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a, \(\frac{6}{7}.\frac{16}{15}.\frac{7}{6}.\frac{21}{32}=\frac{6}{7}.\frac{7}{6}.\frac{16}{15}.\frac{21}{32}\)=\(1.\frac{16}{15}.\frac{21}{32}=\frac{7}{5.2}=\frac{7}{10}\)
Phần b T2
c,\(\frac{7}{4}.\frac{11}{21}+\frac{11}{21}.\frac{5}{4}=\frac{11}{21}.\left(\frac{7}{4}+\frac{5}{4}\right)\)=\(\frac{11}{21}.3=\frac{11}{7}\)
=(1+1+1+1+1+1+1+1)+(1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45)
Đặt A = 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
Ta có:
A x 1/2= 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
1/6=1/2x3=1/2-1/3
1/12=1/3x4=1/3-1/4
……………………
1/90=1/9x10=1/9-1/10
A x 1/2=1/2-1/3+1/3-1/4+1/4-1/5+…+1/9-1/10
A x 1/2=1/2-1/10=4/10
A=4/10:1/2=4/5
Vậy 4/3+7/6+11/10+16/15+22/21+29/28+37/36+46/45=1+1+1+1+1+1+1+1+4/5=8+4/5=44/5
\(\frac{4}{3}+\frac{7}{6}+\frac{11}{10}+...+\frac{46}{45}\)
\(=1+\frac{1}{3}+1+\frac{1}{6}+1+\frac{1}{10}+...+1+\frac{1}{45}\)
\(=\left(1+1+1+...+1\right)+\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)(8 chữ số 1)
\(=8+\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)
Đặt A = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
=> \(\frac{1}{2}\)A = \(\frac{1}{2}\times\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\)
= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
Vậy A = \(\frac{2}{5}:\frac{1}{2}=\frac{4}{5}\)
Do đó biểu thức trên là 8 + \(\frac{4}{5}\) = \(\frac{44}{5}\)
Đáp số: \(\frac{44}{5}\)
Câu a: \(\frac{54}{63}\) và \(\frac{28}{63}\)
Câu b: \(\frac{55}{88}\)và \(\frac{24}{88}\)
a) \(\frac{6}{7}=\frac{6.9}{7.9}=\frac{54}{63}\)
\(\frac{4}{9}=\frac{4.7}{9.7}=\frac{28}{63}\)
b) \(\frac{5}{8}=\frac{5.11}{8.11}=\frac{55}{88}\)
\(\frac{3}{11}=\frac{3.8}{11.8}=\frac{24}{88}\)
c) \(\frac{6}{7}=\frac{6.3}{3.7}=\frac{18}{21}\)
\(\frac{5}{21}=\frac{5}{21}\)
d) \(\frac{7}{21}=\frac{7.4}{21.4}=\frac{28}{84}\)
Ta có: \(\frac{54}{11}.\frac{121}{27}< n< \frac{100}{21}:\frac{25}{126}\)
\(\Rightarrow\frac{2.11}{1.1}< n< \frac{100}{21}.\frac{126}{25}\)
\(\Rightarrow22< n< 24\)
\(\Rightarrow n=23\)
Ta có:
\(\frac{54}{11}\cdot\frac{121}{27}=\frac{54\cdot121}{11\cdot27}=22\)
\(\frac{100}{21}:\frac{25}{126}=\frac{100}{21}\cdot\frac{126}{25}=\frac{100\cdot126}{21\cdot25}=24\)
\(\Rightarrow22< n< 24\)
\(\Rightarrow x=23\)
\(a.\frac{4}{3}-\frac{3}{2}:X=\frac{1}{6}\)
\(\frac{3}{2}:X=\frac{4}{3}-\frac{1}{6}\)
\(\frac{3}{2}:X=\frac{8}{6}-\frac{1}{6}\)
\(\frac{3}{2}:X=\frac{7}{6}\)
\(X=\frac{3}{2}:\frac{7}{6}\)
\(X=\frac{3}{2}\times\frac{6}{7}\)
\(X=\frac{9}{7}\)
\(b.\left(X+\frac{2}{3}\right):\frac{1}{3}=\frac{41}{3}\)
\(X-\frac{2}{3}=\frac{41}{3}.\frac{1}{3}\)
\(X-\frac{2}{3}=\frac{41}{9}\)
\(X=\frac{41}{9}+\frac{2}{3}\)
\(X=\frac{41}{9}+\frac{6}{9}\)
\(X=\frac{47}{9}\)
ta chon phan so chung gian la:13/23
ta co: 13/23<13/21 ; 13/23>11/23
=>11/23<13/23<13/21
vay 13/21>11/23
\(\frac{69}{77}\times\frac{21}{11}=\frac{69\times21}{77\times11}=\frac{1449}{847}=\frac{207}{121}\)
\(\frac{69}{77}:\frac{21}{11}=\frac{69}{77}\times\frac{11}{21}=\frac{69\times11}{77\times21}=\frac{759}{1617}=\frac{23}{49}\)
\(\frac{66}{77}-\frac{21}{11}=\frac{66}{77}-\frac{147}{77}=\frac{66-147}{77}=\frac{-81}{77}\)
\(\frac{69}{77}+\frac{21}{11}=\frac{69}{77}+\frac{147}{77}=\frac{69+147}{77}=\frac{216}{77}\)
~ Hok tốt ~
\(\frac{69}{77}.\frac{21}{11}=\frac{207}{121}\)
\(\frac{69}{77}:\frac{21}{11}=\frac{23}{49}\)
\(\frac{69}{77}-\frac{21}{11}=-\frac{78}{77}\)
\(\frac{69}{77}+\frac{21}{11}=\frac{216}{77}\)
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