What is a Ratio?
A ratio compares two quantities by showing how much of one there is relative to the other. It is one of the most practical math concepts in everyday life , from recipes to maps to financial analysis.
A ratio is a comparison of two quantities by division. Written as 3:2, 3/2, or "3 to 2." It means for every 3 of the first thing, there are 2 of the second. A class with 18 boys and 12 girls has a ratio of 18:12, which simplifies to 3:2.
In this lesson
1 What a Ratio Means
A ratio expresses how much of one thing there is compared to another. If a bag has 3 red balls and 5 blue balls, the ratio of red to blue is 3:5. That means for every 3 red balls, there are 5 blue ones.
Ratios don't tell you the actual quantities , only their relationship. A ratio of 3:5 could mean 3 and 5, or 30 and 50, or 300 and 500. They all share the same proportional relationship.
3:5 looks like the fraction 3/5, but they represent different ideas. The fraction 3/5 means 3 out of 5 total. The ratio 3:5 means 3 of one thing for every 5 of another , a total of 8 parts. Context determines which interpretation applies.
2 How to Write and Read Ratios
Three equivalent notations: 3:5 (colon form), 3/5 (fraction form), "3 to 5" (word form). They all mean the same thing. Colon form is most common in everyday use; fraction form is most useful for calculations.
Order always matters. The ratio of cats to dogs (3:2) is different from the ratio of dogs to cats (2:3). Always read carefully to identify which quantity comes first.
3 Simplifying Ratios
Like fractions, ratios can be simplified by dividing both parts by their GCF (greatest common factor). This gives an equivalent ratio in smaller numbers.
To scale a ratio up or down, always multiply or divide both parts by the same number. Adding doesn't preserve the relationship: 2:3 and 4:5 are NOT the same ratio even though you added 2 to both.
4 Part-to-Part vs Part-to-Whole
Part-to-part ratio compares one part of a group to another part. In a class of 30 with 18 girls and 12 boys, the girl-to-boy ratio is 18:12 = 3:2.
Part-to-whole ratio compares one part to the entire group. The ratio of girls to all students is 18:30 = 3:5. This is equivalent to the fraction 3/5 (or 60%) of the class.
If the part-to-part ratio is 3:2, you know there are 3+2 = 5 total parts. Girls are 3 out of 5 total, so the part-to-whole ratio is 3:5. You can always convert between types by adding the parts to get the whole.
5 Using Ratios to Solve Problems
Practice Problems
Sources & Further Reading
The explanations on this page draw on the following established sources. We link to primary and secondary sources so you can verify claims and go deeper on any topic.