Question

Solve x - 3 1/8 = 5/12

Answer 1

`\large\boxed{x=(85)/(24)=3(13)/(24)}`

Explanation:

Convert the mixed number to the fraction:

`3(1)/(8)=(3\cdot8+1)/(8)=(25)/(8)`

METHOD 1:

`x-3(1)/(8)=(5)/(12)\\\\x-(25)/(8)=(5)/(12)\\\\\text{the common denominator is 24}\\\\x-(25)/(8)=(5)/(12)\qquad\text{multiply both sides by 24}\\\\24x-(3)(25)=(2)(5)\\\\24x-75=10\qquad\text{add 75 to both sides}\\\\24x=85\qquad\text{divide both sides by 24}\\\\\boxed{x=(85)/(24)}`

METHOD 2:

`x-3(1)/(8)=(5)/(12)\qquad\text{add}\ 3(1)/(8)\ \text{to oboth sides}\\\\x=(5)/(12)+3(1)/(8)\\\\x=(5\cdot2)/(12\cdot2)+3(1\cdot3)/(8\cdot3)\\\\x=(10)/(24)+3(3)/(24)\\\\x=3(10+3)/(24)\\\\\boxed{x=3(13)/(24)}`