How to Write Ratios

By Kristy Wedel
The number of marbles in the boy's hand to the number on the table forms a ratio.
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Two-term ratios are very similar to a fraction, except they use a ":" symbol instead of a "/" sign. When saying "a:b," you would read it as "a to b." Like fractions, two-term ratios reduce to lowest terms by factoring out the GCF (or greatest common factor) from the left and right sides of the ratio and canceling. The difference between ratios and fractions is that operations are not defined on ratios. Ratios cannot be added, subtracted, multiplied or divided. You can write a ratio as a:b where "a" is a portion of the whole "b" and you can write a ratio as c:d where "c" is a portion of the whole "x" and "d" is a portion of the whole "x."

Determine how many of each component you have and then determine the total number. For example, if you have six blue marbles and four red marbles, you have 10 total marbles. The components are "six blue marbles" and "four red marbles" and the total is "10 marbles."

Find a relationship of "a to b" with the given information. This could be six blue marbles to 10 total marbles, four red marbles to 10 total marbles, six blue marbles to four red marbles, or four red marbles to six blue marbles.

Reduce the ratio to lowest terms. Using the ratio 4:10 from four red marbles to 10 total marbles, the expression reduces from 2(2):5(2) to 2:10 where the GCF is "2."

About the Author

I have a bachelor’s degree in mathematics from OSU and have written numerous articles on mathematics for eHow. I also have over 5 years experience in computer software/hardware troubleshooting. I have written many software troubleshooting documents as well as user guides for software packages such as MS Office and popular media software.