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1./ \(\frac{X+\frac{5}{3}}{2}=\frac{7}{3}\Leftrightarrow X+\frac{5}{3}=\frac{14}{3}\Leftrightarrow X=\frac{14-5}{3}=\frac{9}{3}=3.\)
2./ \(\frac{21}{4}dm^2=\frac{21}{4}\cdot\left(100\right)^2mm^2=52.500mm^2.\)
\(75000m^2=75000\cdot\frac{1}{100^2}hm^2=7,5hm^2\)
3./
a) Tổng bằng 8; Tỷ bằng 1/3. Tổng số phần bằng nhau là 1+3=4. =>\(a=\frac{8}{4}\cdot1=2\)và \(b=\frac{8}{4}\cdot3=6\)
b) Hiệu bằng 50; Tỷ bằng 5/3. Hiệu số phần bằng nhau là: 5-3=2 =>\(a=\frac{50}{2}\cdot5=125\)và \(b=\frac{50}{2}\cdot3=75\).
a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8
= 1 + 1 + 8
= 2 + 8
= 10
b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8
= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8
= \(\dfrac{1}{2}\) + 4
= \(\dfrac{9}{2}\)
a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8
= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8
= 1 + 1 + 8
= 2 + 8
= 10
b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)
= \(\dfrac{1}{2}\) x 10
= 5
a) Ta có : \(\frac{a}{b}+\frac{5}{6}=\frac{7}{8}\)=> \(\frac{a}{b}=\frac{7}{8}-\frac{5}{6}\)
=> \(\frac{a}{b}=\frac{21}{24}-\frac{20}{24}=\frac{1}{24}\)
Vậy \(\frac{a}{b}=\frac{1}{24}\)
b) \(\frac{a}{b}\times\frac{2}{3}=\frac{3}{4}\)
=> \(\frac{a}{b}=\frac{3}{4}:\frac{2}{3}=\frac{3}{4}\times\frac{3}{2}=\frac{9}{8}\)
Vậy \(\frac{a}{b}=\frac{9}{8}\)
c) \(\frac{5}{8}-\frac{a}{b}=\frac{5}{12}\)
=> \(\frac{a}{b}=\frac{5}{8}-\frac{5}{12}=\frac{15}{24}-\frac{10}{24}=\frac{5}{24}\)
Vậy \(\frac{a}{b}=\frac{5}{24}\)
d) \(\frac{5}{8}+\frac{a}{b}=\frac{13}{8}\)
=> \(\frac{a}{b}=\frac{13}{8}-\frac{5}{8}=\frac{8}{8}=1\)
Vậy : ....
\(5-\left(\frac{a}{b}+\frac{1}{2}\right)=\frac{7}{3}\)
\(\Leftrightarrow\frac{a}{b}+\frac{1}{2}=5-\frac{7}{3}=\frac{8}{3}\)
\(\Leftrightarrow\frac{a}{b}=\frac{8}{3}-\frac{1}{2}=\frac{13}{6}\)
Vậy phân số \(\frac{a}{b}\) là \(\frac{13}{6}\)