A ratio is a comparison of two numbers. They take the form of two numbers side by side, separated by a semi-colon. The left number is how much you have of one quantity, and the right is how much you have of another. Adding ratios is a straight forward process. The most important steps are converting the ratios to common fractions and finding their common denominator. When fractions have a common denominator the bottom numbers are the same. We'll add together the ratios 1:3 and 2:4 to illustrate how it's done.
Convert the ratios to fractions. For example, the ratio 1:3 means there is one of something, three of something else, and four units total. A fraction is a relationship of one part to a whole. So the ratio 1:3 is converted to the fraction 1/(1+3), or 1/4. Using the same methodology, the ratio 2:4 is converted to the fraction 2/6.
Multiply each number in the first fraction by the denominator in the second. The numerator is the number on top, and the denominator is the number on the bottom. Multiplying by this number allows the first fraction to have a common denominator with the second fraction. In the example, we multiply 1 × 6 = 6, and 4 × 6 = 24. The new ratio is 6/24, which has the same value as 1/4.
Multiply each number in the second ratio with the denominator in the first ratio. This step is handled the same way as step one. In our example, we multiply 2/6 by 4. 2 × 4 = 8, and 6 × 4 = 24. The new fraction is 8/24. The two fractions now have a common denominator and can be added together.
Add the two numerators. Do not add the denominators. In our example, to add 6/24 to 8/24, we find the sum of the numerators (6 + 8 = 14) and keep the denominator the same; the result is 14/24.
Simplify the fraction. Perform this task by finding the biggest number that divides evenly into both the numerator and denominator. For the fraction 14/24, the biggest number is 2. Divide both numbers by 2 and you get 7/12.
Double check your answer by plugging the values into a calculator. In our example the decimal value of our final fraction is 0.583, with repeating three's. If you get the same number, you know you added them together correctly.
Convert the fraction back to ratio. A fraction is converted to a ratio by subtracting the numerator from the denominator and using that value for the other half of the ratio. In our example, 7/12 is converted to the ratio 7:(12 - 7) = 7:5. Double check your answer by converting the ratio back to a fraction: 7/(5 + 7) = 7/12.