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7-1 Ratios and Proportions

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1 7-1 Ratios and Proportions
You solved problems by writing and solving equations. Write ratios. Write and solve proportions.

2 Ratio A ratio is a comparison of two quantities using division.
The ratio of quantities π‘Ž and 𝑏 can be expresses as π‘Ž to 𝑏, π‘Ž:𝑏, or π‘Ž 𝑏 where 𝑏≠0. Ratios are usually expressed in simplest form. 32:18 = 16:9 π‘€π‘–π‘‘π‘‘β„Ž π‘œπ‘“ π‘ π‘π‘Ÿπ‘’π‘’π‘› β„Žπ‘’π‘–π‘”β„Žπ‘‘ π‘œπ‘“ π‘ π‘π‘Ÿπ‘’π‘’π‘› = 32 𝑖𝑛 18 𝑖𝑛 = 32Γ·2 18Γ·2 = 16 9

3 SCHOOL The 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.

4 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.) A. 0.3 B. 0.5 C. 0.7 D. 0.8

5 Extended Ratios Extended ratios can be used to compare three or more quantities. The expression π‘Ž:𝑏:𝑐 means the ratio of the first two quantities is π‘Ž:𝑏, the ratio of the last two quantities is 𝑏:𝑐, the ratio of the first and last quantities is π‘Ž:𝑐.

6 In Ξ”EFG, the ratio of the measures of the angles is 5:12:13
In Ξ”EFG, the ratio of the measures of the angles is 5:12:13. Find the measures of the angles. Just as the ratio or 5:12 is equivalent to or 5x:12x, the extended ratio 5:12:13 can be written as 5x:12x:13x. Write and solve an equation to find the value of x. ___ 5 12 ______ 5x 12x 5x + 12x + 13x = 180 Triangle Sum Theorem 30x = 180 Combine like terms. x = 6 Divide each side by 30. Answer: So, the measures of the angles are 5(6) or 30, 12(6) or 72, and 13(6) or 78.

7 The ratios of the angles in Ξ”ABC is 3:5:7
The ratios of the angles in Ξ”ABC is 3:5:7. Find the measure of the angles. A. 30, 50, 70 B. 36, 60, 84 C. 45, 60, 75 D. 54, 90, 126

8 Definition Proportion--an equation stating that two ratios are equal.

9 Properties of Proportions
Proportion – an equation stating that two ratios are equal. In the proportion 𝒂 𝒃 = 𝒄 𝒅 , the numbers π‘Ž and 𝑑 are called the extremes of the proportion. the numbers 𝒃 and 𝒄 are called the means of the proportion. 𝒂 𝒃 = 𝒄 𝒅 extreme mean Cross products - the products of the extremes 𝒂𝒅 and the product of the means 𝒃𝒄

10 Page 462

11 A. Original proportion Cross Products Property Multiply. y = 27.3 Divide each side by 6. Answer: y = 27.3

12 B. Original proportion Cross Products Property Simplify. Add 30 to each side. Divide each side by 24. Answer: x = –2

13 A. A. b = 0.65 B. b = 4.5 C. b = –14.5 D. b = 147

14 Use Proportions to Make Predictions
PETS Monique randomly surveyed 30 students from her class and found that 18 had a dog or a cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog or a cat. Write and solve a proportion that compares the number of students who have a pet to the number of students in the school. ← Students who have a pet ← total number of students 18 ● 870 = 30x Cross Products Property 15,660 = 30x Simplify. 522 = x Divide each side by 30. Answer: Based on Monique's survey, about 522 students at her school have a dog or a cat for a pet.

15 Brittany randomly surveyed 50 students and found that 20 had a part-time job. If there are 810 students in Brittany's school, predict the total number of students with a part-time job. A. 324 students B. 344 students C. 405 students D. 486 students

16 miles gallon or gallons mile
Page 463 When setting up proportions, the trick is to have all of the same information in the numerators and all of the same information in the denominators. miles gallon or gallons mile

17 7-1 Assignment Page 464, even, 29-30 Show your work…


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