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30 tháng 8 2023
\(\dfrac{2}{3}+\dfrac{5}{6}+\dfrac{9}{10}+\dfrac{14}{15}+\dfrac{20}{21}+\dfrac{27}{28}+\dfrac{35}{36}+\dfrac{44}{45}\\ =\left(1-\dfrac{1}{3}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{10}\right)+\left(1-\dfrac{1}{15}\right)+\left(1-\dfrac{1}{21}\right)+\left(1-\dfrac{1}{28}\right)+\left(1-\dfrac{1}{36}\right)+\left(1-\dfrac{1}{45}\right)\\ =8-\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}\right)\\ =8-\left(\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\\ =8-\left(\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+\dfrac{2}{9.10}\right)\\ =8-2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\\ =8-2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =8-2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=8-2.\dfrac{2}{5}=8-\dfrac{4}{5}=\dfrac{36}{5}\)
HT
Hồ Tuyết Anh
VIP
16 tháng 3 2022
\(e.\dfrac{7}{10}\cdot\dfrac{-3}{5}+\dfrac{7}{10}\cdot\dfrac{-2}{5}-\dfrac{3}{10}\)
\(=\dfrac{7}{10}\cdot\left[\left(\dfrac{-3}{5}\right)+\left(\dfrac{-2}{5}\right)\right]-\dfrac{3}{10}\)
\(=\dfrac{7}{10}\cdot1-\dfrac{3}{10}=\dfrac{4}{10}=\dfrac{2}{5}\)
\(f.\dfrac{-3}{7}\cdot\dfrac{5}{9}+\dfrac{4}{9}\cdot\dfrac{-3}{7}+2\dfrac{3}{7}\)
\(=\dfrac{-3}{7}\cdot\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{17}{3}\)
\(=\dfrac{-3}{7}\cdot1+\dfrac{17}{3}=\dfrac{-9}{21}+\dfrac{119}{21}=\dfrac{110}{21}\)
\(g.\dfrac{5}{9}\cdot\dfrac{10}{17}+\dfrac{5}{9}\cdot\dfrac{9}{17}-\dfrac{5}{9}\cdot\dfrac{2}{17}\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{10}{17}+\dfrac{9}{17}-\dfrac{2}{17}\right)\)
\(=\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)
19 tháng 2 2022
a: =-10/21
b: =-5/27
c: =-20/20=-1
d: =-15/105=-1/7
e: =-63/63=-1
AK
19 tháng 2 2022
\(\dfrac{10}{21}\)
\(\dfrac{5}{27}\)
\(1\)
\(\dfrac{1}{7}\)
\(1\)
21 tháng 2 2022
\(=\dfrac{85}{18}:\dfrac{85}{9}-\dfrac{136}{45}:\dfrac{136}{15}=\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{1}{6}\)
74
22 tháng 4
Để tính tổng của biểu thức này, chúng ta cần thực hiện các phép cộng và trừ theo thứ tự từ trái sang phải.
\[4 + \frac{5}{6} - \frac{1}{9} \times \frac{1}{10} - \frac{7}{12} + \frac{1}{36} - 3 - \frac{1}{5} + \frac{1}{3} - \frac{1}{9} \times \frac{9}{5} + 1 - \frac{1}{3}\]
Đầu tiên, chúng ta sẽ làm các phép tính liên quan đến phân số:
\[= 4 + \frac{5}{6} - \frac{1}{90} - \frac{7}{12} + \frac{1}{36} - 3 - \frac{1}{5} + \frac{1}{3} - \frac{1}{5} + 1 - \frac{1}{3}\]
Tiếp theo, chúng ta sẽ tổng hợp các phân số:
\[= 4 + \frac{5}{6} - \frac{1}{90} - \frac{35}{90} + \frac{5}{180} - 3 - \frac{18}{90} + \frac{60}{180} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{1}{90} - \frac{35}{90} + \frac{5}{180} - 3 - \frac{2}{10} + \frac{10}{30} - \frac{2}{10} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{1}{90} - \frac{35}{90} + \frac{5}{180} - 3 - \frac{1}{5} + \frac{1}{3} - \frac{1}{5} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{36 + 35}{90} + \frac{5}{180} - 3 - \frac{1}{5} + \frac{2}{6} - \frac{1}{5} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - 3 - \frac{1}{5} + \frac{1}{3} - \frac{1}{5} + 1 - \frac{1}{3}\]
