Ratios, Rates, & Proportions

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In this lesson, we will review ratios, rates, and proportions. A ratio is a comparison of two quantities. Basically, it’s used when we want to compare the quantity of one thing versus the quantity of something else. As an easy example, suppose in a classroom there are 12 girls and 14 boys. We can write the ratio of girls to boys in the following three ways » 12:14 with a colon, 12/14 as a fraction, or 12 to 14, with the word "to". Additionally, we can simplify a ratio when there is a common factor other than 1. Notice how 12 and 14 are each divisible by 2, this means we can simplify this ratio of girls to boys by dividing each part by 2. This will give us the simplified ratio of girls to boys as: 6 to 7. A rate is a special type of ratio where the comparison involves different units. Most often, we are looking for a unit rate. A unit rate is the amount of one thing when compared to a single unit of another. For this situation, we will use the keyword "per" to refer to how much of one thing per one unit of another. As an easy example, suppose a car can go 100 miles on 10 gallons of gas. This car has a fuel efficiency rating of 10 miles per 1 gallon of gas. Lastly, we will review proportions. When two ratios or two rates are equal, they are known as a proportion. We can always check to see if we have a proportion by using the equality test for fractions. The equality test for fractions tells us that if two fractions are equal, their cross products are equal. Once more, for an easy example: 3/4 = 6/8 would represent a proportion.
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