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# Introduction to Ratios

• The ratio of cats to dogs at the animal shelter is 4 to 1.
• There are 3 boys for every 4 girls at the school.
• For every 2 bowls of soup sold at the restaurant, there were 5 sandwiches and 3 desserts sold.
All three of the statements describe the relationship between two or more quantities. This comparison is called a ratio. A ratio compares amounts or quantities.

In written form, the word "to" shows a ratio. When expressed mathematically, a colon or a fraction bar is used. You can reduce ratios, just as you do fractions. Ratio problems may ask you to compare one part of the set to the other part of the set (Part-to-Part). Ratio problems may also ask you to compare part of the set to the whole set (Part-to-Whole). For example:

Part-to-Part Example:  What is the ratio of tents to boats?
• 2 tents to 4 boats = 2 to 4 = 1 to 2
• tents:boats = 2:4 = 1:2
• $"tents"/"boats" = 2/4 = 1/2$

Part-to-Whole Example: What is the ratio of boats to total pictures?
• 4 boats to 6 pictures = 4 to 6 = 2 to 3
• boats:pictures = 4:6 = 2:3
• $"boats"/"pictures" = 4/6 = 2/3$

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