1.

Simplify each of the following and express the result as a rational number in standard form:i) \(\frac{-16}{21}\times\frac{14}{5}\)ii) \(\frac{7}{6}\times\frac{-3}{28}\)iii) \(\frac{-19}{36}\times16\)iv) \(\frac{-13}{9}\times\frac{27}{-26}\)v) \(\frac{-5}{9}\times\frac{72}{-25}\)

Answer»

i) (-16/21) × (14/5)

\(=\frac{-16}{21}\times\frac{14}{5}\\=\frac{-16}{3}\times\frac{2}{5}\\=\frac{-16\times2}{3\times5}\\=\frac{-32}{15}\) 

ii) (7/6) × (-3/28)

\(=\frac{7}{6}\times\frac{-3}{28}\\=\frac{1}{2}\times\frac{-1}{4}\\=\frac{-1}{8}\)

iii) (-19/36) × 16

\(=\frac{-19}{36}\times16\\=\frac{-19}{9}\times4\\=\frac{-19\times4}{9}\\=\frac{-76}{9}\)

iv) (-13/9) × (27/-26)

\(=\frac{-13}{9}\times\frac{27}{-26}\\=\frac{-1}{1}\times\frac{-3}{2}\\=\frac{-3}{-2}\\=\frac{3}{2}\)

v) (-5/9) × (72/-25)

\(=\frac{-5}{9}\times\frac{72}{-25}\\=\frac{-1}{1}\times\frac{8}{-5}\\=\frac{-1\times8}{1\times-5}\\=\frac{-8}{-5}\\=\frac{8}{5}\)


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