Ch. 7 Ratios and Proportions

Ch 7 Getting Started (p.287) Ratio Percent 48.1 77.5 7.4 2.9 1/5 2/3 19/23 3/5 39/50 8/25 3/50 9/10 24 40 5.5 3 1/3 6 ft 3 lb 1 ½ yd 195 min

7-1 Ratios Fractions and in simplest form Write each ratio as a fraction 25 to 10 6:18 8 to 56 27:15

7-1 Ratios Equivalent ratios have same value = should simplify to the same thing Is each set equivalent? (prove with work) 6 to 8 and 36 to 48 9 to 2 and 45 to 6 3 to 8 and 6 to 12 35:5 and 14:2

7-1 Ratios It is recommended that no more than one person be allowed into the shallow end of an outdoor public pool for every 15 feet of surface area. If a local pool’s shallow end has a surface area of 1800 square feet, are the lifeguards correct to allow 120 people into that part of the pool?

7-1 Ratios p. 290 #15-31 odd 15. 1/5 17. 15/7 19. 11/30 21. 3/16 23. 5/1 25. 3/8 27. yes both simplify to 3/5 29. yes both simplify to 8/21 31. yes both simplify to 4/3

7-2 Rates Ratios with different labels UNIT rates have a denominator of ONE rate: 24 miles in 3 hours or 24 mi/3 hr unit rate: 24 (÷3) = 8 mi or 8 mi/hr 3 (÷3) 1 hr

7-2 Rates Make each ratio into a unit rate 228 feet in 24 seconds $2 for six oranges 300 tickets in 6 days 220 miles on 8 gallons of gas

7-2 Rates Best Buy (not the store) the best option for buying an item is to get the one with the lowest unit rate 3 sizes of peanut butter, which is the best buy? $2.49 for 12 oz. $5.30 for 40 oz. $10.89 for 80 oz.

7-2 Rates Best Buy (not the store) 4 sizes of OJ, which is the best buy? $1.28 for 16 oz. $1.92 for 32 oz. $2.56 for 64 oz. $3.36 for 96 oz.

7-2 Rates p. 294 #10-17 all 10. 60 mi.hr 11. 152 cust./day 12. 30 ppl/cls 13. $1.48/lb 14. $0.14/oz 15. 270 cal/serv. 16. 3.08 m/s 17. 32 mi/gal 18. 12 oz bag 19. 150 aspirin 20. B it has 4.38 mg/oz instead of 5.83 21. 4,000 gal/min

7-3 Solving Proportions proportions state that two ratios are equal if two ratios are equal (proportional), then they have the same cross products Are the ratios proportional? 6 = 3 10 5 $5 = $18 8oz 32 oz

7-3 Proportions Check to see if each set of ratios can form a proportion 21 mi/6 hr and 14.3 mi/3 hr $8/20 lb and $24/60 lb 27/6 and 9/2

7-3 Proportions Solving Proportions We can use proportions any time that we are comparing two similar things Can use the complete information we know to fill in other missing information Use cross products and basic equations to solve proportions

7-3 Proportions Cross Products to solve 5 = 10 9 x 2 = x 12 36

7-3 Proportions Cross Products to solve 6 = 3 5 x 3 = 760

7-3 Proportions The toy car shown below is modeled after a real car. If the real car is 4.79 meters long, how wide is it? 6.6 cm 15.4 cm

7-3 Proportions An 8 oz. glass of orange juice contains 72 mg of vitamin C. How much juice contains 60 mg of vitamin C? p. 300 #42-46

Review p.300 #48-60

Quiz 3-D: Wednesday 2/1 write and simplify ratios (7-1) calculate unit rates (7-2) confirm proportions (7-3) solve proportions (7-3)