A ratio is a mathematical comparison of two values. Ratios can be written in phrase form or with the use of a colon, as in "5 to 3" or "5:3." You also can express ratios as a fraction, as in "5/3." Solving ratio fractions is a process of simplifying the fraction to its lowest terms. You also may have to compare ratio fractions to see which fraction is greater or which one is less.

Write down the ratio fraction. For example, you might have 4:10 or 4/10.

Find the greatest common factor for the numerator (upper number) and denominator (lower number) of the fraction. This is the largest number that will divide into both values evenly. In this case, 2 is the greatest common factor for 4 and 10.

Divide both numbers in the ratio fraction by the greatest common factor. In this example, you would divide 4 by 2 to get 2 and 10 by 2 to get 5. Therefore, your simplified fraction would be 2/5.

Find a common denominator to solve a comparison between two ratio fractions with unlike denominators. A common denominator is a number into which both denominators will divide evenly. For example, compare the following ratio fractions: 1/10 and 3/4. The denominators 10 and 4 will both divide into 20 evenly. Multiply the numerators by the quotient of the common denominator divided by each original denominator. In this case, 20 divided by 10 is 2. So you would multiply 2 by 1 to get the new ratio fraction 2/20. Then 20 divided by 4 is 5, so you would multiply 5 by 3 to get 15. This would construct the new ratio fraction, 15/20. Then you can compare the ratio fractions 2/20 and 15/20 so see that the second fraction is larger.