The use of **one-half**, vs **half**.

Question

I don't know what category this would go in, so please help me with that.

Something I have noticed is that people use the word one-half, and half interchangeably.

Suppose you have 6 milk cartons.

One would say, "I'll take half of those cartons.

Suppose you have $50$$.

One would say, Give me one-half of your money.

Both of these words in the english language imply $50%$. These words are used interchangeably, but doesn't one-half correspond to $1\frac{1}{2}$, which is clearly not half. Why is this, why do people use it interchangeably? (Please add a tag I don't know the right one).

Answer 1

Both "one-half" and "half" refer to $1/2=0.5$. To say $1\frac{1}{2}$, we would say either "one and a half" or "three halves."

Answer 2

The issue is one of spoken English usage.

There are no formal written rules.

In general, you use the form "one half" when you want to be exact and accurate and to stress the precise value of a mathematical expression, but you say "a half" or "half of" in more casual speech and expressions.

Casual: "Give me half a pound (or kilogram) of cheese, please." "There's only about half a liter of gas (petrol) left in the motorscooter; I have to fill it up right away." "Nearly half of the class were absent with flu yesterday."

Exact-mathematical-scientific "The integral of x dx is one half x squared." "Measure one half liter of water and place in your flask." "The length of cloth needed for this pattern is one and one half meters." "Find the length of time it will take for the population to reduce to one half of its original level.

Again these are not strict rules but matters of preferred usage.