LESSON 1 Ratios, Recipes, and Proportions

Peanut Brittle

Mr. Moreno's class is reviewing ratios using recipes. They are using two recipes for peanut brittle they found in a publication written by George Washington Carver at Tuskegee Institute in 1925.
Remember, a ratio is a way to compare two quantities or numbers. Ratios are often written as fractions. The ratio of peanuts to sugar in the recipe for Peanut Brittle Number One is 1 cup peanuts to 3 cups sugar. We can write this ratio as a fraction: .

We also write:

where P stands for cups of peanuts
and S stands for cups of sugar.

The ratio of peanuts to sugar can also be written with a colon between the quantities:

1 : 3

We can choose to compare the quantities in a different order. For example, we can compare the amount of sugar to the amount of peanuts. In words we say, “The ratio of sugar to peanuts is 3 cups to 1 cup.” Using a fraction, we write this as . Using a colon we write the ratio of sugar to peanuts as 3 : 1.