2. The World of Ratios Using what you know to find something new!

3. We will determine what a ratio is….. We will learn the “rules” for writing ratios. We will discover the hidden parts of ratios. We write equivalent ratios using scaling. We will discuss the types of ratios that we can write What are we doing here????

4. First things first…. A ratio is defined as “a comparison of numbers by division.” You will notice many similarities between ratios and fractions. Hopefully you will also note some important differences. Skim over the front page of your notes. Add information if you think you need to.

5. Vocabulary Ratio: Two values compared by division Equivalent ratios: Different ratios that have the same comparisons

6. What are Ratios? A ratio is a mathematical way to compare values. 4 : 2 If I want to give the ratio of triangles to circles, it could be written in several forms. 4 to 2 If I want to give the ratio of circles to triangles, the ratio forms could be: There are important rules that guide us when writing and using ratios:  Order matters  Values stay in fractional form 2 : 4 2 to 4

7. What changed? We were still talking about the same shapes. Why did we write a different ratio? ORDER MATTERS !!!! The ratio values must be written in the state order. What would the ratio 6:2 represent? Let’s use this ratio box to organize our information. 4242 We have a “hidden” value in that it was not given to us…. Total 6 part whole

8. Important Points! I used pictures of triangles and circles in my display of ratios. What purpose did these pictures serve???? LABELING your values when working with ratios is very, very important. Let’s look at the ratios we have written. What could we do to change these numbers without changing the comparisons the ratios represent? ÷2

9. What is the meaning? These ratios are telling us something about the comparison of triangles to circles. What is it? For every 4 triangles, we will have 2 circles…..or….. for every two circles, we will have 4 triangles. For every 2 triangles, we will have 1 circles…..or….. for every one circle, we will have 2 triangles.

10. Equivalent Ratios and Scaling 4 2 2 1 If you had 8 triangles, how many circles would you have? ______ If you had 6 triangles, how many circles would you have?_______ The mathematical process used (multiplying or dividing each term) to find equivalent ratios is called ________________________. Include the processes you used in your notes, please. ÷ 2 ÷ 2 x ? x ? 8 48 4 x ? 6 36 3 4 3 Scaling: Scaling forward or scaling backward

11. Tables and Categorical Data FlavorNumber of Responses Peppermint9 Cinnamon8 Fruit3 Spearmint1 Several students named their favorite type of gum. Write the ratio that compares those that prefer peppermint to the total number of students. TOTAL 21 Many times you will need to find this “hidden” value when working with ratio tables. Three out of every seven students prefer peppermint gum.

12. Students surveyed = Students w/o jobs = ≠ 1 Students surveyed = Students with jobs Equivalent ratios = Write each of these ratios in simplest form: Job Survey Let’s try another one……..

13. Types of Ratios Let’s look at one more table to discuss the TYPES of ratios we can write. 14 Tom’s Pet service takes care of cats and dogs. Currently, there are more dogs than cats. Compare the number of cats to the number of dogs. Then compare the number of cats to the total number of pets at Tom’s Pet Service. 17 31total Organizational tool We now have all the information we need to write several types of ratios. The information we have represents two values that are “parts” of the total, or “whole” amount. The “total,” or our hidden number, is 31. When we compare cats to dogs, we are writing a part:part ratio. When we compare cats to all the animals, we are writing a part:whole ratio. What is the ratio for the total of animals to dogs? This is a whole:part ratio. It can also be written as 31:17, or 31 to 17

14. Rely on Process….. All of us have used a pattern that we see to complete tables like the one below. When working with equivalent ratios, it’s important to identify the process used to create the ratios. The pattern may not be consistent! Students with pets 1392781 Total number of students 392781243 For discussion

15. part 15 part20 Think creatively! 30 40 Changing direction will change your operation within one ratio!!! 3 4 18 24 6 8 9 12 Changing direction will change your operation within one ratio!!! 12 16 21 28

16. What have we accomplished? We have defined ratios. We have written ratios in different forms. We have written equivalent ratios. We have written part:part ratios, part: whole ratios, whole:part ratios…… We have written ratios in simplified (equivalent) forms.

17. Ratios ARE Amazing! Comparison of numbers by division!!