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\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)
\(=\frac{14}{6}+\frac{1}{3}+\frac{14}{9}+\frac{7}{15}+\frac{14}{14}+\frac{6}{4}\)
\(=\frac{42+6+28}{18}+\frac{7}{15}+\frac{2}{2}+\frac{3}{2}\)
\(=\frac{76}{18}+\frac{7}{15}+\frac{5}{2}\)
\(=\frac{76}{18}+\frac{5}{2}+\frac{7}{15}\)
\(=\frac{76+45}{18}+\frac{7}{15}\)
\(=\frac{121}{18}+\frac{7}{15}\)
\(=\frac{605+42}{90}\)
\(=\frac{647}{90}\)
\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)
\(=(\frac{7}{3}+\frac{1}{3})+1+(\frac{14}{9}+\frac{7}{15})+\frac{3}{2}\)
\(=\frac{8}{3}+1+\frac{91}{45}+\frac{3}{2}\)
\(=2+\frac{2}{3}+1+2+\frac{1}{45}+1+\frac{1}{2}\)
\(=\left(\frac{2}{3}+\frac{1}{45}+\frac{1}{2}\right)+\left(2+1+2+1\right)\)
\(=1+\frac{17}{90}+6\)
\(=7+\frac{17}{90}\)
\(=7\frac{17}{90}\)
8. Find the value of 14 x 14 + 2 x 14 x 86 + 86 x 86.
\(=\left(14\times3\right)+\left(86\times3\right)+2\)
\(=42+258+2\)
\(=300+2\)
\(=302\)
14 x 14 + 2 x 14 x 86 + 86 x 86
= 14 x 14 + 14 x 86 + 14 x 86 + 86 x 86
= 14 x ( 14 + 86 ) + 86 x ( 14 + 86 )
= 14 x 100 + 86 x 100
= 100 x ( 14 + 86 )
= 100 x 100
= 10000
\(\dfrac{7}{15}< \dfrac{14}{a}< \dfrac{7}{14}\Rightarrow\dfrac{14}{30}< \dfrac{14}{a}< \dfrac{14}{28}\\ \Rightarrow a=29\)
Vậy số đó là \(\dfrac{14}{29}\)
`@` `\text {Ans}`
`\downarrow`
\(\dfrac{14}{18}< \dfrac{20}{x}< \dfrac{14}{17}\)
`=>`\(\dfrac{14\times20}{18\times20}< \dfrac{20\times14}{14\times x}< \dfrac{14\times20}{17\times20}\)
`=>`\(\dfrac{280}{360}< \dfrac{280}{14x}< \dfrac{280}{340}\)
`=>` `360 > 14x > 340`
`=>` `14x = 350`
`-> x=25`
Vậy, `x=25`
37.0035714286
10361/280 hoặc 37,00357143