Converting a mixed number into an improper fraction is an example of how to add fractions. Before we discuss how to add and subtract fractions more generally in Section 4.8, we need to address a related issue that will help you add and subtract fractions more easily.

Let's return to your aunt's coffee shop for a delicious and motivating example. Your aunt recently added a second breakfast sandwich to her menu, the Vegan Supreme. Like her original Bacon Breakfast Sandwich, her customers love her new addition.

However, your aunt can only prepare one type of breakfast sandwich next weekend due to some scheduled kitchen maintenance. She decides to conduct a survey to help choose which one she should offer and learns that 600 out of 1,000 customers prefer the Vegan Supreme. We can record this figure as a fraction, namely \frac{600}{1000}, but it turns out that this fraction is equivalent to a smaller, easier-to-read-and-understand expression. Namely

\frac{600}{1000} = \frac{3}{5}

It is easier to interpret this smaller-looking-but-equivalent fraction than to work with the original figure 600/1000. When we reduce the complex appearance of the original fraction – a process we call reducing the fraction or expressing it in lowest terms – it is clear that your aunt should offer the Vegan Supreme. Three-fifths of the customers she surveyed preferred it!

Reducing fractions not only helps us make sandwich decisions. It also makes arithmetic computations easier. Reducing fractions to their lowest terms simplifies and clarifies how we combine these numbers via our standard operations.
Back to '4.6 Fractions in Lowest Terms'