Question

Which expression is equivalent to (-5/6) / (10/3)?

Answer 1

`(\left(-(5)/(6)\right))/(\left((10)/(3)\right))=-(1)/(4)`

Explanation:

Given the expression

`(\left(-(5)/(6)\right))/(\left((10)/(3)\right))`

Let us solve the expression

`(\left(-(5)/(6)\right))/(\left((10)/(3)\right))=(-(5)/(6))/((10)/(3))`

Apply fraction rule:
`(-a)/(b)=-(a)/(b)`

`=-((5)/(6))/((10)/(3))`

Divide fractions:
`((a)/(b))/((c)/(d))=(a\cdot \:d)/(b\cdot \:c)`

`=-(5\cdot \:3)/(6\cdot \:10)`

Multiply the numbers:
`6\cdot \:10=60`

`=-(5\cdot \:3)/(60)`

Multiply the numbers:
`5\cdot \:3=15`

`=-(15)/(60)`

Cancel the common factor: 15

`=-(1)/(4)`

Therefore, we conclude that the equivalent expression is:

`(\left(-(5)/(6)\right))/(\left((10)/(3)\right))=-(1)/(4)`