{16}.\frac{8}{25}=\frac{-120}{400}=\frac{-3}{10}\)

Bài 2 :

\(6\frac{4}{5}-\left(1\frac{2}{3}+3\frac{4}{5}\right)\)

\(=\frac{34}{5}-\left(\frac{5}{3}+\frac{19}{5}\right)\)

\(=\frac{34}{5}-\frac{5}{3}-\frac{19}{5}\)

\(=\left(\frac{34}{5}-\frac{19}{5}\right)-\frac{5}{3}\)

\(=3-\frac{5}{3}\)

\(=\frac{4}{3}\)

\(6\frac{5}{7}-\left(1\frac{2}{3}+2\frac{5}{7}\right)\)

\(=\frac{47}{7}-\left(\frac{5}{3}+\frac{19}{7}\right)\)

\(=\frac{47}{7}-\frac{5}{3}-\frac{19}{7}\)

\(=\left(\frac{47}{7}-\frac{19}{7}\right)-\frac{5}{3}\)

\(=4-\frac{5}{3}\)

\(=\frac{7}{3}\)

\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)

\(=\left(\frac{4}{19}+\frac{15}{19}\right).\frac{-3}{7}+\frac{5}{7}\)

\(=1.\frac{-3}{7}+\frac{5}{7}\)

\(=\frac{-3}{7}+\frac{5}{7}\)

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

\(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

\(=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)\)

\(=\frac{5}{9}.1\)

\(=\frac{5}{9}\)

Bài 3 :

\(\frac{x}{5}=\frac{2}{3}\)

\(\Rightarrow x.3=5.2\)

\(\Rightarrow x.3=10\)

\(\Rightarrow x=\frac{10}{3}\)

\(\frac{x}{3}-\frac{1}{2}=\frac{1}{5}\)

\(\frac{x}{3}=\frac{1}{5}+\frac{1}{2}\)

\(\frac{x}{3}=\frac{7}{10}\)

\(\Rightarrow x.10=3.7\)

\(\Rightarrow x.10=21\)

\(\Rightarrow x=\frac{21}{10}\)

\(\frac{4}{5}+x=\frac{2}{3}\)

\(x=\frac{2}{3}-\frac{4}{5}\)

\(x=\frac{-2}{15}\)

\(\frac{3}{4}-x=\frac{1}{3}\)

\(x=\frac{3}{4}-\frac{1}{3}\)

\(x=\frac{5}{12}\)

\(x-\frac{5}{9}=\frac{-2}{3}\)

\(x=\frac{-2}{3}+\frac{5}{9}\)

\(x=\frac{-1}{9}\)

\(\frac{1}{2}x+\frac{1}{2}=\frac{5}{2}\)

\(\frac{1}{2}x=\frac{5}{2}-\frac{1}{2}\)

\(\frac{1}{2}x=2\)

\(x=2:\frac{1}{2}\)

\(x=4\)

\(\frac{-2}{3}-\frac{1}{3}.\left(2x-5\right)=\frac{3}{2}\)

\(\frac{1}{3}.\left(2x-5\right)=\frac{-2}{3}-\frac{3}{2}\)

\(\frac{1}{3}.\left(2x-5\right)=\frac{-19}{10}\)

\(2x-5=\frac{-19}{10}:\frac{1}{3}\)

\(2x-5=\frac{-57}{10}\)

\(2x=\frac{-57}{10}+5\)

\(2x=\frac{-7}{10}\)

\(x=\frac{-7}{10}:2\)

\(x=\frac{-7}{20}\)

\(3\frac{1}{3}+\frac{5}{6}x=3\frac{2}{1}\)

\(\frac{10}{3}+\frac{5}{6}x=5\)

\(\frac{5}{6}x=5-\frac{10}{3}\)

\(\frac{5}{6}x=\frac{5}{3}\)

\(x=\frac{5}{3}:\frac{5}{6}\)

\(x=2\)

\(\frac{3}{8}-\frac{1}{6}x=\frac{1}{4}\)

\(\frac{1}{6}x=\frac{3}{8}-\frac{1}{4}\)

\(\frac{1}{6}x=\frac{1}{8}\)

\(x=\frac{1}{8}:\frac{1}{6}\)

