wow, i feel really stupid!?

The word "of " implies multiplication.
½ x ⅔ = ⅓ (the 2`s cancel)
OR
½ x ⅔ = 2 / 6 = ⅓

Write out the fractions: 1/2 2/3

Multiply the top numbers (numerators) : 1 * 2 = 2
Multiply the bottom numbers (denominators) : 2 * 3 = 6

Numerator over denominator = 2/6
Simplify by dividing by 2/2 = 1/3

1/3

its simple, a half of 2/3rds is 2/6ths or 1/3rd

Mathmatically, "of" means multiply.
You're looking to multiply 1/2 by 2/3.

when multiplying fractions, always multiply numerators by numerators and denominators by denominators.

So, 1/2 times 2/3 = (1*2) / (2*3) = 2/6 or 1/3.

Simple check: You have two apples, two oranges, two thirds.

Half of them are one apple, one orange, one third.

well by saying one half of two thirds it actually means that you multiply the two fractions: 1/2*2/3 wich is performed as 1*2 / 2*3= 2/6 = 1/3...........

i think it is 1/3.
half 2/3 it is 1/3

1/2 of 2/3 is one third!
imagine you have TWO thirds. HALF it, you have ONE third!
If you put it into an equation, just mutliply the two- ie
1/2 * 2/3 = 2/6 = 1/3
Hope that helps.
happy new year!

one-half = 1/2
two-third = 2/3

one third

half of two is one... so if you have two thirds and halve it you get one third

QED

As you should!!!!
If you have TWO of ANYTHING, & take ONE of them away you only have ONE remaining.

Was this part of a "blond joke"?