What is one-half of one and two thirds?

1 Answer
Dec 19, 2016

Answer:

#r = 2/3#

Explanation:

We can rewrite this problem as

What is #1/2# of #1 1/3#?

When dealing with fractions the word "of" means "times" or "to multiply".

Also, let's call the value we are looking for #r#:

So we can again rewrite this as:

#r = 1/2 xx 1 1/3#

To complete this problem we need to convert the mixed fraction to an improper fraction. We do this by multiplying the integer by the proper form of #1# and then adding it to the fraction:

#r = 1/2 xx ((color(red)(3/3) xx 1) + 1/3)#

#r = 1/2 xx (color(red)(3/3) + 1/3)#

#r = 1/2 xx (3 + 1)/3#

#r = 1/2 xx 4/3#

#r = (1 xx 4)/(2 xx 3)#

#r = 4/6#

#r = (2 xx 2)/(2 xx 3)#

#r = (2/2) xx (2/3)#

#r = 1 xx 2/3#

#r = 2/3#