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A ratio is a comparison between two quantities of the same kind, for example:

There are 3 red sweets and 5 yellow sweets in the box. We can say the ratio of red sweets to yellow sweets is 3 to 5. Ratio can be written with the symbol ':' or as a fraction.

'3 to 5' can be written as '3:5' or

When writing a ratio,

- change the quantities to the same unit if necessary
- reduce the ratio to its simplest form.

For example: What is the ratio of 5 minutes to 5 hours? First change the hours to minutes. 5 hours = 300 minutes Ratio = 5:300 = 1:60

The following video explains more about two-term ratios.

A three-term ratio can be used to compare three quantities, for example:

There are 5 red sweets, 15 yellow sweets and 30 blue sweets in the box

5 to 15 to 30 = 5:15:30 = =1:3:6

Sometimes, you may need to convert 2 two-term ratios into 1 three-term ratio, for example:

If the ratio of the number of red shirts to the number of blue shirts is 1:2 and the ratio of blue shirts to green shirts is 1:3. What is the ratio of red shirts to green shirts?

First, you need to make the common item (in this case blue shirts) the same for both ratios. Convert the ratio of blue shirts to green shirts to its equivalent:

Next, combine to form three-term ratio: 1:2:6

Two-Term and Three-Term Ratios

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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