8/19, 16/?, 8/18

=> 16/? = 8/17

=> 16/? = 16/34

=> ? = 34

\(\frac{8}{19}< \frac{16}{?}< \frac{8}{18}\)

\(\Leftrightarrow\frac{16}{38}< \frac{16}{?}< \frac{16}{36}\)

Từ đây dễ thấy ? = 37

1+2-3-4+5+6-7-8+9+10-11-12+13+14....................+301+302
=1+(2-3-4+5)+(6-7-8+9)+(10-11-12+13)+...................+(298-299-300+301)+302
=1+302
=303

1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 + ... + 301 + 302

= (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) + (9 + 10 - 11 - 12) + ... + (297 + 298 - 299 - 300) + 301 + 302

= -4 - 4 - 4 - ... - 4 + 301 + 302

= -(4 + 4 + ... + 4) + 603

= -300 + 603 = 303

=16/27

\(\frac{4}{3}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}:\frac{9}{8}\)

=\(\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)

=\(\frac{16}{27}\)   

\(\frac{6\cdot35\cdot24}{7\cdot18\cdot96}=\frac{6\cdot7\cdot5\cdot24}{7\cdot6\cdot3\cdot24\cdot4}=\frac{5}{12}\)

Chọn a

1. a

\(\dfrac{8}{5}-\dfrac{5}{6}\cdot\dfrac{3}{4}\)

\(=\dfrac{8}{5}-\dfrac{5\cdot3}{3\cdot2\cdot4}\)

\(=\dfrac{8}{5}-\dfrac{5}{8}=\dfrac{39}{40}\)

1.b

\(=\dfrac{7}{8}+\dfrac{5}{6}\cdot\dfrac{3}{2}\)

\(=\dfrac{7}{8}+\dfrac{5\cdot3}{3\cdot2\cdot2}\)

\(=\dfrac{7}{8}+\dfrac{5}{4}=\dfrac{17}{8}\)

2.a

\(\dfrac{4}{5}+x=\dfrac{11}{10}\)

\(x=\dfrac{11}{10}-\dfrac{4}{5}=\dfrac{3}{10}\)

2.b

\(x-\dfrac{3}{4}=\dfrac{5}{7}\)

\(x=\dfrac{5}{7}+\dfrac{3}{4}=\dfrac{41}{28}\)

Câu 1 bạn làm vậy đúng rồi 

Câu 2 

ab x 8 +ab = 2ab 

abx8 = 2ab-ab

abx8 =200

     ab = 200 : 8

     ab = 25

câu 2 này:

      ab x 8 + ab =2ab

     ab x 8          =2ab-ab

     ab x 8          =200

        ab            =200:8

            ab        = 25 

 Vậy ab bằng 25 thử lại  25 x 8 +25=225 (đúng)

\(\frac{5}{6}+\frac{7}{9}:\frac{5}{6}-\frac{1}{6}\)

\(=\left(\frac{5}{6}-\frac{1}{6}\right)+\frac{7}{9}.\frac{6}{5}\)

\(=\frac{2}{3}+\frac{14}{15}\)

\(=\frac{10}{15}+\frac{14}{15}=\frac{24}{15}\)

\(\frac{8}{11}.\frac{7}{8}+\frac{8}{11}:\frac{4}{5}\)

\(=\frac{7}{11}+\frac{8}{11}.\frac{5}{4}\)

\(=\frac{7}{11}+\frac{10}{11}\)

\(=\frac{17}{11}\)

\(\frac{5}{6}+\frac{7}{9}:\frac{5}{6}-\frac{1}{6}\)                                                                        \(\frac{8}{11}x\frac{7}{8}+\frac{8}{11}:\frac{4}{5}\)

\(=\frac{5}{6}+\frac{14}{15}-\frac{1}{6}\)                                                                    \(=\frac{8}{11}x\frac{7}{8}+\frac{8}{11}x\frac{5}{4}\)

\(=\left(\frac{5}{6}-\frac{1}{6}\right)+\frac{14}{15}\)                                                                 \(=\frac{8}{11}x\left(\frac{7}{8}+\frac{5}{4}\right)\)

\(=\frac{2}{3}+\frac{14}{15}\)                                                                                     \(=\frac{8}{11}x\frac{17}{8}\)

\(=\frac{8}{5}\)                                                                                                      \(=\frac{17}{11}\)

1.3.77−1​+3.7.99−3​+7.9.1313−7​+9.13.1515−9​+\frac{19-13}{13.15.19}+13.15.1919−13​

=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}=1.31​−3.71​+3.71​−7.91​+7.91​−9.131​+9.131​−13.151​+13.151​−15.191​

=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31​−15.191​=28595​−2851​=28594​

b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)b,=61​.(1.3.76​+3.7.96​+7.9.136​+9.13.156​+13.15.196​)

làm giống như trên

c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)c,=81​.(1.2.31​+2.3.41​+3.4.51​+...+48.49.501​)

=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)=161​.(1.2.32​+2.3.42​+3.4.52​+...+48.49.502​)

=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)=161​.(1.2.33−1​+2.3.44−2​+3.4.55−3​+...+48.49.5050−48​)

=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)=161​.(1.21​−2.31​+2.31​−3.41​+3.41​−4.51​+...+48.491​−49.501​)

=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}=161​.(21​−24501​)=161​.(24501225​−24501​)=4900153​

d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)d,=75​.(1.5.87​+5.8.127​+8.12.157​+...+33.36.407​)

=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)=75​.(1.5.88−1​+5.8.1212−5​+8.12.1515−8​+...+33.36.4040−33​)

=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)=75​.(1.51​−5.81​+5.81​−8.121​+8.121​−12.151​+...+33.361​−36.401​)

=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}=75​.(51​−14401​)=75​.(1440288​−14401​)=28841​

P/S: . là nhân nha