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\(1\)\(\frac{1}{3}x1\)\(\frac{1}{4}x1\)\(\frac{1}{5}x...x1\)\(\frac{1}{8}\)
\(=\frac{4}{3}x\)\(\frac{5}{4}x\)\(\frac{6}{5}\)\(x...x\)\(\frac{9}{8}\)
Tự tính nốt
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}.\)
= \(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\times\frac{10}{9}\)
= \(\frac{4\times5\times6\times7\times8\times9\times10}{3\times4\times5\times6\times7\times8\times9}\)
= \(\frac{10}{3}\)
A = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 99 x 100
A = 2 + 6 + 12 + 20 + ... 9900
A = [2+9900] rồi bn nhân tổng số từ số 2 - 9900
\(3A=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)
\(3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)
\(3A=99.100.101\)
\(\Rightarrow A=\frac{99.100.101}{3}\)
Bài giải
\(\frac{2}{3}+\frac{3}{4}+\frac{4}{5}=\frac{40}{60}+\frac{45}{60}+\frac{48}{60}=\frac{133}{60}\)
\(\frac{8}{5}+\frac{7}{6}+\frac{10}{9}+\frac{1}{2}=\frac{144}{90}+\frac{105}{90}+\frac{100}{90}+\frac{45}{90}=\frac{394}{90}\)
\(\frac{15}{17}-\frac{11}{13}+\frac{3}{26}=\frac{390}{442}+\frac{374}{442}+\frac{51}{442}=\frac{815}{442}\)
\(\frac{9}{12}\text{ x }\frac{4}{3}\text{ : }\frac{8}{5}=\frac{9}{12}\text{ x }\frac{4}{3}\text{ x }\frac{5}{8}=\frac{9\text{ x }4\text{ x }5}{12\text{ x }3\text{ x }8}=\frac{5}{8}\)
\(\frac{4}{5}\text{ x }\frac{15}{8}\text{ : }\frac{5}{7}=\frac{4}{5}\text{ x }\frac{15}{8}\text{ x }\frac{7}{5}=\frac{4\text{ x }15\text{ x }7}{5\text{ x }8\text{ x }5}=\frac{21}{10}\)
\(\frac{2}{3}+\frac{3}{4}+\frac{4}{5}=\frac{40}{60}+\frac{45}{60}+\frac{48}{60}=\frac{133}{60}\)
\(\frac{8}{5}+\frac{7}{6}+\frac{10}{9}+\frac{1}{2}=\frac{144}{90}+\frac{105}{90}+\frac{100}{90}+\frac{45}{90}=\frac{197}{45}\)
\(\frac{15}{17}-\frac{11}{13}+\frac{1}{26}=\frac{390}{442}+\frac{374}{442}+\frac{51}{442}=\frac{815}{442}\)
\(\frac{9}{12}\times\frac{4}{3}:\frac{8}{5}=1:\frac{8}{5}=\frac{5}{8}\)
\(\frac{4}{5}\times\frac{15}{8}:\frac{5}{7}=\frac{3}{2}:\frac{5}{7}=\frac{21}{10}\)
a, 2/3+1/2+1/6
=4/6+3/6+1/6
=4/3
b, 5/12+5/6-3/4
=10/24+20/24-18/24
=1/2
c, 1/3*3/5*2/5
=(1*3*2)/(3*5*5)
=2/25
d, 15/16:3/8*3/4
= 15/16*8/3*3/4
= 15/8
a) \(\frac{2}{3}\)+\(\frac{1}{2}\)+\(\frac{1}{6}\) = \(\frac{4}{6}\)+\(\frac{3}{6}\)+\(\frac{1}{6}\) =\(\frac{8}{6}\) =\(\frac{4}{3}\)
b)\(\frac{5}{12}+\frac{5}{6}-\frac{3}{4}\)=\(\frac{5}{12}+\frac{10}{12}-\frac{9}{12}\)=\(\frac{6}{12}\)= \(\frac{1}{2}\)
c) \(\frac{1}{3}\cdot\frac{3}{5}\cdot\frac{2}{5}\) =\(\frac{6}{75}\)=\(\frac{2}{25}\)
a; 3 giờ 5 phút + 6 giờ 32 phút 9 giờ 37 phút
b; 23 phút 25 giây - 15 phút 12 giây 8 phút 13 giây
a) \(\left(\frac{1}{3}+\frac{1}{5}\right)+\left(\frac{1}{6}-\frac{1}{5}\right)=\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)=\frac{1}{2}\)
b) \(\frac{3}{16}\times\frac{7}{5}+\frac{3}{5}\times\frac{9}{16}=\frac{21}{80}+\frac{27}{80}=\frac{48}{80}=\frac{3}{5}\)
c) \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2020\times2021}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2020}-\frac{1}{2021}\)
\(=1-\frac{1}{2021}=\frac{2020}{2021}\)
d) \(\frac{1}{1\times3}+\frac{1}{3\times5}+...+\frac{1}{2021\times2023}=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{2021\times2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2021}-\frac{1}{2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{2023}\right)=\frac{1}{2}\times\frac{2022}{2023}=\frac{1011}{2023}\)
e) \(\frac{3}{2}\times\frac{1}{7}\times\frac{5}{4}+\frac{15}{2}\times\frac{6}{7}\times\frac{1}{4}==\frac{15}{56}+\frac{80}{56}=\frac{95}{56}\)
`5/6-(x-1/3)=5/12-1/4`
`5/6-(x-1/3)=5/12 - 3/12`
`5/6-(x-1/3)=2/12`
`5/6-(x-1/3)=1/6`
`x-1/3=5/6-1/6`
`x-1/3=4/6`
`x-1/3=2/3`
`x=2/3+1/3`
`x=3/3`
`x=1`
Vậy `x=1`
\(\dfrac{5}{6}-\left(x-\dfrac{1}{3}\right)=\dfrac{5}{12}-\dfrac{1}{4}\)
\(\dfrac{5}{6}-\left(x-\dfrac{1}{3}\right)=\dfrac{5}{12}-\dfrac{3}{12}\)
\(\dfrac{5}{6}-\left(x-\dfrac{1}{3}\right)=\dfrac{1}{6}\)
\(x-\dfrac{1}{3}=\dfrac{2}{3}\)
\(x=\dfrac{2}{3}+\dfrac{1}{3}\)
\(x=1\)