– Áp dụng tính chất phân phối của phép nhân với phép cộng: a.c+b.c=(a+b).c
– Áp dụng tính chất giao hoán của phép cộng
Lời giải chi tiết
a)
(begin{array}{l}frac{3}{7}.left( { – frac{1}{9}} right) + frac{3}{7}.left( { – frac{2}{3}} right)\ = frac{3}{7}.left( { – frac{1}{9} + frac{-2}{3}} right)\ = frac{3}{7}.left( { – frac{1}{9} – frac{6}{9}} right)\ = frac{3}{7}.frac{{ – 7}}{9} = frac{{ – 1}}{3}end{array})
b)
(begin{array}{l}left( {frac{{ – 7}}{{13}}} right).frac{5}{{12}} + left( {frac{{ – 7}}{{13}}} right).frac{7}{{12}} + left( {frac{{ – 6}}{{13}}} right)\ = frac{{ – 7}}{{13}}.left( {frac{5}{{12}} + frac{7}{{12}}} right) + left( {frac{{ – 6}}{{13}}} right)\ = frac{{ – 7}}{{13}}.1 + left( {frac{{ – 6}}{{13}}} right)\ = frac{{ – 7}}{{13}} + left( {frac{{ – 6}}{{13}}} right)\ = frac{{ – 13}}{{13}}\ = -1end{array})
c)
(begin{array}{l}left[ {left( {frac{{ – 2}}{3} + frac{3}{7}} right)} right]:frac{5}{9} + left( {frac{4}{7} – frac{1}{3}} right):frac{5}{9}\ = left[ {left( {frac{{ – 2}}{3} + frac{3}{7}} right)} right].frac{9}{5} + left( {frac{4}{7} – frac{1}{3}} right).frac{9}{5}\ = left( {frac{{ – 2}}{3} + frac{3}{7} + frac{4}{7} – frac{1}{3}} right).frac{9}{5}\ = left[ {left( {frac{{ – 2}}{3} – frac{1}{3}} right) + left( {frac{3}{7} + frac{4}{7}} right)} right].frac{9}{5}\ = left( { – 1 + 1} right).frac{9}{5}\ = 0.frac{9}{5} = 0end{array})
d)
(begin{array}{l}frac{5}{9}:left( {frac{1}{{11}} – frac{5}{{22}}} right) + frac{5}{9}:left( {frac{1}{{15}} – frac{2}{3}} right)\ = frac{5}{9}:left( {frac{2}{{22}} – frac{5}{{22}}} right) + frac{5}{9}:left( {frac{1}{{15}} – frac{{10}}{{15}}} right)\ = frac{5}{9}:frac{{ – 3}}{{22}} + frac{5}{9}:frac{{ – 9}}{15}\= frac{5}{9}:frac{{ – 3}}{{22}} + frac{5}{9}:frac{{ – 3}}{5}\ = frac{5}{9}.frac{{ – 22}}{3} + frac{5}{9}.frac{{ – 5}}{3}\ = frac{5}{9}.left( {frac{{ – 22}}{3} – frac{5}{3}} right)\ = frac{5}{9}.frac{-27}{3}= frac{5}{9}.left( { – 9} right) = – 5end{array})
e)
(begin{array}{l}frac{3}{5} + frac{3}{{11}} – left( {frac{{ – 3}}{7}} right) + left( {frac{{ – 2}}{{97}}} right) – frac{1}{{35}} – frac{3}{4} + left( {frac{{ – 23}}{{44}}} right)\ = frac{3}{5} + frac{3}{{11}} + frac{3}{7} – frac{2}{{97}} – frac{1}{{35}} – frac{3}{4} – frac{{23}}{{44}}\ = left( {frac{3}{5} + frac{3}{7} – frac{1}{{35}}} right) + left( {frac{3}{{11}} – frac{3}{4} – frac{{23}}{{44}}} right) – frac{2}{{97}}\ = left( {frac{{21}}{{35}} + frac{{15}}{{35}} – frac{1}{{35}}} right) + left( {frac{{12}}{{44}} – frac{{33}}{{44}} – frac{{23}}{{44}}} right) – frac{2}{{97}}\ = 1 + left( { – 1} right) – frac{2}{{97}}\ = – frac{2}{{97}}end{array})
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