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**New Mexico Standards: AFG.D.2, GT.B.4**

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**Ratio: A comparison of two quantities. a : b, or**

Ratios can be expressed as where b ≠ 0, a : b, or a to b The total number of students who participate in sports programs at Central High School is 520. The total number of students in the school is Find the athlete-to-student ratio to the nearest tenth. To find this ratio, divide the number of athletes by the total number of students. 0.3 can be written as Answer: The athlete-to-student ratio is 0.3. Example 1-1a

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**The country with the longest school year is China with 251 days**

The country with the longest school year is China with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.) Answer: 0.7 Example 1-1b

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**Do these sides have a perimeter of 90 cm?**

Example 1-2a Multiple- Choice Test Item In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle. A 15 cm B 18 cm C 36 cm D 39 cm What are you being asked to do? You are asked determine the true length of the side of the triangle. Ratio means all the sides are a multiple of the same number, which is unknown, so . . . 5 12 13 Draw a picture 13x 5x Do these sides have a perimeter of 90 cm? 12x Write an equation & solve it:

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**Which side will be the longest side?**

Example 1-2b Perimeter Combine like terms. Divide each side by 30. Which side will be the longest side? A 15 cm B 18 cm C 36 cm D 39 cm Answer: A

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**Use this value of x to find the measures of the sides of the triangle.**

The shortest side is 15 centimeters. The answer is A. Check Add the lengths of the sides to make sure that the perimeter is 90. Example 1-2c

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**Proportion An equation stating that two ratios are equal.**

Equivalent fractions set equal to each other form a proportion. To determine if the two ratios are a proportion, the most useful way is to use cross-products. Criss-cross and multiply. If the results are equal, the two ratios are a proportion. What are some other methods?

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**Proportion: An equation stating that two ratios are equal. Solve**

Original proportion Cross products Multiply. Divide each side by 6. Answer: 27.3 How can you quickly check that your answer is correct? Example 1-3a

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**How can you quickly check that your answer is correct?**

Solve Original proportion Cross products Simplify. Add 30 to each side. Divide each side by 24. Answer: –2 How can you quickly check that your answer is correct? Example 1-3b

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Solve each proportion. a. b. Answer: 4.5 Answer: 9 Example 1-3c

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**Answer: The width of the model is 3.6 inches.**

A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model. Because the scale model of the boxcar and the boxcar are in proportion, you can write a proportion to show the relationship between their measures. Since both ratios compare feet to inches, you need not convert all the lengths to the same unit of measure. Substitution Cross products Multiply. Divide each side by 40. Answer: The width of the model is 3.6 inches. Example 1-4a

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**Two large cylindrical containers are in proportion**

Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container. Answer: m Example 1-4c

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HW #2: Page 286

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7-1 Ratios and Proportions

7-1 Ratios and Proportions

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