When is a whole not a whole? (again)

When it’s two wholes (or more) :-

John eats 1/2 of his pizza, Mary eats 3/4 of her pizza. So between them they ate 1/2 + 3/4 of a pizza, or 5/4 of a pizza.

So which whole are we referring to ? John’s pizza ……. No. Mary’s pizza ……. No. Both pizzas …….. No. John’s pizza and Mary’s pizza and both pizzas …….. No.

Conclusion: What we are referring to as “the same whole” is an abstract unit of one pizza, and the fractions are measurements using this unit. Wouldn’t it be a good idea to start off like this, with fractions as measurements, and avoid years of misunderstanding, stress and confusion.

Is this so different from adding whole(adjective!) numbers , as when adding two numbers they have to be counts of the same thing (or whole(!) before it is chopped up).?

Fun arithmetic: 3 apples + 4 bananas = 7 applanas

Desperately fun arithmetic : 1/2 of my money + 1/2 of your money = 1/2 of our money