Solving Equivalent Ratio Problems

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Finding Equivalent Ratios to a Given Ratio.

  • Check the “Pattern 1” box to see the ratio of red to blue beads. Note that the ratio is in the simplest form. The beads are also represented on a line. Now, we want to find an equivalent ratio using the orange and green beads down below.
  • Check the “Pattern 2” box. A ratio of 1:1 is displayed. To choose another ratio that is equivalent to 1:2, use located at the bottom right corner.
  • As soon as you get an equivalent ratio, you are greeted with a smile.
  • Use the same at the top right to change the original ratio and follow the steps again. Have fun!

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Finding Equivalent Ratios to a Given Ratio on a Graph.

  • Move the “reveal” slider in the applet below to the right to see the ratios that are equivalent to 1 : 2. At the end of the bar, a striaght line links all the points in the graph.​
  • Now, use the two other sliders to change the ratio and repeat the step above. When equivalent ratios are graphed, they form a straight line through the origin. The applet demonstrates that fact.

Do you agree that all points on the line will be equivalent ratios? Explain why you think so.

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Creating Equivalent Ratios from a Diagram.

Follow the instructions in the box below.

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Lin read the first 54 pages from a 270-page book in the last 3 days. Diego read the first 100 pages from a 320-page book in the last 4 days. Elena read the first 160 pages from a 480-page book in the last 5 days.​

If they continue to read every day at these rates, who will finish first, second, and third? Explain or show your reasoning.

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Consider the problem: A red car and a blue car enter the highway at the same time and travel at a constant speed. How far apart are they after 4 hours? What information would you need to be able to solve the problem?

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The ratio of cats to dogs in a room is 2 : 3. Five more cats enter the room, and then the ratio of cats to dogs is 9 : 11. How many cats and dogs were in the room to begin with?