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Bellwork: There are 18 bulls and 45 cows on a ranch. If 4 more bulls and 4 more cows were added, will the ratio of bulls to cows remain the same? Justify your answer using a table.
A punch recipe uses one container of soda and three containers of juice to make one batch of punch. 1. Draw red circles to show the number of containers of soda and draw yellow circles to show the number of containers of juice needed to make 2 batches of punch. 2. Draw red circles to show the number of containers of soda and draw yellow circles to show the number of containers of juice needed to make 3 batches of punch. 3. Find the ratio in simplest form of soda to juice needed for 1, 2, and 3 batches. What do you notice?
The quantities in the last three questions can be organized into a table. This table is called a ratio table because the columns are filled with pairs of numbers that have the same ratio. Equivalent ratios express the same relationship between quantities. Example 1: To make yellow icing you mix 6 drops of yellow food coloring with 1 cup of white icing. How much yellow food coloring should you mix with 5 cups of white icing to get the same shade? Example 2: In a recent year, Joey Chestnut won a hot dog eating contest by eating nearly 66 hotdogs in 12 minutes. If he ate at a constant rate determine about how many hot dogs he ate every 2 minutes. Got it? A. and B.
Multiplying or dividing two related quantities by the same number is called scaling. Sometimes you may need to scale back and then scale forward to find an equivalent ratio. Example 3: Cans of corn are on sale at 10 for $4. Find the cost of 15 cans. Example 4: Joe mows lawns during his summer vacation to earn money. He took 14 hours last week to mow 8 lawns. At this rate, how many lawns could he mow in 49 hours? GOT IT? C.
Example 5: On her vacation, Leya exchanged $50 American and received $60 Canadian. Use a ratio table to find how many Canadian dollars she would receive for $20 American. Guided Practice 1-4. Independent Practice 1-8. Classwork:
Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80. • The following tables show how many words each person can text in a given amount of time. Compare the rates of texting for each person using the ratio table. • Complete the table so that it shows Max has a texting rate of 55 words per minute.
The tables below show the comparison of the amount of water to the amount of juice concentrate (JC) in grape juice made by three different people. Whose juice has the greatest water-to-juice concentrate ratio, and whose juice would taste strongest? Be sure to justify your answer. • The next day, each of the three people made juice again, but this time they were making apple juice. Whose juice has the greatest water-to-juice concentrate ratio, and whose juice would taste the strongest? Be sure to justify your answer. • Max and Sheila are making orange juice. Max has mixed 15 cups of water with 4 cups of juice concentrate. Sheila has made her juice by mixing 8 cups water with 3 cups of juice concentrate. Compare the ratios of juice concentrate to water using ratio tables. State which beverage has a higher juice concentrate-to-water ratio. • Victor is making recipes for smoothies. His first recipe calls for 2 cups of strawberries and 7 cups of other ingredients. His second recipe says that 3 cups of strawberries are combined with 9 cups of other ingredients. Which smoothie recipe has more strawberries compared to other ingredients? Use ratio tables to justify your answer. • Problem SET: ?