Question

Решите пожалуйста:
(21/113 - 14/19 + 7/8 - 28/41) + (4/41 - 1/8 + 2/19 - 3/113) : 1/7=?

Answer 1

$(frac{21}{113}-frac{14}{19}+frac{7}{8}-frac{28}{41})+(frac{4}{41}-frac{1}{8}+frac{2}{19}-frac{3}{113}):frac{1}{7}$

$1) frac{21}{113}-frac{14}{19}= frac{21*19-14*113}{113*19}= frac{399-1582}{2147} = frac{-1183}{2147}$

$2) frac{7}{8}-frac{28}{41}= frac{7*41-28*8}{8*41} = frac{287-224}{328} = frac{63}{328}$

$3) frac{-1183}{2147}+frac{63}{328}= frac{-1183*328+63*2147}{2147*328} = frac{-388024+135261}{704216} = frac{-252763}{704216}$

$4) frac{4}{41}-frac{1}{8}= frac{4*8-1*41}{41*8} = frac{32-41}{328}= frac{-9}{328}$

$5) frac{2}{19}-frac{3}{113}= frac{2*113-3*19}{19*113} = frac{226-57}{2147} = frac{169}{2147}$

$6) frac{-9}{328}+frac{169}{2147}= frac{-9*2147+169*328}{328*2147} = frac{-19323+55432}{704216} = frac{36109}{704216}$

$7) frac{36109}{704216}:frac{1}{7}=frac{36109}{704216}*7=frac{252763}{704216}$

$8) frac{-252763}{704216}+frac{252763}{704216}=0$