where [D'.sub.f] and m' are obtained by reduction of a fraction to the

lowest terms. If [H.sub.P,m] = [D.sub.f]/m is reduced to

lowest terms such that [H.sub.P,m] = [D'.sub.f]/m', one can see that an integer value [D'.sub.f] is a multiple of [H.sub.P,m] and [H.sub.l](k) [approximately equal to] [H.sub.l](k + [D'.sub.f]), which says that the channel [H.sub.l](k) is periodically flat every [D'.sub.f] subcarriers.

If the numerator and denominator can be divided evenly by the same number, simplify to lowest terms. For example:

Simplified or reduced to lowest terms, it is 13/60.

give your answers as a fraction in its

lowest terms.

For years, teachers' language implied that reducing fractions meant simplifying them, or putting them in

lowest terms. Some students are confused by this implication.

The following six examples were selected to check the algorithms that students use for finding sums, products, and differences, and for reducing fractions to lowest terms.

Most of the students multiplied the numerators together, multiplied the denominators together, and then reduced the fraction to lowest terms. This works, but is not very efficient.

The fractions always had to be in

lowest terms; other forms, which might promote greater understanding, were not allowed.

They discovered that a fraction is in lowest terms if the numerator and the denominator do not have any common factors other than 1.

RELATED ARTICLE: FIGURE 1 Kristy's running record through the eighteenth day reveals when she started reducing to lowest terms.

These kits are to be used in conjunction with the FraConcepts manipulatives and illustrate such concepts as identifying and naming fractions, equivalent fractions, fractions expressed in

lowest terms, and adding and subtracting fractions.