2. Writing a Ratio Write the ratio 3 feet (ft) to 8 inches (in) as a fraction in simplest form. A ratio is a comparison of 2 values. Compare these 2 values as a fraction. 3 ft 8 in Convert to the same unit. Hint: Always convert to the smaller unit. = 36 in 8 in 12 = Now, reduce = 9 in 2 in 9 2 There are other ways to write a ratio, also. 9 in 2 in or 9 2 9:2 or 9 to 2

3. Finding a Unit Rate In 1987, Bo Jackson ran the 40 yd (yard) dash in 4.12 s (seconds). In 1989, Deion Sanders ran the 60 yd dash in 6.68 s. Who ran at a faster rate? To compare these runners, find each players yards seconds BoDeion 40 yd 4.12 s = 9.708 ≈ 9.7 yd s 60 yd 6.68 s = 8.982 ≈ 9.0 yd s Bo Jackson ran at the faster rate. Emerald’s 11 oz (ounce) can of almonds sells for $7.69. Planters 5 oz bag of Trail Mix sells for $3.25. Which has the lower unit rate? Emerald’s $7.69 11 oz =0.699≈ $0.70 oz Planters $3.25 5 oz 0.65≈$0.65 oz

5. Proportions Dana earned a salary of $27,000/mo, and Teresa earned a salary of $6,500/mo. Dana paid $10,530 in income taxes, but Teresa paid $1,625 in income taxes. Did they pay a proportional amount of taxes? When two ratios are equal, they form a proportion So, let’s set Dana’s ratio of tax salary DanaTeresa = 10,530 27,000 1,625 6,500... equal to Teresa’s ratio of tax salary Now, find the cross products. = 68,445,000 = 43,875,000 Are they equal? No -- the ratios don’t form a proportion

6. Writing & Solving Proportions Jack’s recipe makes 2.25 pounds (lb) of chili, and it calls for 1.5 tablespoons of lime juice. If he wanted to make 5.1 lb of chili, how many tablespoons of lime juice should he use? To write a proportion, each ratio must be set up the same way. juice Chili #1 = 2.25 1.5 5.1 l chili Now, find the cross products. Jack should use 3.4 tablespoons of lime juice. Let’s set up both ratios as Chili #2 2.25 l = 5.1 1.5 2.25 l = 7.65 2.25 l = 3.4 Simplify, then solve

7. Scale Models Harmony MS has the longest bus rides in the county. Here’s a map showing the route from Loudoun Heights (next to Harper’s Ferry) to Harmony. If their map length is 1 3 inches apart, then how far apart are they actually apart? 4 Let’s make a proportion. For scale model problems, your proportion will have: scale ratio = distance ratio actual map this is what the map tells you in the corner this is distance between the 2 places actual map = m Since we don’t like fractions, let’s change them to decimals. 0.25 m = 1.75 2 0.25 m = 3.5 0.25 m = 14...so the actual distance is 14 miles. 0.251.75

9. Finding a Scale Ratio The longest drive in the contiguous U.S. is from Key West, FL to Seattle, WA. If the actual distance of the drive is 3,450 miles, what is the scale of the map. You’ll need a ruler with inches for this one. Set up your proportion. scale ratio = distance ratio = scale ratios Usually, scale ratios set the first value as 1 1 in map distance Measure to find the map distance between them. Solve. in 3450 = a a = so, the scale is 1 in = mi

11. Using a Map’s Scale Ratio Set up your proportion.scale ratio = distance ratio = distance Measure the distance in cm. cm scale ratio Now, measure the map’s scale ratio in cm... scale ratio... and fill it in your scale ratio. cm a Solve. a = a = The distance between Lisbon, Portugal and Vladivostok, Russia is miles. José and Rosa, from Lisbon, Portugal, are going to visit the grandparents, in Vladivostok, Russia, for the holidays.. What will be the actual distance of their drive?