\(x=\frac{3}{4}\)

a )  \(-\frac{3}{7}.\frac{3}{11}+-\frac{3}{7}.\frac{8}{11}+1\frac{3}{7}\)

\(=-\frac{3}{7}.\left(\frac{3}{11}+\frac{8}{11}\right)+\frac{10}{7}\)

\(=-\frac{3}{7}.\frac{11}{11}+\frac{10}{7}\)

\(=-\frac{3}{7}.1+\frac{10}{7}\)

\(=\frac{10}{7}\)

b )   \(75\%.10,5=\frac{3}{4}.10,5=7,875\)

c )  \(5-3.\left(\left|-4\right|-30:15\right)\)

\(=5-3.\left(4-2\right)\)

\(=5-3.2\)

\(=5-6\)

\(=-1\)

d )  \(-\frac{5}{7}.\frac{2}{11}+-\frac{5}{7}.\frac{9}{11}+1\frac{5}{7}\)

\(=-\frac{5}{7}.\left(\frac{2}{11}+\frac{9}{11}\right)+\frac{12}{7}\)

\(=-\frac{5}{7}.1+\frac{12}{7}\)

\(=\frac{7}{7}\)

\(=1\)

Chúc bạn học tốt !!! 

đặt tên biểu thức là S

ta có :

S = 7⁰ + 7¹ + 7² + ... + 7⁹⁹

7S = 7 . ( 7⁰ + 7¹ + 7² + ... + 7⁹⁹ )

7S = 7¹ + 7² + 7³ + ... + 7¹⁰⁰

7S - S = ( 7¹ + 7² + 7³ + ... + 7¹⁰⁰ ) - ( 7⁰ + 7¹ + 7² + ... + 7⁹⁹ )

6S = 7¹⁰⁰ - 7⁰

S = ( 7¹⁰⁰ - 7⁰ ) : 6

7^{0+1+2+3+4+5+...+99}

Đặt A=7⁰+7¹+7²+...+7⁹⁹

=>7A=7¹+7²+7³+...+7¹⁰⁰

=>7A-A=(7¹+7²+7³+...+7¹⁰⁰) - (7⁰+7¹+7²+...+7⁹⁹)

=>6A=7¹⁰⁰-7⁰

=>A=\(\frac{7^{100}-1}{6}\)

= không có đâu

tik nha Trúc Vũ

ủng hộ mình nha

Bạn trả lời đi

a) \(6.\left(-3\right)+\left(-4\right).\left(-5\right)=\left(-18\right)+20=2\)

b) \(\dfrac{2}{5}-\dfrac{1}{3}=\dfrac{6}{15}-\dfrac{5}{15}=\dfrac{1}{15}\) ( cái này hình như k chuyển dc thành hỗn số bn à)

c) \(\dfrac{-3}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-3}{5}+\dfrac{3}{5}\)\(=\dfrac{-3}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-3}{5}+\left(-1\right).\dfrac{-3}{5}\)

\(=\dfrac{-3}{5}.\left(\dfrac{4}{7}+\dfrac{3}{7}+\left(-1\right)\right)=\dfrac{-3}{5}.0=0\)

Chúc bn học tốt

\(a,6.\left(-3\right)+\left(-4\right).\left(-5\right)\)

\(=-18+20\)

\(=2\)

\(b,2\dfrac{3}{5}-1\dfrac{2}{3}\)

\(=\dfrac{13}{5}-\dfrac{5}{3}\)

=\(\dfrac{14}{15}\)

\(c,\dfrac{-3}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-3}{5}+\dfrac{3}{5}\)

\(=\dfrac{-3}{5}.\left[\dfrac{4}{7}+\dfrac{3}{7}+\left(-1\right)\right]\)

\(=\dfrac{-3}{5}.0\)

\(=0\)

a) 5.(-2)-(-3).(-4)=(-10).(-3).(-4)
=30.(-4)
=-120

b) \(\dfrac{13}{7}-\dfrac{3}{14}=\dfrac{13}{7}+\dfrac{-3}{14}=\dfrac{26}{14}+\dfrac{-3}{14}=\dfrac{23}{14}\)

c) chả biết bạn viết cái j

= 3

:>>>

giải thích: \(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}=\dfrac{21}{7}=3\)

:>>>

= 3 nhé