1. Ratio (Pronounced “ray – shee – o”)

2. What is a ratio? A ratio is a comparison of two quantities. For instance, someone can look at a group of people, count 15 men and 20 women in the group, and refer to “the ratio of men to women” in the group as 15 to 20.

3. The order of ratios Notice that, in the expression “the ratio of men to women”, “men” came first. Whichever word comes first will be the first number in the ratio. If the expression had been “the ratio of women to men”, then the ratio would have been “20 to 15”. This order is very important, and must be respected.

4. How do you write a ratio? A ratio can be written in a variety of ways. There are two other notations for this “15 to 20” ratio: 15:20 and You should be able to recognize all three notations. 15 20

5. Can you write the ratios in all three formats? There are 16 ducks and 9 geese in the park. Express the ratio of: ducks to geese geese to ducks

6. Simplifying Ratios We can often make the numbers in ratios smaller so they are easier to compare. You do this by dividing each part of the ratio by the same number, the Greatest Common Factor. Equivalent ratios all simplify to the same value.

7. Let’s return to the 15 men and 20 women in our original group. Someone can look at a group of people, count 15 men and 20 women in the group, and refer to “the ratio of men to women” in the group as 15 to 20. If we had expressed the ratio as a fraction,, we could simplify it to write an equivalent fraction of. (Also 3:4 or “3 to 4”) 15 20 3 4

8. Equivalent Ratios All of the following are equivalent: 3/15 1/5 1 to 5 3:15 1 out of 5 0.2 Since a ratio can be written as a fraction, it can also be written in any form that is equivalent to that fraction.

9. What’s the difference? The ratio “15 to 20” in our first problem refers to the absolute numbers of men and women in the group. But “3 to 4” just tells us that, for every three men, there are four women. This also tells us that, in any representative set of 7 people (3 + 4 = 7) from this group, will be men and will be women. 3 7 4 7

10. Jeannine has a bag with 3 CD’s, 4 marbles, 7 books, and 1 orange. 1) What is the ratio of books to marbles? Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 7/4. Two other ways of writing the ratio are 7 to 4, and 7:4.

11. 2) What is the ratio of CD’s to the total number of items in the bag? There are 3 CD’, and 3 + 4 + 7 + 1 = 15 items total. The answer can be expressed as 3/15 or 1/5, 3 to 15 or 1 to 5, and 3:15 or 1:5.

12. Guided Practice Try these…. Write each ratio as a fraction in simplest form. 1.2 guppies out of 6 fish 2.12 puppies to 15 kittens 3.5 boys out of 10 students

13. Ratios - Problem Solving A famous Texas chef has a secret recipe for her chili. When people ask her for it, she hands them a card with the complete recipe except for 1 detail. For the missing detail, she gives them the following clue: For a 3- quart pot of chili, use a combination of peppers and tomatoes totaling 12 items in one of the following ratios. If the answer is in whole numbers, how many peppers and how many tomatoes should you use? A B C D E Which ratio is correct? Then how many peppers & how many tomatoes will you actually use?

14. A rate is a ratio of two measurements having different kinds of units. When a rate is simplified so that it has a denominator of 1, it is called a unit rate. Fourth period math class has 20 students and meets in a classroom with 5 computers. Write the ratio of students to computers as a unit rate. Divide the numerator and the denominator by 5 to get a denominator of 1. The ratio written as a unit rate is 4 students to 1 computer.

15. More Practice Write each rate as a unit rate. 4. 6 eggs for 3 people 5. $12 for 4 pounds 6. 40 pages in 8 days