What is an unlike fraction and like fraction

Unlike fractions: ones with different denominators.

Like fractions: ones with the same denominator.

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Examples:

1/3 and 1/4 are unlike fractions, because their denominators are different.

1/3 and 1/6 are also unlike fractions, because their denominators are different.

2/13 and 17/13 are like fractions, because their denominators are the same.

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Comment on like/unlike fractions

In general, addition and subtraction must be carried out on like fractions. That is, for unlike fractions to be added or subtracted, they must first be converted to like fractions. This is done by expressing both fractions using a common denominator. The common denominator is often chosen as the Least Common Multiple (LCM) of the two denominators, but it can be simply the product of the denominators:

a/b + c/d = (ad) / (bd) + (bc) / (bd) = (ad + bc) / (bd)

The reason for using the LCM of the denominators is that it may save work in reducing the final sum to lowest terms.