Fraction must be equal.
As teachers we make the mistake of teaching children the concept of fraction using apples.
We overlook that 1/2 of the apple is not equal. What do I mean?
One half of the apple could be bigger or smaller than another half and hence, it is not equal.
Although the item used (apple) is concrete but it is not Concrete Pictorial Approach. (CPA)
When the parts are equal, we can name them.
3/4 can be said as 3 out of 4 or 3 fourths or 3 quarters.
It should never be said as 3 upon 4.
3 - number; while 4 is the name (noun)
1/5 + 2/5 is the same as saying 1/cat + 2/cat
However, if the denominator is different, then we cannot add them up together because they are considered to be of different noun.
1/2 + 1/4 (it has different denominator - different names)
1/apple + 1/orange
2/4 + 1/4 = 3/4
Another example of fraction:
3/4 x 2 = 6/4
3 apples x 2 = 6 apples
Whole number and Fraction
7/5 = 1 + 2/5 = 1 2/5
1 and 2 fifths
"And" separates whole number with the fraction.