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    The value of 55+14−178+7107 \frac{5}{5+\frac{1}{4-\frac{1}{\frac78}}}+\frac{7}{107}5+4−87​1​1​5​+1077​​ is:
    Question

    The value of 55+14178+7107 \frac{5}{5+\frac{1}{4-\frac{1}{\frac78}}}+\frac{7}{107}​ is:

    A.

    2

    B.

    1/2

    C.

    1

    D.

    -1

    Correct option is C

    Given:
    Expression: 55+14178+7107 \frac{5}{5+\frac{1}{4-\frac{1}{\frac78}}}+\frac{7}{107}​​
    Solution:
    55+1417/8+7107 =55+1487+7107 =55+128787+7107 =55+1207+7107 =55+720+7107 =510020+720+7107 =510720+7107 =5×20107+7107 =100107+7107 =107107 =1\frac{5}{5+\frac{1}{4-\frac{1}{7/8}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{4-\frac{8}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{\frac{28}{7}-\frac{8}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{1}{\frac{20}{7}}}+\frac{7}{107} \\ \ \\= \frac{5}{5+\frac{7}{20}}+\frac{7}{107} \\ \ \\= \frac{5}{\frac{100}{20}+\frac{7}{20}}+\frac{7}{107} \\ \ \\= \frac{5}{\frac{107}{20}}+\frac{7}{107} \\ \ \\= \frac{5 \times 20}{107}+\frac{7}{107} \\ \ \\= \frac{100}{107}+\frac{7}{107} \\ \ \\= \frac{107}{107} \\ \ \\= 1​​

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