bài 1b)

\(8\frac{1}{14}-6\frac37\)

C1:\(\frac{113}{14}-\frac{45}{7}\) =\(\frac{113}{14}-\frac{90}{14}=\frac{23}{14}\)

C2:\(8\frac{1}{14}-6\frac37=\left(8-6\right)+\left(\frac{1}{14}-\frac37\right)=2+\left(\frac{1}{14}-\frac{6}{14}\right)\)

\(=2+\frac{-5}{14}=\frac{28}{14}-\frac{5}{14}=\frac{23}{14}\)

bài 1 c)\(7-3\frac67\)

C1:\(\) \(7-3\frac67=7-\frac{27}{7}=\frac{49}{7}-\frac{27}{7}=\frac{22}{7}\)

C2:\(7-3\frac67=\left(7-3\right)-\frac67=4-\frac67=\frac{28}{7}-\frac67=\frac{22}{7}\)

a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)

\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)

b)\(5+\dfrac{3}{5}=\dfrac{25}{5}+\dfrac{3}{5}=\dfrac{28}{5};10-\dfrac{9}{16}=\dfrac{160}{16}-\dfrac{9}{16}=\dfrac{151}{16}\)

\(\dfrac{2}{3}-\left(\dfrac{1}{6}+\dfrac{1}{8}\right)=\dfrac{2}{3}-\left(\dfrac{8}{48}+\dfrac{6}{48}\right)=\dfrac{2}{3}-\dfrac{14}{48}=\dfrac{32}{48}-\dfrac{14}{48}=\dfrac{3}{8}\)

Cây a, bạn nhân cả 2 vế với 3

Lấy vế nhân với 3 trừ đi ban đầu tất cả chia 2

b) Tính như bình thường

Câu c hình như sai đề

a) \(1-\frac{1}{3^{101}}\)

1. a) Ta có BCNN(12, 15) = 60 nên ta lấy mẫu chung của hai phân số là 60. 

Thừa số phụ:

60:12 =5; 60:15=4

Ta được:

\(\frac{5}{{12}} = \frac{{5.5}}{{12.5}} = \frac{{25}}{{60}}\)

\(\frac{7}{{15}} = \frac{{7.4}}{{15.4}} = \frac{{28}}{{60}}\)

 b) Ta có BCNN(7, 9, 12) = 252 nên ta lấy mẫu chung của ba phân số là 252. 

Thừa số phụ:

252:7 = 36; 252:9 = 28; 252:12 = 21

Ta được:

\(\frac{2}{7} = \frac{{2.36}}{{7.36}} = \frac{{72}}{{252}}\)

\(\frac{4}{9} = \frac{{4.28}}{{9.28}} = \frac{{112}}{{252}}\)

\(\frac{7}{{12}} = \frac{{7.21}}{{12.21}} = \frac{{147}}{{252}}\)

2. a) Ta có BCNN(8, 24) = 24 nên:

\(\frac{3}{8} + \frac{5}{{24}} = \frac{{3.3}}{{8.3}} + \frac{5}{{24}} = \frac{9}{{24}} + \frac{5}{{24}} = \frac{{14}}{{24}} = \frac{7}{{12}}\)

 b) Ta có BCNN(12, 16) = 48 nên:

\(\frac{7}{{16}} - \frac{5}{{12}} = \frac{{7.3}}{{16.3}} - \frac{{5.4}}{{12.4}} = \frac{{21}}{{48}} - \frac{{20}}{{48}} = \frac{1}{{48}}\).

