* Player 2 now needs to create a

proper fraction that meets the criterion established by Player 1 from the remaining seven cards.

According to the construction of {[a.sub.i]} and (11), we have [f.sub.2]/[f.sub.1] = [a.sub.1] = n/m, so [f.sub.2]/[f.sub.1] is the simplest

proper fraction of n/m.

where the remainder term [[??].sub.ij] (s)/[u.sub.ij] (s) is a

proper fraction.

In Lessons 1 through 15, the focus was on

proper fractions and improper fractions equal to 1.

A comparison of the part-whole and partitive reasoning with unit and non-unit

proper fractions. In Proceedings of the Thirtieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, edited by D.Y.

Start with the first five digits as denominators respectively (excluding unity) and only consider

proper fractions (p/q with p < q), not those improper or vulgar ones where the numerator is greater than the denominator.

Ounces are displayed as

proper fractions. A good quality choice if you don't need to weigh more than 3kg.

Thus, they will pose questions such as, "What are the lengths equivalent to two, three, or four 1/3 m?" This meaning of fractions is then used to expand the range of fractions beyond

proper fractions. Diagrams similar to Figure 3 are often included in the textbooks.

"Locating

Proper Fractions on Number Lines: Effect of Length and Equivalence." School Science and Mathematics 80(1980): 423-28.

Locating

proper fractions on number lines: Effects of length and equivalence.

Thus 3/2 or improper fractions are more difficult for students to conceptualise than

proper fractions.