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Ratio: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">RatioRatio: Definition and ExampleTable of ContentsDefinition of Ratio

A ratio is a mathematical comparison between two or more numbers that shows how many times one value contains or is contained within another. It expresses the relationship between quantities and is typically written using a colon (:), the word "to," or as a fraction. For example, if there are 333 apples and 555 oranges, the ratio of apples to oranges is 3:53:53:5.

Ratios help us understand proportional relationships between quantities and allow us to scale quantities while maintaining their relative sizes. Unlike fractions, ratios can compare more than two numbers (such as 2:3:42:3:42:3:4), and they don't always represent parts of a whole. When working with ratios, we often reduce them to their simplest form by dividing all parts by their greatest common factor. Understanding ratios is essential for solving problems involving proportions, scaling, mixtures, and many other real-world applications.

Examples of Ratio Example 1: Simplifying a Ratio Problem:

Express the ratio 24:3624:3624:36 in its simplest form.

Step-by-step solution:

Step 1, Write down the given ratio.

24:3624:3624:36

Step 2, Find the greatest common factor (GCF) of 242424 and 363636.

Factors of 242424: 1,2,3,4,6,8,12,241, 2, 3, 4, 6, 8, 12, 241,2,3,4,6,8,12,24 Factors of 363636: 1,2,3,4,6,9,12,18,361, 2, 3, 4, 6, 9, 12, 18, 361,2,3,4,6,9,12,18,36 Common factors: 1,2,3,4,6,121, 2, 3, 4, 6, 121,2,3,4,6,12 The GCF is 121212

Step 3, Divide both parts of the ratio by the GCF.

2412:3612=2:3\frac{24}{12}:\frac{36}{12} = 2:31224​:1236​=2:3

Step 4, Therefore, the ratio 24:3624:3624:36 simplifies to 2:32:32:3.

Example 2: Using Ratios to Solve a Word Problem Problem:

A fruit salad is made with strawberries and blueberries in the ratio 5:35:35:3. If 404040 strawberries were used, how many blueberries were used?

Step-by-step solution:

Step 1, Understand what the ratio 5:35:35:3 tells us. For every 555 strawberries, there are 333 blueberries.

Step 2, Set up a proportion to find the number of blueberries.

StrawberriesBlueberries=53\frac{\text{Strawberries}}{\text{Blueberries}} = \frac{5}{3}BlueberriesStrawberries​=35​

Step 3, Substitute what we know. There are 40 strawberries.

40Blueberries=53\frac{40}{\text{Blueberries}} = \frac{5}{3}Blueberries40​=35​

Step 4, Cross multiply to solve for the number of blueberries.

3×40=5×Blueberries3 \times 40 = 5 \times \text{Blueberries}3×40=5×Blueberries 120=5×Blueberries120 = 5 \times \text{Blueberries}120=5×Blueberries Blueberries=1205=24\text{Blueberries} = \frac{120}{5} = 24Blueberries=5120​=24

Step 5, Therefore, 242424 blueberries were used in the fruit salad.

Example 3: Working with Part-to-Whole Ratios Problem:

In a class of 282828 students, the ratio of boys to girls is 3:43:43:4. How many boys and how many girls are in the class?

Step-by-step solution:

Step 1, Understand the ratio 3:43:43:4. It means that for every 333 boys, there are 444 girls.

Step 2, Find the total parts in the ratio.

Total parts=3+4=7 parts\text{Total parts} = 3 + 4 = 7 \text{ parts}Total parts=3+4=7 parts

Step 3, Calculate the value of each part.

Each part=Total studentsTotal parts=287=4 students\text{Each part} = \frac{\text{Total students}}{\text{Total parts}} = \frac{28}{7} = 4 \text{ students}Each part=Total partsTotal students​=728​=4 students

Step 4, Find the number of boys.

Boys=3×Each part=3×4=12 boys\text{Boys} = 3 \times \text{Each part} = 3 \times 4 = 12 \text{ boys}Boys=3×Each part=3×4=12 boys

Step 5, Find the number of girls.

Girls=4×Each part=4×4=16 girls\text{Girls} = 4 \times \text{Each part} = 4 \times 4 = 16 \text{ girls}Girls=4×Each part=4×4=16 girls

Step 6, Therefore, there are 121212 boys and 161616 girls in the class.

Comments(1)GGymnasticsFanaticYvonneNovember 4, 2025This ratio def is great! I've used it to help my students grasp the concept. The real - world examples made it super relatable.

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