# Writing a Proportion To write a proportion proportion

- Slides: 21

Writing a Proportion To write a proportion, proportion you set one ratio equal to another ratio. The only rule is this: Your left side and right side must be set up the same way. So, to see the Eiffel Tower was really 1064 feet tall, you measured it’s shadow to be 798 feet long. Then, you held up a 4 foot broom, and the broom’s shadow was 3 feet long. Write 2 different proportions that compare height and shadow. EF height broom height EF shadow broom shadow 1064 ft 798 ft 3 ft 4 ft 3 ft 1. 333. . . 266 1. 333. . . When you write a proportion, your left side and right side must be set up the same way.

Is it a Proportion? 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? Step 1: 1 Make a ratio (fraction) with Dana’s Step 2: 2 Set that equal to Teresa’s Step 3: 3 Cross-multiply. Are the cross products equal? Dana Teresa 10, 530 1, 62 5 6, 500 27, 000 = 10, 530 27, 000 • 1, 62 5 6, 500 43, 875, 000 68, 445, 000 Since cross products are NOT equal, they do NOT pay a proportional amount of taxes. When cross products are EQUAL, it IS a proportion When cross products are NOT equal, it is NOT a proportion

Solving a Proportion Drew was bragging that he could bench press 245 newtons (N). To convert that weight to pounds (lb), use the chart to the right: 100 ounces (oz) = 6. 25 pounds (lb) 8 newtons (N) = 1. 8 pounds (lb) 25 ounces (oz) = 6. 95 newtons (N) Step 1: 1 Write your empty proportion. Step 2: 2 Set up your left side anyway you want. * I’d recommend starting with “ 245 N ” Step 3: 3 Find the correct conversion. . . then write it as your Since right side ratio. newtons (N) is on top on. . . since you’re trying the left, then put newtons to find weight in (N) on top on pounds, call that x. the right. Step 4: 4 Cross-multiply, then set the cross-products equal to each other Step 5: 5 Solve the equation you made. To solve a proportion, cross multiply, set the products equal to each other, then solve. 8 N x lb 1. 8 lb • 8●x 8 x = 245● 1. 8 = 441 8 8 x = 55. 125 Drew bench pressed, about, 55 pounds (lb).

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 2. 25 5. 1 1. 5 2. 25 • l • = = l To write a proportion, each ratio must be set up the same way. Let’s set up both ratios as 5. 1 • 1. 5 chili juice Now, find the cross products. 2. 25 l = 2. 25 l 7. 65 2. 25 = 3. 4 Simplify, then solve Jack should use 3. 4 tablespoons of lime juice.

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 4 is 1 3 inches apart, then how far apart are they actually apart? Step 1: Write an empty proportion. Step 2: On the left side, write the map scale as a fraction. Step 3: On the Let’s change those fractions to decimals. right side, fill in the distance given in the problem. Step 4: Call the missing distance, m. m 0. 25 1. 75 2 map scale Step 5: Cross 0. 25 • m = 1. 75 • 2 multiply, then solve 0. 25 m = for m. 3. 5 The bus ride would 0. 25 be, about, 14 miles. m = 14

Finding the Map Scale 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 map scale? scale Step 1: 1 Write your empty proportion. Step 2: 2 Set your left side as Why 1 ? Since it’s your map scale, scale you get to pick the numerator. Why x ? That’s the part you are trying to find. Step 3: 3 Write the map distance. as your numerator (top) … Step 4: 4 Write the actual distance. as your denominator (bottom) Step 5: 5 Solve the proportion. 1 x in = 3450 = The map scale is x 1 in mi

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 cm cm = a Set up your proportion. Measure the distance in cm. Now, measure the map’s scale ratio in cm. . . and fill it in your scale ratio a= Solve. The distance between Lisbon, Portugal and Vladivostok, Russia is miles.

Using the Percent Proportion 1. 8 is 124% of what number? (If needed, round to the nearest tenth. ) part Proportions compare a part/whole ratio = whole to another part/whole ratio. This is the percent proportion. is p = of 100 1. 8 124 = x 100 180 ____= 124 x ____ 124 x = 1. 5 A percent proportion compares a ratio to a percent/100. Which number is the “part”? It’s 1. 8 What little word is next to it? “is” I dunno. Let’s say x. Which number is the “whole”? What little word is next to it? “of” Write and solve the proportion 1. 8 is 124% of 1. 5

Using the Percent Proportion What number is 56. 1% of 31? p_ _ = of 100 is (If needed, round to the nearest tenth. ) Which number is the “percent”? Which number is the “is”? Which number is the “of”? x 17. 4 p_ _ = of 100 p 87. 2% (I dunno ? !) let’s call it x it’s 31 Solve for x What percent of 47 is 41 ? is it’s 56. 1 (If needed, round your percent to the nearest tenth. ) Which number is the “percent”? I dunno…let’s call it p Which number is the “is”? 41 Which number is the “of”? 47 Solve for p

Using the Percent Proportion In 2009, Loudoun Valley High School had a capacity of 1350 students, but 1497 students are enrolled. What percent of capacity was Valley running? part = _p_ 100 whole Which number is the “percent”? x it’s actually 1497 Which number is the “part”? Which number is the “whole”? 1350 Solve for x x 110. 9 Valley was running at 110. 9% capacity. Harvard University accepted 4, 983 freshman applications last year. Only 7% of all students who applied were accepted. How many students applied? part whole p_ _ Which number is the “percent”? = 100 Which number is the “part”? Which number is the “whole”? x 71, 186 Solve for x it’s 7 4983 (I dunno ? !) let’s call it x 71, 186 students applied.

Are They Similar? K J The triangles are SIMILAR Polygons are similar when: PR ? QR = JL KL 1. Corresponding angles are congruent. * * QPR PRQ KJL JLK 2. Corresponding sides are in proportion *Put a pair of corresponding sides in a ratio. *Set them equal to another pair of corresponding sides. *Cross-multiply – Are they equal? http: //www. mathopenref. com/similartriangles. html L 21. 8 10. 9 23. 2 11. 6 252. 88 = 252. 88

Finding Missing Measures of Similar Figures 25 W 20 V 15 U T

Finding Missing Measures of Similar Figures 30 12 19 x

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

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 Deion 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 Planters 11 oz = 0. 699 ≈ $0. 70 oz 5 oz 0. 65 ≈ $0. 65 oz

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