Common fractions that have the same denominator are called homonymous. If fractions are expanded so that they have the same denominators, they are called homonymous. For example, two fractions can be made homonymous by expanding one fraction with the denominator of the other fraction. This means that both the numerator and the denominator of one fraction are multiplied by the denominator of the other fraction. Since the two denominators are always multiplied, the values of the expanded fractions can often become very large, which could make further calculations more complicated. In practical calculations, the smallest common denominator (main denominator) of the fractions should therefore be determined in order to make them equal. The main denominator is the lowest common multiple (LCM) of the denominators, which is often smaller than the multiplication of the two denominators. We will explain this in more detail in the next section.
Making them have the same denominator is used, for example, in the addition and subtraction of fractions: If the two fractions have the same denominator, the numerators of the two fractions can be added or subtracted, while the denominator, which is the same for both fractions, remains unchanged.
Example: Making fractions equal
The fractions 16 and
38 are to be given the same name.
Widening the left fraction 16 with 8, i.e., with the denominator of the right-hand fraction.
Extend the right fraction 38 with the denominator 6 of the left fraction.
This is how you get the fractions of the same denominator
848 and
1848.