When adding two fractions
Take care, delay your actions.
You must allow the whole
To exercise its role.
(Possibly and unwittingly owing something to Ogden Nash)
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
When is a whole not a whole ?
When it’s a hole.
(which half of the hole shall we fill first, the top half or the bottom half?)
Besides, I thought whole was an adjective.