4.2 Introduction and Key Insights

Just as different words can represent the same concept (the synonyms big and large), different mathematical expressions can represent the same quantity. For example, imagine a pizza cut into four slices. Each slice represents $\frac{1}{4}$ of the pizza. If you eat two of the four slices, you can say you ate $\frac{2}{4}$ of the entire pizza. As this image indicates, our two $\frac{1}{4}$ slices make up an entire $\frac{1}{2}$ of the pizza.

This is all to say that for our pizza example, $\frac{2}{4}=\frac{1}{2}$. Each of these fractions has a different numerator and denominator, but they both represent the same quantity or value. We say these two fractions are equivalent. Equivalent fractions may be written to look different, but they represent the same value.

As practice, can you determine equivalent ways to write the fraction $\frac{2}{6}$? Are $\frac{3}{4}$ and $\frac{75}{100}$ equivalent? How can you tell?