Chapter 5 Ratios & Proportions 5-1: Ratios 5-2: Proportions and Unit Conversions A proportion is an equation stating that two ratios are equal. 5-3: Proportions You can use unit rates to solve a proportion. First find the unit rate. Then mulitply to solve the problem. 5-4 Solving Proportions Similar figures have the same shape but not necessarily the same size. 5-5 Similar Figures Scale Drawing- an enlarged or reduced drawing of an object that is similar to the actual object 5-6 Maps and Scale Drawings One way to see if ratios form a proportion is to write both in simplest form. Then see if they are equal Using the table above, write the ratio of the number of students who saw a movie to the total number of students. Do the ratios form a proportion? Writing Ratios in Simplest Form YES NO A B 24 25 60 Did you see a movie this weekend? 10 5+7= (cc) image by anemoneprojectors on Flickr Class A 10/24 CLASS B 25/60 SIMPLIFY! 5/12 5/12 Since both ratios are equal to 5/12 then they are proportional. 10/12 and 40/56 Are they proportional? 5/6 5/7 1st Simplify NO! because they are not equal Cross Product Property You can also determine if ratios are proportional in another way! 6

8 9

12 = 72 72 72 = 72 so they are proportional a) 5/9 = 30/32

b) 7/8 and 55/65 Are they proportional a) Yes B) NO Fill in the blank so that the ratios form proportions CLASS WORK 3. 1 4

2 7. 2 8

3 Determine if they are ratios 10. 1/2 and 14/28 13. 21/24 and 56/64

17. 17/34 and 2/3 24. 12/15 and 20/25 35. An astronaut who weighs 174lb on Earth weighs 29 lb on the moon. If you weigh 102 lb on Earth, would you weigh 17lb on the moon? 8 12 YES YES NO YES Yes because they are proportional The price for 6 oranges is $2.34. You want to find the cost of 8 oranges. USING UNIT RATES First. Find the unit price $2.34 / 6 = $0.39/ orange Now, you can figure out the cost of 8 since you know the cost of 1. = $3.12 .39 x 8 Try it at your desk! 1. Postcards cost $2.45 for 5 cards. How much will 13 cards cost? $6.37 When the proportion involves a variable, solve the proportion by finding the value of the variable. Solving Using Mental Math x 21

12 36 = How did 12 become 36? Multiply by 3! so x times 3 is 21. What is x? x=7 Try it at your desk: 8 n

10 40 = 10 -->40... you multiply by 4 so 8 times 4 is n=32 Many proportions can not be solved using mental math! However, using cross products is a simple way to solve. Using Cross Products 25 15

38 x = 25x = 38(15) 25x = 570 x= 22.8 Try it at your desk. 12 x

15 21 12 x

15 21 = x= 16.8 CLASSWORK Solve by finding a unit rate. Then multiply. 6. If 5 goldfish cost $6.45, what is the cost of 8 goldfish?

8. If 3 oninions weigh 0.75lb, how much do 10 onions weigh?

9. If 13 keychains cost $38.35, what is the cost of 20 key chains? Similar polygons have corresponding angles with the same measurements and the lengths of corresponding sides form ratios. Polygon- a closed plane figure formed by three or more line segments that do not cross. 83* 50 34 40 C B A 44* 53* H F G 44* 53* 83* 60 51 75 Corresponding Angles Sides that form ratios 40 60

50 75 = Finding a Missing Measure since the sides of a similar polygon are proportional, set up a ratio to find the missing side. 50 cm 30 cm G D O T C A 24cm 32cm ?cm 40cm FH ACT and ODG are similar. Find the missing side ? 32

50 40 just pick one given side to equate with All small l>

All large l> 40 Find the Missing Length F E G D 10 6 3 6 12 10 ? x ? is 20

x is 5 Using Indirect Measurements Board Work CLASS WORK Scale- a ratio that compares length in a drawing or model to the corresponding length in the actual object. If a 15 ft boat is 1 inch in a drawing write it as a ratio 1in to 15 feet 1in : 15 ft

1in/ 15 ft The scale for a house drawing is 1cm=2.5m. If the length of the side of the house is 3 cm on a drawing, what is the actual size? 1 3

2.5 ? = __ __ 7.5 meters

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# 7th Grade Chapter 4: Ratios & Proportions

September 17th - September 28

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