Using Manipulatives to Reduce Fractions

Property We can use fraction manipulatives to reduce a given fraction by making an equivalent model that uses the fewest pieces. For example, the fractions $\frac{4}{8}$, $\frac{3}{6}$, and $\frac{2}{4}$ all reduce to $\frac{1}{2}$.

Examples Using manipulatives shows that $\frac{2}{6}$ is equivalent to one $\frac{1}{3}$ piece. Using manipulatives shows that $\frac{4}{8}$ is equivalent to one $\frac{1}{2}$ piece. Using manipulatives shows that $\frac{6}{8}$ is equivalent to three $\frac{1}{4}$ pieces, so it reduces to $\frac{3}{4}$.

Explanation Think of reducing fractions like swapping your piggy bank change for bigger bills. Four quarters and a one dollar bill are worth the same, but the bill is simpler! Reducing fractions is about finding the simplest name for that amount by using the biggest, fewest pieces possible. This makes fractions much easier to work with and compare.