Bài 1:
A=($\frac{5}{2}$+$\frac{1}{3}$):(1-$\frac{2}{3}$)
=($\frac{15}{6}$+$\frac{2}{6}$):($\frac{3}{3}$-$\frac{2}{3}$)
=$\frac{15+2}{6}$÷$\frac{3-2}{3}$
=$\frac{17}{6}$÷$\frac{1}{3}$
=$\frac{17}{6}×3=$\frac{17×3}{6}$=$\frac{17}{2}$
B=($\frac{5}{2}$-$\frac{1}{7}$)×$\frac{9}{2}$-$\frac{6}{7}$
=($\frac{35}{14}$-$\frac{2}{14}$)×$\frac{9}{2}$-$\frac{6}{7}$
=$\frac{35-2}{14}$×$\frac{9}{2}$-$\frac{6}{7}$
=$\frac{33}{14}$×$\frac{9}{2}$-$\frac{6}{7}$
=$\frac{33×9}{14×2}-$\frac{6}{7}$
=$\frac{297}{28}$-$\frac{6}{7}$
=$\frac{297}{28}$-$\frac{24}{28}$
=$\frac{297-24}{28}$=$\frac{39}{4}$
C=$\frac{254×399-145}{254+399×253}$ (mình có thay đổi đề bài chút)
=$\frac{253×399+399-145}{254+399×253}$
=$\frac{253×399+254}{254+399×253}$
=1
D=$\frac{5863+6001×5932}{5932×6002-69}$ (mình có thay đổi đề bài chút)
=$\frac{5863+6001×5932}{5932×6001+5932-69}$
=$\frac{5863+6001×5932}{5932×6001+5863}$
=1
Bài 2:
B=(1-$\frac{1}{2}$)×(1-$\frac{1}{3}$)×(1-$\frac{1}{4}$)×...×(1-$\frac{1}{2019}$)×(1-$\frac{1}{2020}$) (mình thay đổi đề 1 chút nhé)
=($\frac{2}{2}$-$\frac{1}{2}$)×($\frac{3}{3}$-$\frac{1}{3}$)×($\frac{4}{4}$-$\frac{1}{4}$)×...×($\frac{2019}{2019}$-$\frac{1}{2019}$)×($\frac{2020}{2020}$-$\frac{1}{2020}$)
=$\frac{2-1}{2}$×$\frac{3-1}{3}$×...×$\frac{2020-1}{2020}$
=$\frac{1}{2}$×$\frac{2}{3}$×....×$\frac{2019}{2020}$
=$\frac{1×2×3×...×2019}{2×3×4×...×2020}$
=$\frac{1}{2020}$
E=$5\frac{9}{10}$:$\frac{3}{2}$-(2$\frac{1}{3}$×$4\frac{1}{2}$-2×$2\frac{1}{3}$):$\frac{7}{4}$
=$\frac{59}{10}$×$\frac{2}{3}$-($\frac{7}{3}$×$\frac{9}{2}$-2×$\frac{7}{3}$)×$\frac{4}{7}$
=$\frac{59×2}{10×3}$-($\frac{7×9}{3×2}$-$\frac{2×7}{3}$)×$\frac{4}{7}$
=$\frac{59}{15}$-($\frac{21}{2}$-$\frac{14}{3}$)×$\frac{4}{7}$
=$\frac{59}{15}$-($\frac{63}{6}$-$\frac{28}{6}$)×$\frac{4}{7}$
=$\frac{59}{15}$-$\frac{63-28}{6}$×$\frac{4}{7}$
=$\frac{59}{15}$-$\frac{35}{6}$×$\frac{4}{7}$
=$\frac{59}{15}$-$\frac{35×4}{6×7}$
=$\frac{59}{15}$-$\frac{10}{3}$
=$\frac{59}{15}$-$\frac{50}{15}$
=$\frac{59-50}{15}$=$\frac{9}{15}$=$\frac{3}{5}$
Bài 3:
a) x+$2\frac{3}{4}$=$5\frac{2}{3}$
⇒ x+$\frac{11}{4}$=$\frac{17}{3}$
⇒ x=$\frac{17}{3}$- $\frac{11}{4}$
=$\frac{68}{12}$-$\frac{33}{12}$
=$\frac{68-33}{12}$=$\frac{35}{12}$
b) x-1×$\frac{4}{5}$=$3\frac{2}{7}$
⇒ x-$\frac{4}{5}$=$\frac{23}{7}$
⇒ x=$\frac{23}{7}$+$\frac{4}{5}$
=$\frac{115}{35}$+$\frac{28}{35}$
=$\frac{115+28}{35}$=$\frac{143}{35}$
c) x×$3\frac{1}{2}$=$4\frac{3}{4}$
⇒ x×$\frac{7}{2}$=$\frac{19}{4}$
⇒ x=$\frac{19}{4}$÷$\frac{7}{2}$
=$\frac{19}{4}$×$\frac{2}{7}$
=$\frac{19×2}{4×7}$
=$\frac{19}{14}$
d) x÷$2\frac{2}{3}$=$4\frac{1}{3}$
⇒ x÷$\frac{8}{3}$=$\frac{13}{3}$
⇒ x=$\frac{13}{3}$×$\frac{8}{3}$
=$\frac{13×8}{3×3}$
=$\frac{104}{9}$
