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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

When simplified, the fraction 20+15+20+15\frac{2}{0 + \frac{1}{5 + \frac{2}{0 + \frac{1}{5}}}} equals

A number or a short expression. Spacing and $ signs are ignored.

Solution

20+15+20+15=20+15+25+15=20+15+10=2115=2×15=30 \frac{2}{0 + \frac{1}{5 + \frac{2}{0 + \frac{1}{5}}}} = \frac{2}{0 + \frac{1}{5 + \frac{2}{5 + \frac{1}{5}}}} = \frac{2}{0 + \frac{1}{5 + 10}} = \frac{2}{\frac{1}{15}} = 2 \times 15 = 30

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