15/12-(-5/13)-3/12-8/13
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\(5:8=\dfrac{5}{8}\\ 7:12=\dfrac{7}{12}\\ 13:15=\dfrac{13}{15}\\ 12:17=\dfrac{12}{17}\\ 8:11=\dfrac{8}{11}\\ 6:13=\dfrac{6}{13}\\ 18:21=\dfrac{18}{21}=\dfrac{6}{7}\\ 15:23=\dfrac{15}{23}\)
hiệu là 9;18-9;11-2;14-5
hiệu là 8:17-9;12-4;13-5
hiệu là 7:còn lại
a) \(\dfrac{-5}{9}-\dfrac{-5}{12}=\dfrac{-5}{9}+\dfrac{5}{12}=\dfrac{-20}{36}+\dfrac{15}{36}=-\dfrac{5}{36}\)
b) \(\dfrac{-5}{12}:\dfrac{15}{4}=\dfrac{-5}{12}\times\dfrac{4}{15}=\dfrac{-1}{9}\)
c) \(\dfrac{1}{13}\cdot\dfrac{8}{13}+\dfrac{5}{13}\cdot\dfrac{1}{13}-\dfrac{14}{13}=\dfrac{1}{13}\cdot\left(\dfrac{8}{13}+\dfrac{5}{13}\right)-\dfrac{14}{13}=\dfrac{1}{13}\cdot1-\dfrac{14}{13}=\dfrac{1}{13}-\dfrac{14}{13}=-1\)
\(-\frac{1}{13}+\frac{15}{21}+\frac{\left(-12\right)}{13}+\frac{2}{7}+\frac{2020}{2021}\)
\(=-\frac{1}{13}+\frac{15}{21}-\frac{12}{13}+\frac{6}{21}+\frac{2020}{2021}\)
\(=\left(-\frac{1}{13}-\frac{12}{13}\right)+\left(\frac{15}{21}+\frac{6}{21}\right)+\frac{2020}{2021}\)
\(=-1+1+\frac{2020}{2021}=\frac{2020}{2021}\)
\(\dfrac{12}{6}+\dfrac{15}{7}=2+\dfrac{15}{7}=\dfrac{14}{7}+\dfrac{15}{7}=\dfrac{29}{7}\\ \dfrac{12}{13}-\dfrac{8}{9}=\dfrac{108}{117}-\dfrac{104}{117}=\dfrac{4}{117}\\ \dfrac{43}{54}+\dfrac{76}{8}=\dfrac{43}{54}+\dfrac{19}{2}=\dfrac{43}{54}+\dfrac{513}{54}=\dfrac{556}{54}=\dfrac{278}{27}\)
\(\dfrac{12}{6}+\dfrac{15}{7}=\dfrac{84}{42}+\dfrac{90}{42}=\dfrac{174}{42}=\dfrac{29}{7}\)
\(\dfrac{12}{13}-\dfrac{8}{9}=\dfrac{108}{117}-\dfrac{104}{117}=\dfrac{4}{117}\)
\(\dfrac{43}{54}+\dfrac{76}{8}=\dfrac{344}{432}+\dfrac{4104}{432}=\dfrac{4448}{432}=\dfrac{278}{27}\)
Bài 1
các phân số theo thứ tự từ bé đến lớn là :
5/13; 7/13; 9/13; 11/13
Bài 2
các phân số theo thứ tự từ lớn đến bé là:
11/5; 12/12; 12/15; 9/15
Bài 3
các phân số theo thứ tự từ bé đến lớn là :
20/23; 20/12; 20/8; 20/4.
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
`15/12 -(-5/13) - 3/12 - 18/13`
` = 15/12 + 5/13 - 3/12 - 18/13`
` = (15/12 - 3/12) + (5/13 - 18/13)`
`= 1 + -1`
`= 0`