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a, (1200+60) :12= 1200: 12+ 60:12= 100 +5= 105
b, (2100-42) :21= 2100: 21-42: 21= 100- 2=98
Mình có cách khác nhé :
a ) ( 1200 + 60 ) : 12
= ( 12 x 100 + 12 x 5 ) : 12
= 12 x ( 100 + 5 ) : 12
= 12 x 105 : 12
= 105
b ) ( 2100 - 42 ) : 21
= ( 21 x 100 - 21 x 2 ) : 21
= 21 x ( 100 - 2 ) : 21
= 21 x 98 : 21
= 98
A=1/15+1/21+1/28+....+1/190
1/2A=1/30+1/42+1/56+.....+1/380
1/2A=1/5.6+1/6.7+1/7.8+....+1/19.20
1/2A=1/5-1/6+1/6-1/7+1/7-1/8+......+1/19-1/20
1/2A=1/5-1/20
1/2A=3/20
A=3/20:1/2
A=3/10
Rút gọn biểu thức cho 3 ta được biểu thức mới là
\(\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+...\frac{4}{700}\)
= \(\frac{4}{4.7}+\frac{4}{7.10}+\frac{4}{10.13}+...+\frac{4}{25.28}\)
=\(\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
= \(\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
= \(\frac{4}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
= \(\frac{4}{3}.\frac{3}{14}\)
= \(\frac{2}{7}\)
\(F=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\)
\(\Rightarrow\)\(\frac{1}{2}F=\frac{1}{2}.\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\right)\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{380}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{19.20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{4}{20}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{3}{20}\)
\(\Rightarrow\)\(F=\frac{3}{20}\div\frac{1}{2}\)
\(\Rightarrow\) \(F=\frac{3}{20}.2\)
\(\Rightarrow\)\(F=\frac{3}{10}\)
\(F=\frac{1}{15}+\frac{ 1}{21}+...+\frac{1}{190}\)
\(F=\frac{2}{30}+\frac{2}{21}+...+\frac{2}{380}\)
\(F=\frac{2}{5.6}+...+\frac{2}{19.20}\)
\(F=2.\left(\frac{1}{5.6}+...+\frac{1}{19.20}\right)\)
\(F=2.\left(\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(F=2\left[\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{6}\right)-...-\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{20}\right]\)
\(F=2.\left(\frac{1}{5}-\frac{1}{20}\right)\)
\(F=2.\frac{3}{20}\)
\(F=\frac{6}{20}=\frac{3}{10}\)
\(G=\frac{12}{84}+\frac{12}{210}+...+\frac{12}{2100}\)
\(G=\frac{4}{28}+\frac{4}{70}+...+\frac{4}{700}\)
\(G=\frac{4}{4.7}+\frac{4}{7.10}+...+\frac{4}{25.28}\)
\(G=\frac{4}{3}.\left(\frac{3}{4.7}+...+\frac{3}{25.28}\right)\)
\(G=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{7}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(G=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(G=\frac{4}{3}.\frac{6}{28}\)
\(G=\frac{2}{7}\)
Tổng của G và F là : \(\frac{3}{10}+\frac{2}{7}=\frac{21}{70}+\frac{20}{70}=\frac{41}{70}\)
ai trả lời đúng được k nha các bạn. Giúp mình đi, mình đang vội
Bn tham khảo ở đây nha trang nhí nhảnh
Câu hỏi của Tran Mai - Toán lớp 6 | Học trực tuyến
Tính các tổng dưới đây sau khi đã rút gọn phân số :
a)\(\dfrac{7}{21}\) + \(\dfrac{9}{-36}\) = \(\dfrac{7}{21}\)+\(\dfrac{-9}{36}\)=\(\dfrac{1}{3}\)+\(\dfrac{-1}{4}\)=\(\dfrac{4}{12}\)+\(\dfrac{-3}{12}\)=\(\dfrac{1}{12}\)
b) \(\dfrac{-12}{18}\)+\(\dfrac{-21}{35}\)=\(\dfrac{-2}{3}\)+\(\dfrac{-3}{5}\)=\(\dfrac{-10}{15}\)+\(\dfrac{-9}{15}\)=\(\dfrac{-19}{15}\)
c) \(\dfrac{-3}{21}\)+\(\dfrac{6}{42}\)=\(\dfrac{-1}{7}\)+\(\dfrac{1}{7}\)=0
d) \(\dfrac{-18}{24}\)+\(\dfrac{15}{-21}\)=\(\dfrac{-18}{24}\)+\(\dfrac{-15}{21}\)=\(\dfrac{-3}{4}\)+\(\dfrac{-5}{7}\)=\(\dfrac{-21}{28}\)+\(\dfrac{-20}{28}\)=\(\dfrac{-41}{28}\)
a) \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\frac{1}{5}+\frac{8}{21}+\frac{2}{5}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
= \(\left(\frac{1}{5}+\frac{2}{5}+\frac{-3}{5}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)+\frac{3}{20}\)
\(=\frac{0}{5}+\frac{0}{21}+\frac{3}{20}\)
\(=0+0+\frac{3}{20}\)
\(=\frac{3}{20}\)
b) \(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)
\(=\frac{21}{23}+\frac{125}{93}+\frac{-21}{23}+\frac{-125}{143}\)
\(=\left(\frac{21}{23}+\frac{-21}{23}\right)+\frac{125}{93}+\frac{-125}{143}\)
\(=0+\frac{125}{93}+\frac{-125}{143}\)
\(=\frac{17875}{13299}+\frac{-11625}{13299}\)
\(=\frac{6250}{13299}\)
(Hình như câu b hơi sai)
\(a)\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{10}{21}+\frac{3}{20}\)
\(=\frac{1}{5}+\frac{8}{21}+\frac{2}{5}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\left(\frac{1}{5}+\frac{2}{5}+\frac{-3}{5}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)+\frac{3}{20}\)
\(=0+0+\frac{3}{20}\)
\(=\frac{3}{20}\)
\(\frac{4}{20}+\frac{16}{42}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20} =\left(\frac{4}{20}+\frac{-12}{20}+\frac{3}{20}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)=\frac{-1}{4}\)
(2100 – 42) : 21 = 2100 : 21 – 42 : 21 = 100 – 2 = 98