SETTING UP and SOLVING RATIOS AND PROPORTIONS

Ratio – Comparison of 2 numbers by division. Example: 1:2, ½, 1 to 2 Proportion – An equation stating that 2 ratios are equal. Example: a:b = c:d

Example 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