Tiếp theo, chúng ta sẽ tính tổng các số nguyên:
\[= 4 - 3 + 1\]
Cuối cùng, chúng ta sẽ tổng hợp các phân số:
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{1}{5} + \frac{1}{3} - \frac{1}{5} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{30}{90}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6} - \frac{71}{90} + \frac{5}{180} - \frac{18}{90} + \frac{30}{90} - \frac{18}{90} + 1 - \frac{1}{3}\]
\[= 4 + \frac{5}{6}
1 tháng 7 2023
2:
a: 2/9-x=-5/9
=>x=2/9+5/9=7/9
b: x-7/13=1/2
=>x=1/2+7/13=27/26
S
12 tháng 2
câu a
\(\dfrac{7}{4}+\dfrac{3}{2}+\dfrac{-9}{16}\\ =\dfrac{28}{16}+\dfrac{24}{16}-\dfrac{9}{16}=\dfrac{43}{16}\)
câu b
\(-\dfrac{2}{7}+\dfrac{3}{5}+\dfrac{9}{7}+\dfrac{-18}{5}\\ =-\dfrac{10}{35}+\dfrac{21}{35}+\dfrac{45}{35}-\dfrac{126}{35}\\ =-\dfrac{70}{35}=-2\)
câu c
\(-\dfrac{5}{13}+\dfrac{11}{10}-\dfrac{-9}{10}+\dfrac{-8}{13}\\ =-\dfrac{5}{13}+\dfrac{11}{10}+\dfrac{9}{10}-\dfrac{8}{13}\\ =-\dfrac{50}{130}+\dfrac{143}{130}+\dfrac{117}{130}-\dfrac{80}{130}\\ =\dfrac{130}{130}=1\)
bài 2
câu a
\(\dfrac{2}{9}-x=-\dfrac{5}{9}\\ x=\dfrac{2}{9}-\dfrac{-5}{9}\\ x=\dfrac{7}{9}\)
câu b
\(x+\dfrac{-7}{13}=\dfrac{1}{2}\\ x=\dfrac{1}{2}-\dfrac{-7}{13}\\ x=\dfrac{13}{26}+\dfrac{14}{26}\\ x=\dfrac{17}{26}\)
3 tháng 4 2021
a) Ta có: \(\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-1}{5}\)
\(\Leftrightarrow\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-5}{25}=\dfrac{2}{25}\)
hay \(x=\dfrac{6}{25}\)
Vậy: \(x=\dfrac{6}{25}\)
3 tháng 4 2021
b) Ta có: \(\dfrac{4}{9}+\dfrac{x}{5}=\dfrac{5}{11}\)
\(\Leftrightarrow\dfrac{x}{5}=\dfrac{5}{11}-\dfrac{4}{9}=\dfrac{45}{99}-\dfrac{44}{99}=\dfrac{1}{99}\)
hay \(x=\dfrac{5}{99}\)
Vậy: \(x=\dfrac{5}{99}\)
Y
3 tháng 4 2022
\(a,x=\dfrac{1}{5}+\dfrac{-3}{7}\)
\(x=\dfrac{7}{35}+\dfrac{-15}{35}\)
\(x=-\dfrac{8}{35}\)
\(b,\dfrac{3}{5}-\dfrac{4}{7}:x=\dfrac{-9}{10}\)
\(\dfrac{4}{7}:x=\dfrac{3}{5}-\dfrac{-9}{10}\)
\(\dfrac{4}{7}:x=\dfrac{3}{2}\)
\(x=\dfrac{4}{7}:\dfrac{3}{2}\)
\(x=\dfrac{4}{7}\times\dfrac{2}{3}\)
\(x=\dfrac{8}{21}\)
\(c,x-\left(\dfrac{-3}{4}\right)=\dfrac{-2}{3}-\dfrac{1}{2}\)
\(x+\dfrac{3}{4}=\dfrac{-4}{6}-\dfrac{3}{6}\)
\(x+\dfrac{3}{4}=-\dfrac{7}{6}\)
\(x=-\dfrac{7}{6}-\dfrac{3}{4}\)
\(x=-\dfrac{23}{12}\)
\(d,\dfrac{-5}{9}-x=\dfrac{1}{3}+\dfrac{7}{18}\)
\(\dfrac{-5}{9}-x=\dfrac{6}{18}+\dfrac{7}{18}\)
\(\dfrac{-5}{9}-x=\dfrac{13}{18}\)
\(x=\dfrac{-5}{9}-\dfrac{13}{18}\)
\(x=\dfrac{-10}{18}-\dfrac{13}{18}\)
\(x=-\dfrac{23}{18}\)
S
1 tháng 4 2021
\(\dfrac{2}{3}+\dfrac{1}{5}.\dfrac{10}{7}=\dfrac{2}{3}+\dfrac{10}{35}=\dfrac{70}{105}+\dfrac{30}{105}=\dfrac{100}{105}=\dfrac{50}{21}\)
1 tháng 4 2021
a) Ta có: \(\dfrac{2}{3}+\dfrac{1}{5}\cdot\dfrac{10}{7}\)
\(=\dfrac{2}{3}+\dfrac{2}{7}\)
\(=\dfrac{14}{21}+\dfrac{6}{21}\)
\(=\dfrac{20}{21}\)
\(\dfrac{3}{-5}-\dfrac{9}{10}=\dfrac{-6}{10}-\dfrac{9}{10}=\dfrac{-15}{10}=-\dfrac{3}{2}\)