Question

The value of \((2.3\overline{6}-0.1\overline{4})\) expressed as fraction in lowest terms is:

• A. \(\frac{111}{50}\)
• B. \(\frac{24}{11}\)
• C. \(\frac{20}{9}\)
• D. \(\frac{11}{5}\)

Hint:

\(a.b\overline{c} = \frac{abc - ab}{90}\)

Answer 1

The Correct Option is C

Step 1: Convert \(2.3\overline{6}\) to fraction.
\(2.3\overline{6} = 2 + 0.3\overline{6}\).
\(0.3\overline{6} = \frac{36-3}{90} = \frac{33}{90} = \frac{11}{30}\).
So \(2.3\overline{6} = 2 + \frac{11}{30} = \frac{60}{30} + \frac{11}{30} = \frac{71}{30}\). Step 2: Convert \(0.1\overline{4}\) to fraction.
\(0.1\overline{4} = \frac{14-1}{90} = \frac{13}{90}\). Step 3: Subtract the fractions.
\(\frac{71}{30} - \frac{13}{90}\).
LCM of 30 and 90 is 90.
\(\frac{71}{30} = \frac{213}{90}\).
\(\frac{213}{90} - \frac{13}{90} = \frac{200}{90}\). Step 4: Simplify.
\(\frac{200}{90} = \frac{20}{9}\).