Like fractions

Like fractions are fractions that share the same denominator (the number on the bottom of the fraction). The two fractions below are like fractions.

It is important to learn how to convert fractions into like fractions (it is possible to convert any set of fractions into like fractions), since in order to perform arithmetic operations such as addition and subtraction with fractions, the fractions need to be like fractions.

If the fractions are like fractions, addition and subtraction just involves adding or subtracting the numerators, with the result keeping the same shared denominator. If the denominators are not the same however, the numerators cannot be directly added or subtracted since the different denominators mean that the the whole part of the fractions are different. In order to know how one fraction relates to another, we need to know how many parts of the same whole each fraction represents. We can use fraction bars to depict this.

We cannot add 1/2 and 1/3 because they are broken into a different number of parts, but if we convert them into equivalent fractions with the same number of parts, we can add them. We converted 1/2 to 3/6 by multiplying the numerator and denominator by 3; 1/3 was converted to 2/6 by multiplying the numerator and denominator by 2.

It is possible to convert any unlike fraction to a like fraction. There are various methods for doing this, but the most straightforward (albeit potentially tedious) is to multiply all the denominators of the fractions being added, then multiply each numerator by the appropriate factors. Doing so will ensure that the denominators are the same and the fractions can be added or subtracted.

In the above example, using this method results in a fraction in simplest form, but this is usually not the case. In many cases, using this method will result in having to reduce the fraction to its lowest terms. To avoid having to do this, we can find the least common multiple (LCM) between all the fractions, then convert the fractions to equivalent fractions such that each of the fractions has the least common multiple as the denominator. Refer to the least common multiple page for details on the various methods for finding the LCM. Once we know the LCM, multiply the numerator and denominator of each fraction by the appropriate factor that will result in the denominator being the LCM. Once this is done, the fractions can be added or subtracted as described above.