JAMB - Mathematics (2006 - No. 15)
simplify \(\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}}\)
\(\frac{11}{12}\)
\(\frac{5}{6}\)
\(\frac{1}{5}\)
\(\frac{2}{15}\)
Explanation
\(\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}}\\
=\frac{\frac{7-6}{9}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}}\\
=\frac{\frac{1}{9}}{\frac{1}{3}+\left(\frac{2}{5}\times \frac{5}{4}\right)}\\
=\frac{\frac{1}{9}}{\frac{1}{3}+\frac{1}{2}}\
=\frac{\frac{1}{9}}{\frac{2+3}{6}}\\
=\frac{\frac{1}{9}}{\frac{5}{6}}\\
=\frac{1}{9}\times\frac{6}{5}\\
=\frac{2}{15}\)
=\frac{\frac{7-6}{9}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}}\\
=\frac{\frac{1}{9}}{\frac{1}{3}+\left(\frac{2}{5}\times \frac{5}{4}\right)}\\
=\frac{\frac{1}{9}}{\frac{1}{3}+\frac{1}{2}}\
=\frac{\frac{1}{9}}{\frac{2+3}{6}}\\
=\frac{\frac{1}{9}}{\frac{5}{6}}\\
=\frac{1}{9}\times\frac{6}{5}\\
=\frac{2}{15}\)
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