Question

A piece of metal `3 7/8` inches long is to be cut from a longer piece of `5 1/16` inches. What will be the length of the remaining piece?

Answer 1

`=1 3/16` inches

Explanation:

Remaining piece will be
`5 1/16-3 7/8`
`=81/16-31/8`
`=81/16-62/16`
`=19/16`
`=1 3/16` inches

Answer 2

`1 3/16` inches left

Explanation:

A fraction is split into 2 parts:

`("count")/("size indicator")->("numerator")/("denominator")`

I am calling the denominator 'size indicator' as the number is however many of what you are counting it takes to make a whole of something.

`1/2` takes two of them to make a whole
`1/5` takes five of them to make a whole of something so it is smaller.

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)("You can not "ul("directly") " add or subtract the counts unless"` `color(red)("the size indicators are the same")`

Given:`" "5 1/16-3 7/8`

Write as `81/16-31/8`

Multiply by 1 and you do not change the value, but 1 can come in many forms

`color(brown)(81/16-(31/8xx1))color(blue)(" "->" "81/16-(31/8xx2/2))`

`= 81/16-62/16`

`=19/16`

`= 1 3/16`