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SETTING UP and SOLVING RATIOS AND PROPORTIONS

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Ratio – Comparison of 2 numbers by division. –E–Ex. 1:2, ½, 1 to 2 Proportion – An equation stating that 2 ratios are equal. –a–a:b = c:d Extremes – The last (or end) terms of a proportion. –a–a and d are the extremes Means – The middle terms of the proportion. –b–b and c are the means

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Ex 1 A geometry class consists of 13 males and 16 females. Find the ratio of females to males. Find the ratio of females to the entire class. There are 29 in the class.

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Ex 2 The male to female ratio in Italy is 46 to 54. Express this ratio as a fraction in reduced form. To reduce fraction Math enter enter

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Ex 3 The approximate ratio of the circumference (distance around) to diameter (distance across the top) of an oil barrel is 95.83 inches to 30.5 inches. Express this ratio as a fraction in reduced form. To reduce fraction Math enter enter

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Ex 4 A manufacturer can produce 1140 parts in 4 hours. What is the unit rate in parts per hour? Ex 5 Write the ratio as a rate in lowest terms: $3.90 for 6 muffins

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Ex 6 There is a law stating the ratio of the width to length of the American flag should be 10 to 19. Which is not the correct ratio?

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Ex 7 Which of the following pairs of ratios do not form a proportion? Which ones do? Not a proportion Cross Multiply

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8) 5 is to 4 as 45 is to x. Set up and solve this proportion. ____ = ____ 5 4 45 x Now cross multiply 5x = 180 5 5 x = 36

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First - Set up & solve the proportion. 9) 3 is to 2 as x is to 18. ____ = ____ 3 2 x 18 Now cross multiply 2x = 54 2 2 x =27

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NO set up this time!! Just solve….. 10) 6x = 144 6 6 x = 24

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11) 16m = 8 16 m= Now Reduce

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12) Mr. Jones has taken a survey of college students and found that 40 out of 47 students are liberal arts majors. If a college has 10,827 students, what is the number of students who are liberal arts majors, rounded to the nearest whole number? ____ = _______ First – Set up Your proportion! 40 47 10,827 x Now cross multiply 47x= 433,080 47 x = 9214

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13) Geothermal energy is heat from inside the earth. Underground temperatures generally increase 9°C for every 300 meters of depth. How deep would a well have to be for the temperature to reach 216°C ? First – Set up Your proportion! ____ = _____ 9° 300 m 216° 9m = 64800 9 9 m= 7200

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14) A map has a scale of 1 cm = 30 km. If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km? First – Set up Your proportion! ____ = _____ 1cm 30km 11cm x 1x = 330 330 km x =

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Ex 6 Set up & Solve proportions A regional forestry division wanted to estimate the number of deer in a particular national park. They caught and tagged 76 deer and released them back into the park. Later they selected a sample of 225 deer. Of these 225 deer, 15 were tagged. What is the best estimate of the number of deer in the park?

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