Question

a) 12,5.\(\left(-\dfrac{5}{7}\right)+1,5.\left(-\dfrac{5}{7}\right)\)

b) \(\left(-\dfrac{2}{5}-\dfrac{3}{7}\right):\dfrac{4}{5}+\left(-\dfrac{1}{5}+\dfrac{3}{7}\right);\dfrac{4}{5}\)

c) \(12.\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\)

d) \(1:\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2\)

e) \(15.\left(-\dfrac{2}{3}\right)^{^{ }2}-\dfrac{7}{3}\)

f) \(\dfrac{5^4.20^4}{25^5.4^5}\)

Answer 1

a.\(12,5.\left(-\dfrac{5}{7}\right)+1,5.\left(-\dfrac{5}{7}\right)\)

\(=\left(-\dfrac{5}{7}\right).\left(12,5+1,5\right)\)

\(=-10\)

b,\(\left(-\dfrac{2}{5}-\dfrac{3}{7}\right):\dfrac{4}{5}+\left(-\dfrac{1}{5}+\dfrac{3}{7}\right):\dfrac{4}{5}\)

\(=\left(-\dfrac{2}{5}-\dfrac{3}{7}-\dfrac{1}{5}+\dfrac{3}{7}\right):\dfrac{4}{5}\)

\(=-\dfrac{3}{5}:\dfrac{4}{5}\)

\(=-\dfrac{3}{4}\)

c,\(12.\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\)

\(=12.\dfrac{4}{9}+\dfrac{4}{3}\)

\(=\dfrac{16}{3}+\dfrac{4}{3}\)

\(=\dfrac{20}{3}\)

d,\(1:\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2\)

\(=\dfrac{1}{1}:\dfrac{1}{144}\)

\(=144\)

e,\(15.\left(-\dfrac{2}{3}\right)^2-\dfrac{7}{3}\)

\(=15.\dfrac{4}{9}-\dfrac{7}{3}\)

\(=\dfrac{20}{3}-\dfrac{7}{3}\)

\(=\dfrac{13}{3}\)

Answer 2

a) = ( 12,5 +1,5 ). \(\left(-\dfrac{5}{7}\right)\)

= 14 . \(\left(-\dfrac{5}{7}\right)\)

= -10

b) = (\(-\dfrac{2}{5}+-\dfrac{1}{5}\)) + \(\left(\dfrac{3}{7}-\dfrac{3}{7}\right)\): \(\dfrac{4}{5}\)

= \(\left(-\dfrac{3}{5}+0\right)\): \(\dfrac{4}{5}\)

= \(\dfrac{3}{4}\)

c) = \(\left(12.-\dfrac{2}{9}\right)\) + \(\dfrac{4}{3}\)

= \(\dfrac{8}{3}\) + \(\dfrac{4}{3}\)

= \(-\dfrac{4}{3}\)

d) = 1: \(\dfrac{23}{48}\)

=\(\dfrac{48}{23}\)

e) =\(\left(15.-\dfrac{2}{9}\right)-\dfrac{7}{3}\)

= \(\left(-\dfrac{10}{3}\right)-\dfrac{7}{3}\)

=\(-\dfrac{17}{3}\)

f) = 10 485.76

Answer 3

a, \(12,5.\left(\dfrac{-5}{7}\right)+1,5.\left(\dfrac{-5}{7}\right)\)

\(=\left(\dfrac{-5}{7}\right).\left(12,5+1,5\right)=\left(\dfrac{-5}{7}\right).14=-10\)

b, \(\left(\dfrac{-2}{5}-\dfrac{3}{7}\right):\dfrac{4}{5}+\left(\dfrac{-1}{5}+\dfrac{3}{7}\right):\dfrac{4}{5}\)

\(=\left[\left(-\dfrac{2}{5}-\dfrac{1}{5}\right)+\left(\dfrac{-3}{7}+\dfrac{3}{7}\right)\right]:\dfrac{4}{5}\)

\(=\left(\dfrac{-3}{5}+0\right):\dfrac{4}{5}=\dfrac{-3}{5}.\dfrac{5}{4}=\dfrac{-3}{4}\)

c, \(12.\left(\dfrac{-2}{3}\right)^2+\dfrac{4}{3}\)

\(=12.\left(\dfrac{-2^2}{3^2}\right)+\dfrac{4}{3}=12.\left(\dfrac{4}{9}\right)+\dfrac{4}{3}=\dfrac{16}{3}+\dfrac{4}{3}=5\)

d, \(1:\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2=1:\left(\dfrac{-1}{12}\right)^2=1:\dfrac{1}{144}=144\)

e, \(15.\left(\dfrac{-2}{3}\right)^2-\dfrac{7}{3}\)

\(=15.\dfrac{4}{9}-\dfrac{7}{3}=\dfrac{20}{3}-\dfrac{7}{3}=\dfrac{13}{3}\)