Comparing D

# Comparing Fractions

## Compare fractions with like numerators or denominators using models and symbols

Comparing fractions using like numerators or like denominators helps students to develop a deep understanding of the role of the numerator and the denominator in a fraction as well as the difference in change of magnitude in each (i.e., as the digit in the denominator increases, the size of the fractional unit decreases; as the digit in the numerator increases, the size of the fraction increases).

### Background

Comparing and ordering fractions allows students to develop a sense of fraction as quantity, as well as a sense of the size of a fraction, both necessary prior knowledge components for understanding fraction operations (Johanning, 2011).

Comparing and ordering fractions with different fractional units (or denominators) leads students to identify the need for equivalent fractions. When students determine an equivalent fraction they are changing the unit of measure by either splitting or merging the partitions of the original fraction. The following illustration demonstrates these concepts using an area model:

Splitting to determine an equivalent fraction for ^{2}⁄_{3}

Merging to determine an equivalent fraction for ^{6}⁄_{8}

The exploration of equivalence allows students to develop an understanding of equivalent fractions as simply being a different way of naming the same quantity; it also supports them in viewing the fraction as a numeric value. A solid understanding of equivalence helps students with fractions operations, especially addition and subtraction.

### References:

Johanning, D. I. (2011). Estimation's role in calculations with fractions.Mathematics Teaching In the Middle School, 17(2), 96-102.