\(M=\frac{-3}{4}.\frac{2}{11}+\frac{-3}{4}.\frac{9}{11}+2\frac{3}{4}\)

\(M=\frac{-3}{22}+\frac{-27}{44}+\frac{2\times4+3}{4}\)

\(M=\frac{-3}{22}+\frac{-27}{44}+\frac{11}{4}\)

\(M=\frac{-6}{44}+\frac{-27}{44}+\frac{121}{44}\)

\(M=\frac{-33}{44}+\frac{121}{44}\)

\(M=2\)

\(-\frac{2}{6}+\frac{-8}{6}=\frac{-1}{3}+\frac{-4}{3}=\frac{-5}{3}\)

\(\frac{8}{-9}-\frac{9}{-3}=-\frac{8}{9}-\frac{-9}{3}=-\frac{8}{9}-\frac{-27}{9}=\frac{19}{9}\)

\(\frac{2}{5}\cdot\frac{-2}{-5}=\frac{2}{5}\cdot\frac{2}{5}=\frac{4}{25}\)

\(\frac{6}{150}:\frac{6}{-150}=\frac{6}{150}\cdot\frac{-150}{6}=-1\)

Theo đề ta có:

\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{5}+\frac{5}{6}\right)\)\(-\left(8-\frac{2}{3}-\frac{1}{18}\right)\)

= \(5+\)\(\frac{1}{5}-\frac{2}{9}\)-\(2+\frac{1}{23}+2+\frac{3}{5}+\frac{5}{6}-8+\frac{2}{3}-\frac{1}{18}\)

=\(\left(5+2-8\right)+\left(\frac{1}{5}+\frac{3}{5}\right)-\left(\frac{2}{9}-\frac{5}{6}-\frac{2}{3}+\frac{1}{18}\right)+\frac{1}{23}\)

=  -1 +\(\frac{4}{5}\)\(-\frac{-11}{9}\)+\(\frac{1}{23}\)

= -1 +\(\frac{4}{5}+\frac{11}{9}+\frac{1}{23}\)

\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{5}+\frac{5}{6}\right)-\left(8-\frac{2}{3}-\frac{1}{18}\right)\)

= \(5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+2+\frac{3}{5}-\frac{5}{6}-8+\frac{2}{3}+\frac{1}{18}\)

= \(\left(5-8\right)+\left(\frac{1}{5}+\frac{3}{5}\right)-\left(\frac{2}{9}-\frac{1}{18}-\frac{2}{3}\right)-\left(2-2\right)+\frac{1}{23}-\frac{5}{6}\)

= \(\left(-3\right)+\frac{4}{5}+\frac{1}{2}+\frac{1}{23}-\frac{5}{6}\)

= \(\left(\left(-3\right)+\frac{4}{5}+\frac{1}{2}-\frac{5}{6}\right)+\frac{1}{23}\)

= \(-\frac{38}{15}+\frac{1}{23}\)

= \(-\frac{859}{345}\)

A= 7/8:(4/18-1/18)+7/8:(1/36-15/36)

=7/8:1/6+7/8:(-7/18)

=7/8:(1/6+-7/18)=7/8:(3/18+-7/18)=7/8:(-2/9)=-63/18=-7/2

còn ý b thì sao bạn??????

a. \(1\frac{5}{7}\)-\(\frac{9}{7}\)*\(\frac{16}{9}\)

  =\(\frac{12}{7}\)-\(\frac{16}{7}\)

  =\(\frac{-4}{7}\)

b. \(\frac{-5}{8}\):\(\frac{1}{4}\)-\(\frac{6}{13}\)*4+\(\frac{3}{8}\)

  =\(\frac{-5}{8}\cdot\)4-\(\frac{6}{13}\)*4+\(\frac{3}{8}\)

  =4*(\(\frac{-5}{8}\)-\(\frac{6}{13}\))+\(\frac{3}{8}\)

  =4*\(\frac{-113}{104}\)+\(\frac{3}{8}\)

  =\(\frac{-113}{26}\)+\(\frac{3}{8}\)

  =\(\frac{-413}{104}\)

c.( \(\frac{3}{8}\)+\(\frac{-1}{4}\)-\(\frac{5}{12}\)):\(\frac{1}{3}\)

 =\(\frac{-7}{24}\)*3

 =\(\frac{-7}{8}\)

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