Bài 2 trang 100 SBT toán 7 tập 2

Đề bài

Tính \(\left( {2\dfrac{1}{3} + 3\dfrac{1}{2}} \right):\left( { - 4\dfrac{1}{6} + 3\dfrac{1}{7}} \right) + 7\dfrac{1}{2}.\)

Lời giải chi tiết

Ta có:

\(\left( {2\dfrac{1}{3} + 3\dfrac{1}{2}} \right):\left( { - 4\dfrac{1}{6} + 3\dfrac{1}{7}} \right) \)\(+ 7\dfrac{1}{2}\)

\( = \left( {\dfrac{7}{3} + \dfrac{7}{2}} \right):\left( {\dfrac{{ - 25}}{6} + \dfrac{{22}}{7}} \right) \)\(+ \dfrac{{15}}{2}\)

\( = \left( {\dfrac{{14}}{6} + \dfrac{{21}}{6}} \right):\left( {\dfrac{{ - 175}}{{42}} + \dfrac{{132}}{{42}}} \right)\)\( + \dfrac{{15}}{2}\)

\( = \dfrac{{35}}{6}:\dfrac{{ - 43}}{{42}} + \dfrac{{15}}{2}\)

\( = \dfrac{{35}}{6}.\left( { - \dfrac{{42}}{{43}}} \right) + \dfrac{{15}}{2}\)

\( =  - \dfrac{{245}}{{43}} + \dfrac{{15}}{2}\)

\( = \dfrac{{ - 245.2 + 13.43}}{{86}}\\ = \dfrac{{155}}{{86}}\)

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