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When you divide something into two equal parts you are halving it. This process is often used to teach fractions in school.
An angle bisector.
Bisecting an angle
The number of equal parts in a whole depends on how the whole is divided. If the whole is divided into halves, there are 2 equal parts. If divided into thirds, there are 3 equal parts, and so on. In general, the number of equal parts in a whole is determined by the denominator of the fraction used to represent the parts.
bisect