Question

Reduce to simplest form. -7/8 - (-5/6)

Answer 1

`\large\boxed{-(7)/(8)-\left(-(5)/(6)\right)=-(1)/(24)}`

Explanation:

First step:

Find LCD (Least Common Denominator).

List of multiples of 8: 0, 8, 16, 24, 32, ...

List of multiples of 6: 0, 6, 12, 18, 24, 30, ...

LCD = 24

`(7)/(8)=(7\cdot3)/(8\cdot#)=(21)/(24)\\\\(5)/(6)=(5\cdot4)/(6\cdot4)=(20)/(24)`

We know: (-)(-) = (+), (+)(+) = (+), (-)(+) = (+)(-) = (-)

Therefore:

`-(7)/(8)-\left(-(5)/(6)\right)=-(7)/(8)+(5)/(6)=-(21)/(24)+(20)/(24)=(20)/(24)+\left(-(21)/(24)\right)\\\\=(20)/(24)-(21)/(24)=-(1)/(24)`