Think back to our pancake example. Let's say that a recipe calls for two cups of flour and three cups of water. If you want to double the recipe, then you have to use four cups of flour and six cups of water. What do you know about these ratios (2:3 and 4:6)? Are they related in some way?
Question
Are these ratios related in some way?
In a way, these two fractions or ratios are equal. You can write \(\mathsf{ \frac{2}{3} = \frac{4}{6} }\), and it would be a true statement.
When two ratios are equal, the things they describe are said to be proportional. In a proportion, two ratios are equal, just as our proportions for flour to water are equal, \(\mathsf{ \frac{2}{3} = \frac{4}{6} }\).
Let's look at another example. Suppose you are building a scale model that involves the following two triangles.
You need to make sure that you are building all parts of your model to scale. The first step is to write the proportions for the triangles, making sure they are similar.
Question
What would the proportions be?
\(\mathsf{ \frac{6}{9} }\) = \(\mathsf{ \frac{10}{15} }\) = \(\mathsf{ \frac{8}{12} }\)
All these ratios are equal, and that makes this expression a proportion.
