Algebra LINEAR EQUATIONS Step 3. Check the root. 1 1 2 2 1 1 2 3 1 2¹ 2 1 2¹ 2 2 5 2 5 0 The root checks. Ratio and Proportion One of the most important applications of fractional equations is ratio and proportion.   A ratio is a comparison of two like quantities by division.   It is written by separating the quantities by a colon or by writing them as a fraction.   To write a ratio, the two quantities compared must be of the same kind.  For example, the ratio of $8 to $12 is written as $8:$12 or .  Two unlike $8 $12 quantities cannot be compared by a ratio.   For example, 1 inch and 30 minutes cannot form a ratio.   However, two different units can be compared by a ratio if they measure the same kind of  quantity.    For  example,  1  minute  and  30  seconds  can  form  a  ratio,  but  they  must  first  be converted  to  the  same  units.    Since  1  minute  equals  60  seconds,  the  ratio  of  1  minute  to  30 seconds is written 60 seconds:30 seconds, or , which equals 2:1 or 2. 60  seconds 30  seconds A proportion is a statement of equality between two ratios.  For example, if a car travels 40 miles in  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 these 40  miles 80  miles 1  hour 2  hours two ratios is: 40 miles:80 miles = 1 hour:2 hours 40  miles 80  miles 1  hour 2  hours A proportion consists of four terms.   The first and fourth terms are called the extremes of the proportion; the second and third terms are called the means.   If the letters a, b, c and d are used to represent the terms in a proportion, it can be written in general form. a b c d Rev. 0 Page 13 MA-02