Fundamentals of Mathematics, 2008a

225
Now, consider the following examples by observing the respective shaded areas.
In the shaded region, there are 2 one thirds, or 2 3 .
2 ( )
1
3 =
2
3
There are 3 one thirds, or 3 3
, or 1.
3 ( )
1
3 =
3
3
or 1
Thus,
3
3 = 1
Improper fraction = whole number.
There are 4 one thirds, or 4 3 , or 1 and 1 3 .
4 ( )
1
3 =
4
3 or 1 and 1 3
The terms 1 and 1 3 can be represented as 1 + 1 3 or 1 1 3
Thus,
4
3 = 1 1 3 .
Improper fraction = mixed number.
There are 5 one thirds, or 5 3 , or 1 and 2 3 .
5 ( )
1
3 =
5
3
or 1 and 2 3
The terms 1 and 2 3 can be represented as 1 + 2 3 or 1 2 3 .
Thus,
5
3 = 1 2 3 .
Improper fraction = mixed number.
There are 6 one thirds, or 6 3
, or 2.
6 ( )
1
3 =
6
3 = 2 Available for free at Connexions