# Ratios and Proportions

18.01.2019

Episode #1 of the course Everyday math by Jenn Schilling

Welcome to Everyday Math! This course will present 10 different everyday math concepts. Each day, you will understand the concept through a simple explanation and be presented with examples of that concept in everyday life.

I’m Jenn Schilling and I am a math educator. Prior to becoming an educator, I was an engineer and statistician. One of my favorite things to do as a middle school math teacher is help my students see the applications of math and how the math they are learning is used outside the classroom. I am super excited to go with you on this journey into everyday math, so let’s get started!

Today, we will be exploring ratios and proportions!

The Math

A ratio represents a comparison or relationship between two or more quantities. For example, fruit punch might be made by mixing 2 cups of orange juice with 3 cups of lemonade; the ratio of orange juice to lemonade would be 2 to 3. Ratios can compare quantities that have the same units as in the previous example, or they can compare quantities with different units, such as ten apples picked in four minutes. When ratios have different units, they are often referred to as rates, which we will discuss in more detail tomorrow in Lesson 2.

A ratio can be described in a few different ways. Using our first example, the word “to” can be used as in, 2 cups of orange juice to 3 cups of lemonade. Or we could say, 2 cups of orange juice for every/for each 3 cups of lemonade. Another way to explain this ratio is, 2 cups of orange juice per 3 cups of lemonade.

Ratios are equivalent when they have the same unit rate, which means that the ratios can be simplified to the same quantities. For example, 4 cups of orange juice to 6 cups of lemonade is equivalent to 10 cups of orange juice to 15 cups of lemonade. These ratios are equivalent because they both simplify to 2 cups of orange juice to 3 cups of lemonade, which is our original fruit punch ratio.

To simplify a ratio, you divide both “sides” of the ratio by the same number. So, the first ratio (4 to 6) can be divided on both sides by 2 to get 2 to 3, and the second ratio (10 to 15) can be divided on both sides by 5 to get 2 to 3. Ratios can thus be scaled up or down by multiplying and dividing, which is useful in applying ratios to everyday life.

Everyday Applications

Ratios are used extensively in mathematics and science, but they can also be found in many areas of everyday life. They are particularly useful in cooking. For example, any time you want to scale a recipe up or down, you are using ratios. Just as we did in the examples above, if you wanted to make more or less fruit punch, you would adjust the recipe accordingly. All ingredients must be adjusted in the same way to keep the proportion of each ingredient the same. If the ratio scaling is not done correctly, the recipe will not be the same; for example, the fruit punch ratio of 2 cups of orange juice to 3 cups of lemonade is not the same as 10 cups of orange juice to 12 cups of lemonade.

Ratios also appear any time we want to make comparisons. For example, let’s compare the prices for two different packages of plates. Plates come in a 25-pack and a 35-pack, and the 25-pack costs \$3.75, while the 35-pack costs \$4.20. You’d like to know which is the better deal. To find out, you can calculate the price per unit (a ratio!). By dividing \$3.75 by 25, you can find the price for one plate in the 25-pack, which is \$0.15. By dividing \$4.20 by 35, you can find the price for one plate in the 35-pack, which is \$0.12. So, you would pay \$0.03 more per plate to buy the 25-pack versus the 35-pack. We have now used ratios and unit rates to find the better deal!

Start looking for ratios and proportions in your daily life! You’ll be surprised at how frequently they show up! Tomorrow, we will learn about rates!

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