Question

By what number should $5^{-1}$ be multiplied so that the product may be equal to $(-7{)}^{-1}$ ?

Answer 1

$Letxbemultipliedto{5}^{-1},thenx\times 5^{-1}=(-7{)}^{-1}x\times \frac{1}{5}=\frac{1}{(-7{)}^1}\Rightarrow \frac{x}{5}=\frac{1}{-7}\Rightarrow x=5\times \frac{1}{-7}=\frac{-5}{7}\therefore Requirednumber=\frac{-5}{7}$