## Fractions

A fraction can be used to represent a part of a whole or part of a group or collection of things. For example, a whole circle can be divided into four equal parts and the fraction used to represent three of four equal parts. Children should be reminded that the parts into which the whole is divided must be of equal size.

A fraction can be defined formally as a number that can be expressed in the form , where b ≠ 0, a is the numerator, and b is the denominator. The denominator of a fraction cannot equal zero.

A unit fraction is a fraction with a numerator of 1 (for example, , , , ). The definition of a unit fraction is to take one unit and divide it into n equal pieces. One of these smaller pieces is the amount represented by the unit fraction.

The fraction can represent the quotient of m and n or m ÷ n. If the fraction is defined in terms of the unit fraction , the fraction means m unit fractions of . If m = n, then = 1.

Comparing Fractions
At this grade level, the comparing and ordering of fractions is limited to unit fractions, and pictures are provided to aid a child in deciding which of two fractions is the greater or lesser. For unit fractions, > if and only if a < b. For example, > because 3 < 4.

Children learn that a fractional part of a number, such as of 6, can be found by separating the group of six into the same number of equal groups as the denominator of the fraction, which is 3 in this case, and then counting the number in 1 group, which is 2. So of 6 is 2.

2 is of 6.

Teaching Model 9.4: Comparing Fractions