Compose and decompose fractions flexibly with models and symbols
Composing and decomposing fractions using any combination of fractions (beyond unit fractions) allows students to develop a deeper understanding of fractions as number.
A unit fraction is the base unit of any fraction and always has a numerator of 1; for example, 1⁄4, 1⁄15, 1⁄23 are all unit fractions. Every fraction can be decomposed into unit fractions. For example, 3⁄4 is 3 one-fourth units (so one-fourth is the unit fraction and we are thinking about 3 of them). Partitioning a model involves determining and creating a unit fraction.
Consider the fraction one and three-fourths. This number can be decomposed using a unit fraction.
One and two-fourths can be composed using a unit fraction.