Why can't you add fractions with unlike denominators?

Answer 1

You cannot add fractions with different denominators because they do not represent the same size parts of a whole. (A half is larger than a third, so you cannot add them together as equals until they are expressed with the same denominator.)

When fractions have like denominators, we add the numerators and place them over the denominator, for example:

2/7 + 3/7 = (2 + 3)/7 = 5/7

We can add fractions with unlike denominators by finding their "least common denominator". For example: 2/3 + 5/6 can both be expressed in terms of a least common denominator (6). Multiply the numerator and denominator by the same number to convert the fraction.

2/3 + 5/6 -- multiply the numerator and denominator of 2/3 by 2, and 2/3 = 4/6

4/6 + 5/6 = 9/6 or 11/2

Another example : a common denominator for 3/4 and 1/5 would be 20

and 3/4 = 15/20 [ (3 x 5)/(4 x 5) ]

while 1/5 = 4/20 [ (1 x 4)/(5 x 4)

So 3/4 plus 4/5 would become 15/20 + 4/20 = 19/20.

Answer 2

When adding fractions with unlike denominators, the fractions represent different-sized pieces, making them incompatible for direct addition. In order to add fractions, the denominators must be the same to ensure that the pieces being added are of equal size. To add fractions with unlike denominators, you must first find a common denominator by identifying the least common multiple of the denominators and then adjust the fractions accordingly to have the same denominator before performing the addition.