The document defines and provides examples of ratios. It discusses writing ratios in different forms, equivalent ratios, compound ratios, and solving word problems involving ratios. Examples are provided to show how to write ratios in 3 forms, simplify ratios, determine equivalent ratios, and solve ratio word problems. Readers are given practice problems to work through.

3. DO NOW (not later): Compare the number of boys to girls in the class.

4. The number of boys = The number of girls = If we compare boys to girls we get ___ boys to _____ girls.

5. What do we call a comparison between two or more quantities? RATIO We just found the RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.

6. AIM: What is a ratio?

7. It’s Friday night and your friends are having a party…… The ratio of girls to guys is 2 to 12. Would you want to attend the party?

8. How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs. The ratio is 4 to 6.

9. What are some other ways we can write the ratio of basketball to footballs? 4 to 6 4 : 6 4 6 First quantity to Second quantity First quantity : Second quantity First quantity divided by the second quantity (as a fraction ). Every ratio can be written in 3 ways: Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4

10. Write the ratio of sandwiches to coke bottles 3 different ways. 6:8 , 6 to 8, and 6 8 Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4. In other words, ratios can be simplified to form equivalent ratios.

11. Equivalent Ratios Simplify the following ratios: 4 to 8 10 to 8 8 to 10 Step 1 – Write the ratio as a fraction Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF). Step 3 – Write the equivalent ratio in the same form as the question = 4 / 4 = 1 = 1 to 2 8 8 / 4 2 GCF = 4

12. Equivalent Ratios can be formed by multiplying the ratio by any number. For example, the ratio 2 : 3 can also be written as 4 : 6 (multiply original ratio by by 2) 6 : 9 (multiply original ratio by by 3) 8 : 12 (multiply original ratio by by 4) The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x )

13. Compound Ratios A ratio that compares more than 2 quantities is called a compound ratio. Example: A cake recipe says the ratio of cups of milk , sugar , and batter are 1 : 2 : 4 . This means that there is one cup of milk for every two cups of sugar and four cups of batter.

14. A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3 . Write the ratio of yellow to blue marbles in simplest form. What is the ratio of yellow to red marbles? How many yellow marbles are there? 4 : 2 can be simplified to 2 : 1 4 : 3 Yellow : Blue : Red is 4 : 2 : 3 Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x Let 4x = yellow, 2x = blue , 3x = red 4x + 2x+ 3x = 18 9x = 18 X= 2 Since the question asks for yellow marbles, there are 4 x or 4 ( 2 ) = 8 yellow marbles.

15. Practice problem # 1 (1) You have 100 different shirts. The ratio of blue to black shirts is 20 . 30 a) Write the ratio of blue to black shirts 3 different ways. b) Write the ratio in simplest form. c) Explain what this ratio tells us. d) How many black shirts do you have?

16. Solution - # 1  You have 100 different shirts. The ratio of blue to black shirts is 20 / 30 a) Write the ratio of blue to black shirts 3 different ways. 20 to 30 , 20 : 30, 20 30 b) Write the ratio in simplest form. 2 3 c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts. d) How many black shirts do you have? 2x + 3x = 100 5x = 100 x = 20 There are 2 x black shirts so 2 ( 20 ) = 40 black shirts

17. Practice Word Problems You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form. Explain what this ratio tells us. 28 / 56 = 1 / 2 The ratio of boys to girls is 1 to 2 (2) For every 1 boy there are 2 girls at the party.

18. Practice Word Problems Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. Explain what this ratio tell us.

19. Challenge Question The perimeter of a rectangle is 500 feet. The ratio of the base and height is 3:2. What is the measure of the height?