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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?

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