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A=3/2-5/6+/12-9/20+11/30-13/42+15/56-17/72+19/90
A=11/10
hok tốt nha
a)121212/424242=2/7
1999999999/9999999995=1/5
Sorry bạn mik chỉ bt làm câu a thôi!
HT~
Câu b:
\(\frac{a}{b}:\frac{c}{d}=\frac{ad}{bc}=\frac{6}{5}\Leftrightarrow5ad=6bc\)
\(\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}=\frac{1}{15}\Leftrightarrow5\left(ad-bc\right)=\frac{bd}{3}\)
\(\Rightarrow5ad-5bc=\frac{bd}{3}\)
Thay vào ta có:
\(\frac{a}{b}-\frac{c}{d}=\frac{a}{b}-\frac{1}{3}=\frac{1}{15}\Leftrightarrow\frac{a}{b}=-\frac{4}{15}\)
Có \(P=\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times...\times\frac{399}{400}< \frac{2}{3}\times\frac{4}{5}\times...\times\frac{400}{401}\)
=> \(P^2< \frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{400}{401}=\frac{1}{401}< \frac{1}{400}=\frac{1}{20}\)
=> \(P< \frac{1}{20}\)(đpcm).
\(\frac{3}{-8}=\frac{-3}{8}=\frac{-9}{24}\)
\(\frac{-7}{12}=\frac{-14}{24}\)
\(\frac{2}{3}=\frac{16}{24}\)
\(\frac{5}{6}=\frac{20}{24}\)
Các phân số theo thứ tự tăng dần là: \(\frac{-7}{12};\frac{3}{-8};\frac{2}{3};\frac{5}{6}\)
a)Quy đồng: \(\frac{5}{8}=\frac{5.3}{8.3}=\frac{15}{24}\)
Vì \(\frac{5}{24}< \frac{10+5}{24}=\frac{15}{24}\)
\(\Rightarrow\frac{5}{24}< \frac{5+10}{24}=\frac{5}{8}\)
b) Quy đồng:
\(\frac{4}{9}=\frac{4.6}{9.6}=\frac{24}{9.6}\)
\(\frac{2}{3}=\frac{2.18}{3.18}=\frac{36}{9.6}\)
Vì \(\frac{36}{9.6}>\frac{24}{9.6}>\frac{6+9}{9.6}\)
\(\Rightarrow\frac{2}{3}>\frac{4}{9}>\frac{6+9}{6.9}\)
\(25\%-1\frac{1}{2}+0,5\cdot\frac{12}{5}\)
\(=\frac{1}{4}-\frac{3}{2}+\frac{1}{2}\cdot\frac{12}{5}\)
\(=\frac{1}{4}-\frac{3}{2}+\frac{6}{5}\)
\(=\frac{5}{20}-\frac{30}{20}+\frac{24}{20}\)
\(=\frac{-1}{20}\)
a: \(11\dfrac{3}{4}-\left(6\dfrac{5}{6}-4\dfrac{1}{2}+1\dfrac{2}{3}\right)\)
\(=11+\dfrac{3}{4}-\left(6+\dfrac{5}{6}-4-\dfrac{1}{2}-1-\dfrac{2}{3}\right)\)
\(=11+\dfrac{3}{4}-\left(1+\dfrac{5}{6}-\dfrac{3}{6}-\dfrac{4}{6}\right)\)
\(=11+\dfrac{3}{4}-\left(1-\dfrac{1}{3}\right)\)
\(=11+\dfrac{3}{4}-\dfrac{2}{3}=\dfrac{132+9-8}{12}=\dfrac{133}{12}\)
b: \(\left(5\dfrac{7}{8}-2\dfrac{1}{4}-0,5\right):2\dfrac{23}{26}\)
\(=\left(5+\dfrac{7}{8}-2-\dfrac{1}{4}-\dfrac{1}{2}\right):\dfrac{75}{26}\)
\(=\left(3+\dfrac{1}{8}\right)\cdot\dfrac{26}{75}=\dfrac{25}{8}\cdot\dfrac{26}{75}=\dfrac{1}{3}\cdot\dfrac{26}{8}=\dfrac{13}{12}\)
c: \(\left(17\dfrac{13}{15}-3\dfrac{3}{7}\right)-\left(2\dfrac{12}{15}-4\right)\)
\(=17+\dfrac{13}{15}-3-\dfrac{3}{7}-2-\dfrac{12}{15}+4\)
\(=16+\dfrac{1}{15}-\dfrac{3}{7}=\dfrac{1642}{105}\)
d: \(2\dfrac{2}{3}\cdot\dfrac{-4}{5}\cdot0,375\cdot\left(-10\right)\cdot\dfrac{-15}{24}\)
\(=\dfrac{8}{3}\cdot\dfrac{-4}{5}\cdot\dfrac{3}{8}\cdot\dfrac{150}{24}\)
\(=-\dfrac{4}{5}\cdot\dfrac{25}{4}=-5\)