1. Equivalent Ratios Lesson 2.03

2. After completing this lesson, you will be able to say: I can make tables of equivalent ratios. I can use tables to find missing values and compare ratios. I can solve unit rate problems by reasoning about ratios and rates.

3. Equivalent Ratios Equivalent ratios: Ratios that have the same simplest form and express the same relationship between two quantities. Equivalent ratios are ratios that express the same relationship between two quantities

4. Example of Equivalent Ratios The ratios 2:8, 4:16, 6:24, and 8:32 are examples of equivalent ratios. Ratios that are equivalent have the same simplest form. The simplest form for these ratios is 1:4

5. Ratio Tables Given ratio 2:6. You can begin by first making a table and creating some empty spaces that you know you will have to fill in later. Your table can be horizontal or vertical–it does not matter. Number of subs2 Bag of chips6 Number of SubsBags of chips 26 Horizontal Table Vertical Table

6. Ratio Tables – Using Addition Number of subs2468 Bag of chips6121824 +2 Notice that to find each value, you do something different in each row. +6 Number of subs: The pattern is to add 2 each time, because that is the first term of the ratio. 2+2= 4; 4+2= 6; 6+2= 8 Bags of chips: The pattern is to add 6 each time, because that is the second term of the ratio. 6+6 = 12; 12 + 6 = 18; 18 + 6 = 24 This shows that the ratios 2:6, 4:12, 6:12, and 8:24 are all equivalent.

7. Ratio Tables – Using Multiplication Another way to create a ratio table is by using multiplication Using multiplication you can use any number you want. Start by multiplying the top row by a number, then multiply the bottom row by the same number. Number of subs24816 Bag of chips6122448 x 2 x 2 x 2 Number of subs: 2 x 2 = 4; 4 x 2 = 8; 8 × 2 = 16 Bags of chips: 6 × 2 = 12; 12 × 2 = 24; 24 × 2 = 48 This shows that the ratios 2:6,4:12, 8:24, and 16:48 are all equivalent.

8. Ratio Tables – Using Rate Reasoning Number of SubsBags of chips 13 26 618 54 You can also find the unit ratio to help you fill in the table To make a table using rate reasoning, you have to calculate the unit rate. Start by determining what is being multiplied by 2 to get 6, you can do this by dividing 6 by 2 6 divided by 2 = 3 The unit rate shows that there are 3 bags of chips per sub Then you can use the unit rate and multiply both columns by that number to find equivalent ratios X 3

9. Unit rate A rate expressed such that it reveals how much of the first quantity there is for just one unit of another, such as 2 feet per second or $6 per hour.

10. Using rate tables to find Unit Rate Ellie raised $150 for walking 6 laps. Use a ratio table and unit rate to show her progress LapsAmount Raised 1$25 2 3 4 5 6$150 Your goal is to find out how much Ellie made per lap. This will be the unit rate. Calculate the unit rate by dividing $150 (amount raised) by 6 (number of laps). Now you know your unit rate is $25 per unit, which means for every lap Ellie completes, she earns $25. Fill in the rest of the table to see Ellie's progress.

11. Check your work LapsAmount Raised 1$25 2$50 3$75 4$100 5$125 6$150

12. Determining Unknown Values How can we use equivalent ratios and unit rates to help calculate missing values: After their walk, the walkers will receive oranges as a snack. The event organizers figured out that they would need to order slightly more oranges just in case more people show up. Therefore, they purchased them at a ratio of 3 to 4. For every 3 walkers registered for the event, the organizers will order 4 oranges. How many oranges would be needed for 24 walkers? There are two ways this problem can be solved.

13. Determine Unknown Values Walkers324 Oranges4 Determine what number is being multiplied by 3 to get 24 in the walkers' row. You do the same for the second row. By using ratio reasoning, you multiply the 4 by 8, as well. Walkers3 x 824 Oranges4 x 832 This tells us that for 24 walkers, the organizers need to purchase 32 oranges. Method 1

14. Determining Unknown Values Method 2 Walkers324 Oranges4 This tells us that for 24 walkers, the organizers need to purchase 32 oranges.

15. Comparing Ratios After the walkathon, Ellie’s team decides that they would like to go mini-golfing to celebrate their efforts. They meet at Ellie’s house to decide which place offers the better deal. Ellie finds the following deals: Mini-Adventure Golf: $24 for 6 people Marvelous Mini-Golf: $18 for 4 people Which would be the better deal if there were 12 people playing? Find the Unit Rate for each location Based on the unit rate, Mini-Adventure Golf has a better deal, but is it the best deal?

16. Comparing Unit Rates Use the unit price to complete the rest of the table until you arrive at 12 people PricePeople $4.001 $16.004 $32.008 $48.0012 PricePeople $4.501 $18.004 $36.008 $54.0012 Mini-Adventure Golf Marvelous Mini-Golf It will cost $48 for 12 people at Mini-Adventure Golf and $54 for 12 people at Marvelous Mini-Golf. So Ellie and her friends decide to go to Mini-Adventure.

17. Now that you completed this lesson, you should be able to say: I can make tables of equivalent ratios. I can use tables to find missing values and compare ratios. I can solve unit rate problems by reasoning about ratios and rates.