AlgebraLINEAR EQUATIONSStep 3. Check the root.1122112312^{1}212^{1}225250The root checks.RatioandProportionOne of the most important applications of fractional equations is ratio and proportion. A ratiois a comparison of two like quantities by division. It is written by separating the quantities bya colon or by writing them as a fraction. To write a ratio, the two quantities compared must beof the same kind. For example, the ratio of to is written as : or . Two unlikequantities cannot be compared by a ratio. For example, 1 inch and 30 minutes cannot form aratio. However, two different units can be compared by a ratio if they measure the same kindof quantity. For example, 1 minute and 30 seconds can form a ratio, but they must first beconverted to the same units. Since 1 minute equals 60 seconds, the ratio of 1 minute to 30seconds is written 60 seconds:30 seconds, or , which equals 2:1 or 2.60 seconds30 secondsA proportion is a statement of equality between two ratios. For example, if a car travels 40 milesin 1 hour and 80 miles in 2 hours, the ratio of the distance traveled is 40 miles:80 miles, or, and the ratio of time is 1 hour:2 hours, or . The proportion relating these40 miles80 miles1 hour2 hourstwo ratios is:40 miles:80 miles = 1 hour:2 hours40 miles80 miles1 hour2 hoursA proportion consists of four terms. The first and fourth terms are called the extremes of theproportion; the second and third terms are called the means. If the letters a, b, c and d are usedto represent the terms in a proportion, it can be written in general form.abcdRev. 0 Page 13 MA-02