7-1 Ratios and Proportions
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7-1 Ratios and Proportions
You solved problems by writing and solving equations.
• Write ratios.
• Write and solve proportions.
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Ratio• A ratio is a comparison of two quantities using
division.• The ratio of quantities and can be expresses as
to , , or where .• Ratios are usually expressed in simplest form.
• 32:18 = 16:9
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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 1850. 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.
Answer: The athlete-to-student ratio is 0.3.
0.3 can be written as
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A. 0.3
B. 0.5
C. 0.7
D. 0.8
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.)
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Extended Ratios
Extended ratios can be used to compare three or more quantities. The expression means • the ratio of the first two quantities is • the ratio of the last two quantities is • the ratio of the first and last quantities is
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In ΔEFG, 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.
___512
______5x12x
Answer: So, the measures of the angles are 5(6) or 30, 12(6) or 72, and 13(6) or 78.
5x + 12x + 13x = 180 Triangle Sum Theorem30x = 180 Combine like terms.x = 6 Divide each side by 30.
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A. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.
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Definition
• Proportion--an equation stating that two ratios are equal.
32
128
gal1mi
gal10mi300 x
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Properties of ProportionsProportion – an equation stating that two ratios are equal.In the proportion the numbers and are called the extremes of the proportion.the numbers and are called the means of the proportion.
𝒂𝒃=
𝒄𝒅
extremeextrememeanmean
Cross products - the products of the extremes and the product of the means
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Page 462
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A.
Answer: y = 27.3
Original proportion
Cross Products Property
Multiply.
Divide each side by 6.y = 27.3
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B.
Answer: x = –2
Original proportion
Cross Products PropertySimplify.Add 30 to each side.Divide each side by 24.
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A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
A.
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Use Proportions to Make PredictionsPETS 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.
18 ● 870 = 30x Cross Products Property15,660 = 30x Simplify.
522 = x Divide each side by 30.
← Students who have a pet← total number of students
Answer: Based on Monique's survey, about 522 students at her school have a dog or a cat for a pet.
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A. 324 students
B. 344 students
C. 405 students
D. 486 students
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.
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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.
or
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7-1 Assignment
Page 464, 10-28 even,29-30
Show your work…