1. 1 Lesson 4.1.1 Ratios

2. 2 Lesson 4.1.1 Ratios California Standard: Number Sense 1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a / b, a to b, a : b ). What it means for you: You’ll learn what ratios are and the different ways you can represent them. Key words: ratio fraction

3. 3 Lesson 4.1.1 Ratios You’ve probably come across ratios before — for example, making an orange drink by diluting about one part concentrated drink with about four parts water. This way of stating how the amount of one thing compares with the amount of another thing is called a ratio.

4. 4 Ratios Are a Way of Comparing Amounts of Things Lesson 4.1.1 Ratios A ratio is the amount of one thing compared with the amount of another thing. In the diagram, the ratio of rabbits to cats is 5 to 3. This is because there are 5 rabbits but only 3 cats.

5. 5 Example 1 Solution follows… Lesson 4.1.1 Ratios What is the ratio of carrots to hamsters in the picture? And what is the ratio of hamsters to carrots? Solution Count the number of carrots. There are 3 carrots. Count the number of hamsters. There are 2 hamsters. Make sure you get the order of the numbers right. The ratio of carrots to hamsters has the number of carrots first. The ratio of carrots to hamsters is 3 to 2. In the same way, the ratio of hamsters to carrots is 2 to 3.

6. 6 Guided Practice Solution follows… Lesson 4.1.1 Ratios 1. What is the ratio of tennis rackets to tennis balls in the picture opposite? 2.What is the ratio of tennis balls to tennis rackets in the picture? 3.There are ten people on a basketball court and two baskets. What is the ratio of people to baskets on the court? 4 to 3 3 to 4 10 to 2

7. 7 There Are Three Ways of Writing a Ratio Lesson 4.1.1 Ratios The previous examples used words like “5 to 3” to write a ratio. But there are other ways to write ratios, and they all mean the same thing. There are three ways you need to know about. 5 3 5 to 3 5 : 3 This fraction tells you that there are 5 of one thing for every 3 of another. The colon “:” is another way of writing “to” in ratios. You’d still say this “5 to 3”.

8. 8 Example 2 Solution follows… Lesson 4.1.1 Ratios The ratio of dogs to cats in the picture is 4 to 3. How else could you write this ratio? Write the ratio of cats to dogs in three different ways. Solution There are three ways of writing ratios. You could also write the ratio of dogs to cats as 4 : 3 or. The ratio of cats to dogs is 3 to 4, or 3 : 4, or. 4 3 3 4

9. 9 Guided Practice Solution follows… Lesson 4.1.1 Ratios 4.The ratio of cars to people on a street is 1 : 2. How else can you represent this ratio? 5.The ratio of boys to girls in a class is. Express the ratio of girls to boys in three different ways. 6.What is the ratio of the width of the first rectangle shown below to the second? 2 3 1 to 2, or 1 2 3 to 2, or 3 : 2, or 3 2 4 to 3, or 4 : 3, or 4 3

10. 10 Ratios Don’t Have Any Units Lesson 4.1.1 Ratios Ratios don’t have any units. A ratio is just one number compared with another, such as “3 to 2”. Usually, ratios compare things measured in the same units. Then, the units cancel out when you divide the two quantities.

11. 11 Example 3 Solution follows… Lesson 4.1.1 Ratios What is the ratio of the big square on the right to the smaller one? Solution To form the ratio of the areas, divide one by the other. Ratio of big area to small area = 7 cm 2 4 cm 2 7 4 =

12. 12 Lesson 4.1.1 Ratios But if the units are different, the description of what the ratio shows is usually a bit more detailed. The last example compared things that used the same units: Ratio of big area to small area = 7 cm 2 4 cm 2 7 4 =

13. 13 Example 4 Solution follows… Lesson 4.1.1 Ratios A walker hikes 7 miles in 3 hours. What is the ratio of the distance walked in miles to the time taken in hours? Solution Ratio of the distance walked in miles to the time taken in hours = 7 3 Distance walked in miles Time taken in hours

14. 14 Guided Practice Solution follows… Lesson 4.1.1 Ratios Jess makes purple paint using 4 cans of blue paint to 1 can of red. It takes her 3 hours to paint her bedroom, and she uses all her paint. 7.What is the ratio of cans of blue paint to cans of red paint? 8.What is the ratio of cans of paint used to the time taken in hours? 4 : 1 5 : 3

15. 15 Independent Practice Solution follows… Lesson 4.1.1 Ratios In exercises 1–4, write the ratio shown in two equivalent ways. 1. 7 : 6 2. 3 to 8 3. 4. 7 : 11 11 7 7 to 6, 7 6 3 : 8, 3 8 11 to 7, 11 : 7 7 11 7 to 11,

16. 16 Independent Practice Solution follows… Lesson 4.1.1 Ratios Exercises 5–7 are based on the circle graph on the right. 5. What is the ratio of people working in business to civil servants? 6. What is the ratio of unemployed people to people in business? 7. What is the ratio of people who are working and whose professions are known, to working people whose professions are unknown? 9 : 4 2 : 9 19 : 3 It shows the professions of 24 former pupils of a school.

17. 17 Lesson 4.1.1 Ratios Round Up You’ve now met all of the basics of ratios. Next, you’ll see how to use ratios in real life and how to simplify them to make your calculations easier.