Question

How do you solve `x/2 + 2/3 = 5/6`?

Answer 1

`x = 1/3`

Explanation:

`x/2 + 2/3 =5/6`

`x/2 =5/6 - 2/3`

The L.C.M of the denominators of the fractions of the R.H.S `= 6`

`x/2 =5/6 - (2 *2) / (3 *2)`

`x/2 =5/6 - 4/6`

`x/2 =1/6`

`x =(1/6) *2`

`x = 1/3`

Answer 2

Alternative approach

`x=1/3`

Explanation:

Notice that all the denominators are factors of 6

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To change the way a number looks without changing its value multiply by 1 but where 1 is in another form. For example

Changing `x/2` into `6 "th"^("s")` multiply by 1 but in the form of `1=3/3" "-> x/2xx3/3=(x xx3)/(2xx3) = (3x)/6`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "x/2+2/3=5/6`

Write as:`" " (x/2xx3/3)+(2/3xx2/2)=5/6`

`=> (3x)/6+4/6=5/6`

As everything is divided by 6 the equation is also true if we totally ignored the 6. Alternatively if you are not 'happy' about doing that this will get you to the same point:

Multiply everything by 6 giving:

`3x+4=5`

Subtract 4 from both sides:

`3x=1`

Divide both sides by 3

`x=1/3`