Defining Equivalent Ratios

Find how many dots are in the 2 applets below and explain how you got to the answer.

Dot pattern 1 :

Dot pattern 2 :

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Using a Recipe to find Equivalent Ratios.

Here below is a recipe for tuna casserole.

Mix the following:

  • 3 cups cooked elbow-shaped pasta.
  • 6 ounce can tuna, drained.
  • 10 ounce can cream of chicken soup.
  • 1 cup shredded cheddar cheese.
  • 1 cups French fried onions.
  • Combine the pasta, tuna, soup, and half of the cheese. Transfer into a 9 inch by 18 inch baking dish. Put the remaining cheese on top. Bake 30 minutes at 350 degrees. During the last 5 minutes, add the French fried onions. Let sit for 10 minutes before serving.

(1). What is the ratio of the ounces of soup to the cups of shredded cheese to the cups of pasta in one batch of casserole?

(2). How much of each of these 3 ingredients would be needed to make twice the amount of casserole?

(3). How much of each of these 3 ingredients would be needed to make half the amount of casserole?

(4). How much of each of these 3 ingredients would be needed to make five times the amount of casserole?

(5). How much of each of these 3 ingredients would be needed to make one-fifth the amount of casserole?

(6). What is the ratio of cups of pasta to ounces of tuna in one batch of casserole?

(7). How many batches of casserole would you make if you used the following amounts of ingredients: 9 cups of pasta and 18 ounces of tuna?

(8). How many batches of casserole would you make if you used the following amounts of ingredients: 36 ounces of tuna and 18 cups of pasta?

(9). How many batches of casserole would you make if you used the following amounts of ingredients: 1 cup of pasta and 2 ounces of tuna?

(10). The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold twice the amount of casserole.

(11). The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold half the amount of casserole.

(12). The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold five times the amount of casserole.

(13). The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold one-fifth the amount of casserole.

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Finding Equivalent Ratios.

Each of the following below, is a pair of equivalent ratios. Explain why they are equivalent ratios or draw a diagram in the applet that shows why they are equivalent ratios.

(1). 4 : 5 and 8 : 10.

(2). 18 : 3 and 6 : 1.

(3). 2 : 7 and 10,000 : 35,000.

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Investigating Equivalent Ratios.

A purple frosting recipe requires 3 drops of red food coloring for every 1 drop of blue food coloring. 

  • Use the two sliders on the left to create the ratio(fraction) one third. ​
  • Use the slider at the top to see subsequent ratios. ​
  • Try that with other recipes.

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Write fractions for points A and B on the number line.

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(1). The ratio 5 : 3 and 10 : 6 are equivalent. Is the ratio 15 : 12 equivalent to these? Explain your reasoning.

(2). The ratio 5 : 3 and 10 : 6 are equivalent. Is the ratio 30 : 18 equivalent to these? Explain your reasoning.

(3). Give two more examples of ratios that are equivalent to 5 : 3.

(4). How do you know when ratios are equivalent and when they are not equivalent?

(5). Write a definition of equivalent ratios.

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Are the ratios 3 : 6 and 6 : 3 equivalent? Why or why not?