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**SETTING UP and SOLVING RATIOS AND PROPORTIONS**

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**Ratio – Comparison of 2 numbers by division.**

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

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Ex 1 A geometry class consists of 13 males and 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 to 54. Express this ratio as a fraction in reduced form. To reduce fraction Math enter enter

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**To reduce fraction Math enter enter**

Ex 3 The approximate ratio of the circumference (distance around) to diameter (distance across the top) of an oil barrel is 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 Ex 5 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? Cross Multiply Yes Yes Not a proportion Yes

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**Set up and solve this proportion.**

8) 5 is to 4 as 45 is to x. 5 Now cross multiply 45 ____ = ____ 4 x 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 Now cross multiply x ____ = ____ 2 18 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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You try it!! 11) Now Reduce 16m = 8 16 16 m =

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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 x ____ = _______ 47 10,827 47x = 433,080 Now cross multiply 47 47 x = 9214

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**13) Geothermal energy is heat from inside the earth**

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° 216° ____ = _____ 300 m 9m = 64800 9 9 m = 7200

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**1cm 11cm 30km x 1x = 330 x = 330 km ____ = _____**

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 11cm ____ = _____ 30km x 1x = 330 x = 330 km

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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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SYSTEMS OF EQUATIONS.

SYSTEMS OF EQUATIONS.

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