Multiplication by 2 over 3 in Egyptian Fractions/Examples/1 over 8

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

$\dfrac 2 3 \times \dfrac 1 8 = \dfrac 1 {16} + \dfrac 1 {48}$

despite the fact that it is apparent that:

$\dfrac 2 3 \times \dfrac 1 8 = \dfrac 1 {12}$

$\ds \dfrac 1 {16} + \dfrac 1 {48}$

$=$

$\ds \dfrac 1 {2 \times 8} + \dfrac 1 {6 \times 8}$

$\ds $

$=$

$\ds \dfrac 3 {6 \times 8} + \dfrac 1 {6 \times 8}$

$\ds $

$=$

$\ds \dfrac 4 {6 \times 8}$

$\ds $

$=$

$\ds \dfrac 2 {3 \times 8}$

$\ds $

$=$

$\ds \dfrac 2 3 \times \dfrac 1 8$

$\blacksquare$