Question

a) \(\frac{7}{15}+\frac{9}{10}+\frac{8}{15}-\frac{-1}{10}-\frac{20}{10}+\frac{1}{157}\)

b) \(\frac{1}{13}+\frac{16}{7}+\frac{3}{105}-\frac{9}{7}-\frac{-12}{13}\)

Answer 1

a) \(\frac{7}{15}+\frac{9}{10}+\frac{8}{15}-\frac{-1}{10}-\frac{20}{10}+\frac{1}{157}\)

\(=\frac{7}{15}+\frac{9}{10}+\frac{8}{15}+\frac{1}{10}-\frac{20}{10}+\frac{1}{157}\)

\(=\left(\frac{7}{15}+\frac{8}{15}\right)+\left(\frac{9}{10}+\frac{1}{10}\right)-2+\frac{1}{157}\)

\(=1+1-2+\frac{1}{157}\)

\(=2-2+\frac{1}{157}\)

\(=0+\frac{1}{157}=\frac{1}{157}\)

b) \(\frac{1}{13}+\frac{16}{7}+\frac{3}{105}-\frac{9}{7}-\frac{-12}{13}\)

\(=\frac{1}{13}+\frac{16}{7}+\frac{1}{35}-\frac{9}{7}+\frac{12}{13}\)

\(=\left(\frac{1}{13}+\frac{12}{13}\right)+\left(\frac{16}{7}-\frac{9}{7}\right)+\frac{1}{35}\)

\(=1+1+\frac{1}{35}\)

\(=2+\frac{1}{35}\)

\(=\frac{70}{35}+\frac{1}{35}=\frac{71}{35}\)