How do you evaluate `5\frac { 3} { 4} + 4\frac { 1} { 2}`?

Once well practised you will be able to solve this problem type in just a few lines.

Consider this as `5+3/4+4+1/2`

`color(brown)("The whole number part is "5+4=9)`

Consider the fraction part.

We have `3/4+1/2`
................................................................................................
A fractions structure is such that you have:

`("count")/("indicator the size of what is being counted")->("numerator")/("denominator")`

You can not `ul("directly add")` the counts unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its actual value.
..............................................................................................................

`color(green)(3/4" "+" "[1/2color(red)(xx1)])`

`color(green)(3/4" "+" "[1/2color(red)(xx2/2)])`

`3/4" "+" "2/4" "=" "(3+2)/4=5/4`

but `5/4` is the same as `4/4+1/4=1 +1/4`

`color(brown)("So the fraction part is "3/4+1/2=1 1/4`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`color(blue)(9+1 1/4=10 1/4)`