Question

Write the problem for it take 10 copies of 1 sixth to make the same amount as 5 copies of 1 third? Explain your answer

Answer 1

10 copies of 1 sixth means , 10 times 1 sixth,


`10\cdot \frac { 1 }{ 6 } =\frac { 10\cdot 1 }{ 6 } =\frac { 10 }{ 6 }`

5 copies of 1 third means, 5 times 1 third,


`5\cdot \frac { 1 }{ 3 } =\frac { 5\cdot 1 }{ 3 } =\frac { 5 }{ 3 }`

To see why these two expressions are equal, we will simplify the first one.


`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 }`

As you can see from the simplification of the first expression,

10 copies of 1 sixth
`\frac { 10 }{ 6 }` is equal to 5 copies of 1 third
`\frac { 5 }{ 3 }`