Inverse Element/Examples/Rational Multiplication

Examples of Inverse Elements

Consider the multiplicative group of positive rational numbers $\struct {\Q_{> 0}, \times}$.

$\tfrac 4 {23}$ and $5 \tfrac 3 4$ are inverses of each other.

Proof

\(\ds 5 \tfrac 3 4\)

\(=\)

\(\ds \dfrac {5 \times 4 + 3} 4\)

\(\ds \)

\(=\)

\(\ds \tfrac {23} 4\)

Then we have:

\(\ds \tfrac 4 {23} \times \tfrac {23} 4\)

\(=\)

\(\ds \dfrac {4 \times 23} {23 \times 4}\)

\(\ds \)

\(=\)

\(\ds 1\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse: 2.