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\(\dfrac{-2^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot5^3\cdot2^4\cdot42}\)
\(=\dfrac{-2^6\cdot3^3\cdot5^3\cdot7}{3\cdot5^3\cdot2^4\cdot2\cdot3\cdot7}\)
\(=\dfrac{-2^6\cdot3^3\cdot5^3}{2^5\cdot3^2\cdot5^3}=-2\cdot3=-6\)
\(\frac{7}{8}\div\left(\frac{14}{3}+\frac{14}{4}\right)+\frac{10}{14}\)
\(=\frac{7}{8}\div\left(\frac{56}{12}+\frac{52}{12}\right)+\frac{10}{14}\)
\(=\frac{7}{8}\div\frac{108}{12}+\frac{10}{14}\)
\(=\frac{7}{8}\div9+\frac{5}{7}\)
\(=\frac{7}{8}\times\frac{1}{9}+\frac{5}{7}\)
\(=\frac{7}{72}+\frac{5}{7}\)
\(=\frac{49}{504}+\frac{360}{504}\)
\(=\frac{409}{504}\)
\(\frac{30}{42}\div\left(\frac{5}{7}-\frac{5}{21}\right)+\frac{6}{8}\)
\(=\frac{6}{7}\div\left(\frac{15}{21}-\frac{5}{21}\right)+\frac{3}{4}\)
\(=\frac{6}{7}\div\frac{10}{21}+\frac{3}{4}\)
\(=\frac{6}{7}\times\frac{21}{10}+\frac{3}{4}\)
\(=\frac{126}{70}+\frac{3}{4}\)
\(=\frac{504}{280}+\frac{210}{280}\)
\(=\frac{714}{280}\)
\(\left(6-\frac{14}{15}\right).\frac{50}{38}-\frac{8}{18}\)
\(=\left(\frac{90}{15}-\frac{14}{15}\right).\frac{25}{19}-\frac{4}{9}\)
\(=\frac{76}{15}.\frac{25}{19}-\frac{4}{9}\)
\(=\frac{76.25}{15.19}-\frac{4}{9}\)
\(=\frac{19.2.2.5.5}{3.5.19}-\frac{4}{9}\)
\(=\frac{20}{3}-\frac{4}{9}\)
\(=\frac{60}{9}-\frac{4}{9}\)
\(=\frac{56}{9}\)
\(\frac{4}{6}+\frac{5}{21}.\left(\frac{4}{5}-\frac{2}{6}\right)\)
\(=\frac{2}{3}+\frac{5}{21}.\left(\frac{24}{30}-\frac{10}{30}\right)\)
\(=\frac{2}{3}+\frac{5}{21}.\frac{14}{30}\)
\(=\frac{2}{3}+\frac{70}{630}\)
\(=\frac{420}{630}+\frac{70}{630}\)
\(=\frac{490}{630}\)
\(=\frac{7}{9}\)
a, 24/-42 = -24/42= -4x6/7x6 =-4/7
b,-24/36 = -2x12/3x12 =-2/3
c,-8/56= -1x8/7x8 =-1/7
d,29/-87= -29/87 =-1x29/3x29 =-1/3
e, -3x35/42x9 =-1x3x5x7/6x7x3x3 =-1x5/3x6 =-5/18
f,-45045 / 6006000=-45x1001 /6000x1001=45/6000=3x15/15x400=3/400
\(a.\frac{-4}{7},b.\frac{-2}{3},c.\frac{-1}{7},d.\frac{-1}{3},e.\frac{-5}{18},f.\frac{-3}{400}\)
-24/42=-4/7
-24/36=-2/3
-8/56=-1/7
29/-87=-1/3
51/-18=-17/3
15 x 2 - 15 x 8
3 + 42
15 x ( 2 - 8 )
45
= -6 /3
= -2