Question

a) 4/5 . (7/2 +1/4)^2

b) |-3/8| . 27 1/5 - 51 1/5 . 3/8 + 19

c) (2/3 - 7/15) : (2/3 - 2/5)^2

d) -19/3 . 14/4 - 25/4 . |-19/3| + 4 4/3

Answer 1

\(a,\dfrac{4}{5}.\left(\dfrac{7}{2}+\dfrac{1}{4}\right)^2\)
\(=\dfrac{4}{5}\left(\dfrac{14}{4}+\dfrac{1}{4}\right)^2\)
\(=\dfrac{4}{5}.\left(\dfrac{15}{4}\right)^2\)
\(=\dfrac{4}{5}.\dfrac{225}{16}\)
\(=\dfrac{45}{4}\)
\(b,\left|\dfrac{-3}{8}\right|.27\dfrac{1}{5}-51\dfrac{1}{5}.\dfrac{3}{8}+19\)
\(=\dfrac{3}{8}.\dfrac{136}{5}-\dfrac{256}{5}.\dfrac{3}{8}+19\)
\(=\dfrac{3}{8}.\left(\dfrac{136}{5}-\dfrac{256}{5}\right)+19\)
\(=\dfrac{3}{8}.\dfrac{-120}{5}+19\)
\(=\dfrac{3}{8}.\left(-24\right)+19\)
\(=-9+19\)
\(=10\)
\(c,\left(\dfrac{2}{3}-\dfrac{7}{15}\right):\left(\dfrac{2}{3}-\dfrac{2}{5}\right)^2\)
\(=\left(\dfrac{10}{15}-\dfrac{7}{15}\right):\left(\dfrac{10}{15}-\dfrac{6}{15}\right)^2\)
\(=\dfrac{3}{15}:\left(\dfrac{4}{15}\right)^2\)
\(=\dfrac{1}{5}:\dfrac{16}{225}\)
\(=\dfrac{45}{16}\)
\(d,\dfrac{-19}{3}.\dfrac{14}{4}-\dfrac{25}{4}.\left|\dfrac{-19}{3}\right|+4\dfrac{4}{3}\)
\(=\dfrac{19}{3}.\dfrac{-14}{4}-\dfrac{25}{4}.\dfrac{19}{3}+\dfrac{16}{3}\)
\(=\dfrac{19}{3}.\left(\dfrac{-14}{4}-\dfrac{25}{4}\right)+\dfrac{16}{3}\)
\(=\dfrac{19}{3}.\dfrac{-39}{4}+\dfrac{16}{3}\)
\(=\dfrac{-247}{4}+\dfrac{16}{3}\)
\(=\dfrac{-741}{12}+\dfrac{64}{12}\)
\(=\dfrac{-677}{12}\)