Question

a) 4 + 375 . (9/16 : 125/64 : -27/8)

b) 2/3 - 4 . ( 1/2 + 3/4)

c) ( 12/35 - 6/7 + 18/14) : 6=-7 - -2/5

D) [ -54/64 - (1/9 : 8/27 ) : -1/3] : -81/128

Answer 1

\(a,4+375.\left(\dfrac{9}{16}:\dfrac{125}{64}:\dfrac{-27}{8}\right)\)
\(=4+375.\left(\dfrac{9}{16}.\dfrac{64}{125}.\dfrac{-8}{27}\right)\)
\(=4+375.\left(\dfrac{1.32.\left(-1\right)}{125.3}\right)\)
\(=4+375.\dfrac{-32}{375}\)
\(=4+\left(-32\right)\)
\(=-28\)
\(b,\dfrac{2}{3}-4.\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\)
\(=\dfrac{2}{3}-4.\left(\dfrac{2}{4}+\dfrac{3}{4}\right)\)
\(=\dfrac{2}{3}-4.\dfrac{5}{4}\)
\(=\dfrac{2}{3}-5\)
\(=\dfrac{2}{3}-\dfrac{15}{3}\)
\(=\dfrac{-13}{3}\)
\(d,\left[\dfrac{-54}{64}-\left(\dfrac{1}{9}:\dfrac{8}{27}\right):\dfrac{-1}{3}\right]:\dfrac{-81}{128}\)
\(=\left[\dfrac{-54}{64}-\left(\dfrac{1}{9}.\dfrac{27}{8}\right).\left(-3\right)\right].\dfrac{-128}{81}\)
\(=\left[\dfrac{-54}{64}-\dfrac{3}{8}.\left(-3\right)\right].\dfrac{-128}{81}\)
\(=\left[\dfrac{-54}{64}-\dfrac{-9}{8}\right].\dfrac{-128}{81}\)
\(=\left[\dfrac{-54}{64}+\dfrac{72}{64}\right].\dfrac{-128}{81}\)
\(=\dfrac{18}{64}.\dfrac{-128}{81}\)
\(=\dfrac{9}{32}.\dfrac{-128}{81}\)
\(=\dfrac{1.\left(-4\right)}{1.9}\)
\(=\dfrac{-4}{9}\)