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\(\frac{1}{9\cdot10}+\frac{2}{10\cdot12}+\frac{3}{12\cdot15}+\frac{4}{15\cdot19}+\frac{5}{19\cdot24}+\frac{6}{24\cdot30}
\)
\(=\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{24}+\frac{1}{24}-\frac{1}{30}\)
\(=\frac{1}{9}-\frac{1}{30}\)
\(=\frac{10}{90}-\frac{3}{90}\)
\(=\frac{7}{90}\)
A) \(\frac{7}{8}-\frac{5}{12}=\frac{84}{96}-\frac{40}{96}=\frac{44}{96}=\frac{11}{24}\)
B)\(\frac{8}{15}-\frac{2}{5}=\frac{8}{15}-\frac{6}{15}=\frac{2}{15}\)
C)\(\frac{5}{6}-\frac{3}{10}=\frac{50}{60}-\frac{18}{60}=\frac{32}{60}=\frac{8}{15}\)
D)\(\frac{7}{10}-\frac{1}{5}=\frac{7}{10}-\frac{2}{10}=\frac{5}{10}=\frac{1}{2}\)
2)A)\(\frac{5}{10}-\frac{2}{15}=\frac{1}{2}-\frac{2}{15}=\frac{15}{30}-\frac{4}{30}=\frac{11}{30}\)
B)\(\frac{5}{20}-\frac{1}{6}=\frac{1}{4}-\frac{1}{6}=\frac{6}{24}-\frac{4}{24}=\frac{2}{24}=\frac{1}{12}\)
C)\(\frac{6}{18}-\frac{6}{24}=\frac{1}{3}-\frac{1}{4}=\frac{4}{12}-\frac{3}{12}=\frac{1}{12}\)
D)\(\frac{5}{9}-\frac{3}{12}=\frac{5}{9}-\frac{1}{4}=\frac{20}{36}-\frac{9}{36}=\frac{11}{36}\)
Chúc bạn học tốt
b, 3/5 + 4/7 + 2/8 + 10/25 + 9/21 + 28/16
= 3/5 + 4/7 + 2/8 + 2/5 + 3/7 + 14/8
= (3/5 + 2/5) + ( 4/7 + 3/7) + ( 2/8 + 14/8)
= 1 + 1 + 7/4
= 2 + 7/4 = 15/4
c , 8/7 + 7/6 + 5/8 + 10/12 + 24/28 + 6/16
= c , 8/7 + 7/6 + 5/8 + 5/6 + 6/7 + 1/2
= (8/7 + 6/7) + (7/6 + 5/6) + 5/8 + 1/2
= 14/7 + 12/6 + 5/8 + 1/2
= 2 + 2 + 5/8 + 1/2
= 4 + 9/8 = 41/8
= 4/5 + 1/5 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2
= (4/5 + 1/5) + (1/2 + 1/2) + (1/2 + 1/2) + 1/2
= 1 + 1 + 1 + 1/2
= 3 + 1/2
= 6/2 + 1/2 (Hoặc ra luôn là hỗn số 3 và 1/2)
= 7/2
\(\frac{2}{6}+\frac{9}{24}\)
\(=\frac{8}{24}+\frac{9}{24}\)
\(=\frac{17}{24}\)
Tương Tự vs các câu còn lại
\(\frac{7}{2}+\frac{1}{3}-\frac{5}{2}\)
\(=\left(\frac{7}{2}-\frac{5}{2}\right)+\frac{1}{3}\)
\(=1+\frac{1}{3}\)
\(=\frac{4}{3}\)
\(\dfrac{3}{2}xD=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
Đặt
\(A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
\(2xA=2+1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}\)
\(A=2xA-A=2-\dfrac{1}{256}=\dfrac{511}{256}=\dfrac{3}{2}xD\)
\(\Rightarrow D=\dfrac{511}{256}:\dfrac{3}{2}\)