How to Do Linear Proportions

Learn how to convert fractions, as ratios are simply another way of expressing fractions. For example the ratio 3:4 is spoken as 3 to 4, which is the same as 3/4 and can also be written as 0.75. You may need to calculate a ratio from a written scenario, for instance if I had a bag containing balls of different colors --- 3 blue 5 orange and 7 pink --- and asked you to work out the ratio of orange balls to the total number of all the balls in the bag, then you would write the number of orange balls to the total number of balls, or 5 to 15, which makes 5:15 when written in ratio form. Remember that just like fractions, ratios can be simplified also, meaning the most correct answer would be 1:3.

Compare two proportions. The ratios 1:2 and 6:12 are equal to each other, 1:2 = 1/2, 6:12 = 6/12 = 1/2. Note that the ratios 1:2 and 2:1 are not equal, as each is the inverse of the other. With this in mind it may be easier to compare large ratios to a fixed whole number such as one, for example 23:34 and 78:12 are clearly not equal because 23:34 is less than one, whereas 78:12 is greater than one.

Use algebraic equations when working with linear proportions that involve unknown variables. If you are presented with the proportion 5/10 = y/20, by rearranging the terms you can leave y on the right hand side, with all the numbers on the left hand side: 5*20/10 = y. From here simplify the fraction on the left hand side to solve y = 10. These types of questions are also often combined with the concepts of distance, speed and time. You may be asked these questions in the style "If Mike can run 6km in 45 minutes, how far could he run in 60 minutes?" First place the terms as an algebraic proportion: 6/45 = x/60, shift 60 over to the left hand side, and simplify the fraction, which should produce the result 8, or 8km.