Comparing Fractions

Comparing fractions with Singapore Bar Models

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Because fractions are relative values, that is values arising from the relationship between two numbers, there is more than one way to write any particular fractional value. For example, thinking about the Bar Model representation, if both the number of equal parts and the number of parts shaded are doubled, then the same amount of the whole bar is shaded.

The following pair of bar models show how the fractions
^{2}⁄_{3} and
^{4}⁄_{6} have the same value.

Any fractions that have different number of equal parts (i.e. different denominator) but the same value are said to be equivalent. And given any two equivalent fractions, the one with the smallest denominator is said to be the simpler of the two.

The activities on this page involve comparing Bar Model representations of fractions by finding equivalent fractions, simplifying fractions, and ordering a set of fractions from smallest to largest.

The development of these bar model activities was inspired by William Emeny's Great Maths Teaching Ideas blog entry Bar modelling—a powerful visual approach for introducing number topics.