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Writing a Ratio

Writing a Ratio. Write the ratio 3 feet (ft) to 8 inches (in) as a fraction in simplest form. 9. A ratio is a comparison of 2 values. 3 ft. 36 in. 9 in. •12 =. =. =. Compare these 2 values as a fraction. 8 in. 8 in. 2 in. 2. Convert to the same unit.

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Writing a Ratio

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

  2. 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 Bo Deion 40 yd 60 yd 9.708 9.7 yd = ≈ 8.982 ≈ 9.0 yd = 4.12 s s 6.68 s 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? $7.69 $3.25 Emerald’s $0.70 Planters 0.65 ≈ $0.65 = 0.699 ≈ 11 oz 5 oz oz oz

  3. 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? Dana Teresa When two ratios are equal, they form a proportion 10,530 1,625 So, let’s set Dana’s ratio of tax = salary 27,000 6,500 ... equal to Teresa’s ratio of tax salary Now, find the cross products. No -- the ratios don’t form a proportion = 43,875,000 Are they equal? • = 68,445,000

  4. 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? Chili #1 Chili #2 To write a proportion, each ratio must be set up the same way. 2.25 5.1 • = 1.5 l chili Let’s set up both ratios as juice 2.25 • l = 5.1 • 1.5 Now, find the cross products. 2.25l = 7.65 Simplify, then solve 2.25 2.25 Jack should use 3.4 tablespoons of lime juice. l = 3.4

  5. 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 m = 14 ...so the actual distance is 14 miles. this is what the map tells you in the corner this is distance between the 2 places Since we don’t like fractions, let’s change them to decimals. 0.25 map 1.75 map = actual actual m 0.25 • m = 1.75 • 2 = 0.25m 3.5 0.25 0.25

  6. 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. Usually, scale ratios set the first value as 1 Measure to find the mapdistancebetween them. Solve. scale ratio = distance ratio 1 in in = a = so, the scale is 1 in = mi 3450 = a

  7. Using a Map’s Scale Ratio 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? scale ratio = distance ratio Set up your proportion. cm cm Measure the distancein cm. = a Now, measure the map’s scaleratioin cm... ... and fill it in your scaleratio. Solve. a = The distance between Lisbon, Portugal and Vladivostok, Russia is miles.

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