Understanding Ratios and Ratio Language

Students interpret, write, and explain ratios that compare two quantities in real-world situations.

What Is a Ratio?

A ratio compares two quantities by showing how much of one quantity there is in relation to another. Suppose a bag contains 3 red counters and 5 blue counters. The ratio of red counters to blue counters is 3 to 5. This means that for every 3 red counters, there are 5 blue counters. The order of the quantities matters. The ratio of blue counters to red counters is 5 to 3, which describes the same collection from the opposite order. A ratio does not tell only how many objects there are. It describes a relationship between the quantities. Always name the quantities in the same order as their numbers so that the meaning of the ratio is clear.

Writing Ratios in Three Forms

A ratio can be written in three common forms: with words, with a colon, or as a fraction. If a team has 4 sixth-grade students and 7 seventh-grade students, the ratio of sixth graders to seventh graders can be written as 4 to 7, 4:7, or 4/7. All three forms describe the same comparison. In fraction form, the first quantity is written above the fraction bar and the second quantity is written below it. The order must stay the same in every form. Writing 7:4 would compare seventh graders to sixth graders instead. When you read a ratio, include the names of the quantities. Saying “4 sixth graders to 7 seventh graders” communicates more information than simply saying “4 to 7.”

Part-to-Part and Part-to-Whole Comparisons

Ratios can compare one part with another part or compare one part with the entire group. Imagine a fruit bowl containing 4 apples and 3 oranges. The ratio of apples to oranges is 4:3. This is a part-to-part ratio because apples and oranges are two different parts of the collection. There are 7 pieces of fruit altogether, so the ratio of apples to all the fruit is 4:7. This is a part-to-whole ratio. The ratio of oranges to all the fruit is 3:7. Before writing a ratio, identify exactly which quantities are being compared. Do not use 4:3 for apples to total fruit because the total includes both the 4 apples and the 3 oranges.

Interpreting Ratios in Context

Interpreting a ratio means explaining what its numbers represent in a situation. A paint mixture uses 2 cups of blue paint for every 5 cups of white paint. The ratio of blue paint to white paint is 2:5. In words, this means that for every 2 cups of blue paint, the mixture uses 5 cups of white paint. The ratio does not mean there are 5 cups of paint altogether; one batch contains 7 cups in total. Equivalent batches keep the same relationship. For example, doubling both quantities gives 4 cups of blue paint and 10 cups of white paint. When interpreting any ratio, state the quantities, keep them in order, and use language such as “for every” to make the relationship clear.

Create and Explain a Ratio

To create a ratio, choose two quantities, count or measure them, and list them in a clear order. Suppose your desk cup contains 6 pencils and 2 markers. If you compare pencils to markers, the ratio is 6:2. You can explain it by saying, “For every 6 pencils, there are 2 markers.” You could also compare markers to all the writing tools. Since there are 8 tools altogether, that ratio is 2:8. A complete ratio explanation names both quantities and tells what each number represents. Try creating a ratio from objects in your classroom, such as books and notebooks or chairs and tables. Check that your numbers match the order of the words, then write the ratio in at least two forms.