SETTING UP and SOLVING RATIOS AND PROPORTIONS

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

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.

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

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 95.83 inches to 30.5 inches. Express this ratio as a fraction in reduced form. To reduce fraction Math enter enter

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

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?

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

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

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

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

You try it!! 11) Now Reduce 16m = 8 16 16 m =

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

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

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

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?