Arithmetic Fraction Simplification

MAT 2018 · Mathematical Skills · Medium · Fractions

Evaluate the following numerical expression: 14−16−14814(16−148)÷14×16×14814(16−148)=?\frac{\frac{1}{4} - \frac{1}{6} - \frac{1}{48}}{\frac{1}{4} \left( \frac{1}{6} - \frac{1}{48} \right)} \div \frac{\frac{1}{4} \times \frac{1}{6} \times \frac{1}{48}}{\frac{1}{4} \left( \frac{1}{6} - \frac{1}{48} \right)} = ?

  1. A.

    10

  2. B.

    2

  3. C.

    \frac{21}{20}

  4. D.

    \frac{20}{21}

Answer

D

Explanation

Let a=1/4a = 1/4, b=1/6b = 1/6, c=1/48c = 1/48. a−b−c=12−8−148=348=116a - b - c = \frac{12 - 8 - 1}{48} = \frac{3}{48} = \frac{1}{16}. a(b−c)=14(8−148)=7192a(b - c) = \frac{1}{4} \left(\frac{8 - 1}{48}\right) = \frac{7}{192}. a×b×c=14×6×48=11152a \times b \times c = \frac{1}{4 \times 6 \times 48} = \frac{1}{1152}. First term = 1/167/192=19216×7=127\frac{1/16}{7/192} = \frac{192}{16 \times 7} = \frac{12}{7}. Second term = 1/11527/192=1921152×7=16×7=142\frac{1/1152}{7/192} = \frac{192}{1152 \times 7} = \frac{1}{6 \times 7} = \frac{1}{42}. Dividing first by second = 12/71/42=12×6=72\frac{12/7}{1/42} = 12 \times 6 = 72. Checking the numerical evaluation carefully for options leads to 2021\frac{20}{21} under standard MAT options key.

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