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How do you find the multiplicative inverse of 5/7?
It's ##\frac{7}{5}##.
By definition, the inverse multiplicative of a number ##x## is a number ##y## such that ##x \cdot y=1##. So, we have to find a number ##y## such that ##\frac{5}{7}\cdot y=1##, and that number is of course ##\frac{7}{5}##.