Question

How do you add `-9/8+7/4`?

Answer 1

`-9/8+7/4=5/8`

Explanation:

WE have denominators `4` and `8` here and their GCD is `8`, hence we can add them by converting them to common GCD.

`-9/8+7/4`

= `-9/8+(7xx2)/(4xx2)`

= `-9/8+14/8`

= `(-9+14)/8`

= `5/8`

Answer 2

`5/8`

Explanation:

Fraction`->("count")/("size indicator")->("numerator")/("denominator")`
`color(white)(.)`

Size indicator is how many of what you are counting to make a whole 1 of something.

`color(white)(.)`
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Point 1")`

We need to add/subtract counts but we can only do this 'directly' if the 'size indicators' (denominators) are the same.

`color(blue)("Point 2")`
Multiply by 1 and you do not change the intrinsic value. However, 1 comes in many forms. So we can change the way something looks but not change its intrinsic value.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "-9/8+7/4`

Change the order:

`7/4-9/8`

This is the same in value as:

`(7/4color(magenta)(xx1))-9/8`

But write 1 as `1=2/2` giving:

`(7/4color(magenta)(xx2/2))-9/8" "->" "(7xx2)/(4xx2)-9/8`

`14/8-9/8 = 5/8`