Question

What is `5 1/3 - 7 5/6 + 6 1/4`?

Answer 1

`=3 3/4`

Explanation:

`5 1/3-7 5/6+6 1/4`
`=16/3-47/6+25/4`
`=(16(4)-47(2)+25(3))/12`
`=(64-94+75)/12`
`=45/12`
`=15/4`
`=3 3/4`

Answer 2

`3 3/4 larr" a slightly different approach"`

Answer is given in a lot of detail. With practice you will start to use shortcuts and use less working out.

Explanation:

Splitting the solution

`color(blue)("Solving for the whole numbers")`

`color(brown)(5-7+6 = 4)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Solving for the fractions")" "rarr 1/3-5/6+1/4`

You can not `ul("directly")` add or subtract fraction top numbers (numerators ) unless the bottom numbers (denominators) are the same

Note that 3,6 and 4 will all divide exactly into 12.

So we need to convert all the bottom numbers (denominators) into 12.

`color(brown)("Consider "1/3)`

Multiply by 1 but in the form `1=4/4" "`giving:

`1/3xx1" "->" "1/3xx4/4 = 4/12`

`color(brown)(1/3-=4/12)`
'.........................................................................

`color(brown)("Consider "-5/6)`

Multiply by 1 but in the form of `1=2/2` giving

`-5/6xx1" "->" "-5/6xx2/2 = -10/12`

`color(brown)(-5/6-=-10/12)`
'................................................................................

`color(brown)("Consider "1/4)`

Multiply by 1 but in the form of `1=3/3` giving:

`1/4xx1" "->" "1/4xx3/3=3/12`

`color(brown)(1/4-=3/12)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`4+4/12-10/12+3/12" "=" "4 -3/12`

`3 color(white)(.)(cancel(9)^3)/(cancel(12)^4)" "=" "3 3/4`