These students will need re-teaching, that should include visual and verbal reasoning activities that build a conceptual understanding using the part-whole relationship of

rational numbers (Lamon, 1999).

Although the repeated-addition interpretation of multiplication is ordinarily the first one that students encounter, by the time that operations on whole numbers are expanded to include

rational numbers, the meaning of multiplication must also be expanded.

Students can also use the fraction, percent, and decimal capabilities to link multiple representations of

rational numbers (see fig.

1] > 0 and a are

rational numbers, and D [not equal to] 0,1 is a square-free integer.

Pre-service teachers should be provided with opportunities to make connections among the various types of

rational numbers and with concepts of ratio and proportion.

The sides of this triangle however are

rational numbers 12, 20 4/11 and 23 7/11.

2013; Wu, 2001) have documented that developing proficiency in understanding fractions is critical if strong conceptual understanding of further mathematical concepts such as

rational numbers, proportional reasoning, and algebra is to be built.

Rational numbers and intensive quantities: Challenges and insights to pupils' implicit knowledge.

Contributing to students' low performance was their weak understanding of and computation with

rational numbers.

Those related to number systems are organized by their historical evolution and development in the elementary/middle school curriculum, fractions and integers are treated separately as an extension of whole numbers, and

rational numbers are discussed as extensions of fractions and integers.

Dombrowski has revealed a possible connection of the sizes of planetary orbits to density of

rational numbers on the number axis [1].

On the other hand, we prove in Proposition 7 that, surprisingly enough,

rational numbers are not computable (except for a few explicitly exhibited ones).

Students navigate around obstacles to learn about math facts, algebra, number sense and

rational numbers.

However, it took only a short time to decide to research

rational numbers, specifically fractions.

The study measured teacher knowledge and student achievement with

rational numbers tests developed specifically for this study.