Solving proportions Proportions What are proportions —

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. 1 = 4 8 1: 3 = 3: 9 What do we mean by similar? 2 - Similar describes things which have the same shape but are not the same size.

Solve the proportion. t = 7 16 32 ANSWER 14 18 b 24 = 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. s os cr ly ow ltip N u m 5 45 ____ = ____ 4 x 5 x = 180 5 5 x = 36

First - Set up & solve the proportion. 9) 3 is to 2 as x is to 18. s os cr ly ow ltip N u m 3 x ____ = ____ 2 18 2 x = 54 2 2 x = 27

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

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

EXAMPLE 1 GUIDED PRACTICE Solve the proportion. Check your solution. 4 = 5 a 37 ANSWER 29. 6

Solve the proportion. 21 = 2 n 5 ANSWER 52. 5 4 9 11 = p ANSWER 24. 75

Solve the proportion. 4 = 15 7 x ANSWER 26. 25 5 2 32 = 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 = x 8 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 9 = 7 21 ANSWER 3

Solve the proportion. m 32 = 28 14 ANSWER 16 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 x 3 = 9 ; 36 color pages

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? SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. 8 x = 100 280 amount of food 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 Cincinnati is about 4. 2 centimeters.

Write and solve a proportion to find the distance d between the cities. 1 85 4. 2 = d 1 d = 85 4. 2 ANSWER d = 357 centimeters kilometers Cross products property Simplify. The actual distance between Cleveland Cincinnati is about 357 kilometers.

Use EXAMPLE 4 GUIDED PRACTICE the scale on a map 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? 8 feet 4 feet ANSWER 4 2 feet ? feet

Try One Yourself 8 feet Set up a proportion. What is the width of the larger stick figure? 12 feet 4 feet x feet

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

11) 16 m = 8 16 16 m = Now simplify

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! s os cr ly ow ltip N u m x 40 ____ = _______ 47 10, 827 47 x = 433, 080 47 47 x = 9214

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 9 m = 64800 9 9 m = 7200

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

Practice

Practice

Practice

Practice

Practice

Practice