Multiplication by 2 over 3 in Egyptian Fractions/Examples/1 over 5

Example of Use of Multiplication by 2 over 3 in Egyptian Fractions

$\dfrac 2 3 \times \dfrac 1 5 = \dfrac 1 {10} + \dfrac 1 {30}$

Proof

\(\ds \dfrac 1 {10} + \dfrac 1 {30}\)

\(=\)

\(\ds \dfrac 1 {2 \times 5} + \dfrac 1 {6 \times 5}\)

\(\ds \)

\(=\)

\(\ds \dfrac 3 {6 \times 5} + \dfrac 1 {6 \times 5}\)

\(\ds \)

\(=\)

\(\ds \dfrac 4 {6 \times 5}\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds \dfrac 2 3 \times \dfrac 1 5\)

$\blacksquare$

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Egyptian Fractions