Cancellation of Fraction/Examples/27 over 30

Example of Cancellation of Fraction

The vulgar fraction:

$\dfrac {27} {30}$

after the process of cancellation, can be expressed as:

$\dfrac 9 {10}$

Proof

\(\ds \dfrac {27} {30}\)

\(=\)

\(\ds \dfrac {3 \times 3^2} {2 \times 3 \times 5}\)

expressing numerator and denominator in prime decomposition form

\(\ds \)

\(=\)

\(\ds \dfrac {3^2} {2 \times 5}\)

dividing numerator and denominator by the common divisor $3$

\(\ds \)

\(=\)

\(\ds \dfrac 9 {10}\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cancellation: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cancellation: 1.