Solving proportions

Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? - Similar describes things which have the same shape but are not the same size. 1 2 4 8 = 1:3 = 3:9

Solve the proportion. = t 32 7 16 ANSWER 14 = 18 24 b 12 ANSWER 9

What if….. Sometimes the equivalent ratios are not simple.

Cross multiply

Cross multiply

Cross multiply

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

Use the cross products property Solve the proportion = . 8 x 6 15 = 8 x 6 15 Write original proportion. 8 15 = x 6 Cross products property 120 = 6x Simplify. 20 = x Divide each side by 6.

EXAMPLE 1 GUIDED PRACTICE Solve the proportion. Check your solution. = 4 a 5 37 29.6 ANSWER

Solve the proportion. = 21 n 2 5 ANSWER 52.5 = 4 11 9 p ANSWER 24.75

Solve the proportion. = 4 7 15 x ANSWER 26.25 = 5 32 2 p ANSWER 12.8

Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? SET IT UP

Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? SET IT UP = 30 8 x 12

Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? ANSWER 45 tomatillos

Solve the proportion. a 7 9 21 = ANSWER 3

Solve the proportion. 32 28 = m 14 16 ANSWER A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer. ANSWER 12 3 = x 9 ; 36 color pages

How much food should the seal be fed per day? Seals Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day? Seals SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x 280 = 8 amount of food 100 weight of seal

Use the scale on a map Maps SOLUTION From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters.

Write and solve a proportion to find the distance d between the cities. = 4.2 d 1 centimeters 85 kilometers 1 d = 85 4.2 Cross products property ANSWER The actual distance between Cleveland and Cincinnati is about 357 kilometers. d = 357 Simplify.

EXAMPLE 4 Use the scale on a map GUIDED PRACTICE Model ships 6. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. ANSWER about 960 ft

Solving Proportional Problems So how do we use proportions and similar figures? 8 feet 4 feet 2 feet ? feet

Solving Proportional Problems So how do we use proportions and similar figures? ANSWER 4 8 feet 4 feet 2 feet ? feet

Try One Yourself Set up a proportion. What is the width of the larger stick figure? 8 feet 12 feet Knowing the two figures are similar the proportion between the two stick figures is 8 feet:12 feet. Once written as a fraction 8/12 reduces to 2/3. So the proportion between the two stick figures is 2:3. If the proportion is 2:3 then the student should set up this equation and solve for x: 2 / 3 = 4 / x 2 * x = 3 * 4 x = 12 / 2 x = 6 feet 4 feet x feet

Solving for the Building’s Height Here is a sample calculation for the height of a building: x ft 3 ft = 48 ft 4 ft x feet 48 feet 4x = 144 x = 36 yardstick 3 feet The height of the building is 36 feet. 4 feet

You try it!! 11) Now simplify 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

Practice

Practice

Practice

Practice

Practice

Practice