10 copies of 1 sixth means , 10 times 1 sixth,
[tex]10\cdot \frac { 1 }{ 6 } =\frac { 10\cdot 1 }{ 6 } =\frac { 10 }{ 6 } [/tex]
5 copies of 1 third means, 5 times 1 third,
[tex]5\cdot \frac { 1 }{ 3 } =\frac { 5\cdot 1 }{ 3 } =\frac { 5 }{ 3 } [/tex]
To see why these two expressions are equal, we will simplify the first one.
[tex]10=2\cdot 5\\ 6=2\cdot 3\\ \\ \frac { 10 }{ 6 } =\frac { 2\cdot 5 }{ 2\cdot 3 } =\frac { 2 }{ 2 } \cdot \frac { 5 }{ 3 } =1\cdot \frac { 5 }{ 3 } =\frac { 5 }{ 3 } [/tex]
As you can see from the simplification of the first expression,
10 copies of 1 sixth [tex]\frac { 10 }{ 6 } [/tex] is equal to 5 copies of 1 third [tex]\frac { 5 }{ 3 } [/tex]
