Arithmetic Smart Math

[Smart Math] Arithmetic Problem 12

Here’s and example of a SMART MATH problem for ARITHMETIC.



\frac{409}{4+\frac{3}{4+\frac{3}{4+\frac{3}{4}}}} = ?

  1. 1
  2. 88
  3. \frac{88}{9}
  4. \frac{409}{88}
  5. 409

The Usual Method

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We have to simplify starting from the denominator value of 4+\frac{3}{4}

\therefore \frac{409}{4+\frac{3}{4+\frac{3}{4+\frac{3}{4}}}}=\frac{409}{4+\frac{3}{4+\frac{3}{{}^{19}\!\!\diagup\!\!{}_{4}\;}}}=\frac{409}{4+\frac{3}{4+\frac{12}{19}}}=\frac{409}{4+\frac{3}{\frac{88}{19}}}=\frac{409}{4+\frac{57}{88}}=\frac{409}{\frac{352+57}{88}}=\frac{409\times 88}{409}=88

(Ans: 2)

Estimated Time to arrive at the answer = 120 seconds.

Using Technique

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You can simply approximate the expression 4+\frac{3}{4+\frac{3}{4+\frac{3}{4}}}\approx 5(-) (Note, that the actual value will be less than 5 and hence the ‘–’ sign in brackets)

Hence, \frac{409}{5}\approx 82

Since, the actual denominator is less than 5, the final answer will be greater than 82. The only option coming close to this figure is 88, i.e option ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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