What is a Ratio?
A comparison of two numbers by division. A quotient used to compare two or more quantities of the same units of measure. A statement of the relative size of two quantities (numbers, functions, and so on), expressed as a quotient.
A ratio is a way of comparing two quantities. It tells us how much of one thing there is compared to another. We use division to write this comparison and often express it in three different ways:
- As a fraction: \(\Large\frac{3}{4}\)
- With a colon: 3:4
- With the word "to": 3 to 4
For example, if a fruit basket has 3 apples and 4 oranges, we can describe the ratio of apples to oranges as 3:4. That tells us there are 3 apples for every 4 oranges.
Note that ratios compare things with the same units, like cups to cups, while rates compare different units like miles to hours.
We can use ratios to compare the number of boys to the number of girls. Both quantities are counted in students, so they share the same unit. Similarly, in a trail mix, we might describe the ratio of walnuts to almonds. Since both are types of nuts, we’re comparing like quantities—nuts to nuts.
Other examples of ratios include:
- Comparing ingredients in a recipe (e.g., 2 cups of flour to 1 cup of sugar)
- Reading maps and scale models
- Calculating miles per hour when driving
Ratios help us think in terms of relationships between numbers and understand proportions, rates, and percentages later on.
When Do Students Learn About Ratios?
Students are introduced to the concept of ratios as they begin working with fractions, multiplication, and division. This typically begins in upper elementary and deepens in middle school.
Grades 4–5 – Introduction to Ratios
Students start recognizing simple ratios and use them in basic word problems and measurement activities.
Grades 6–8 – Exploring and Solving Ratio Problems
Students solve ratio and proportion problems, work with unit rates, and apply ratios in tables, graphs, and real-world contexts.
