Writing a Proportion proportion To write a 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 EF shadow broom height broom shadow 4 ft 3 ft EF height broom height EF shadow broom shadow 1064 ft 798ft 3 ft 1064 ft 4 ft 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 Step 1: Make a ratio (fraction) with Dana’s DanaTeresa = 10,530 27,000 1,625 6,500 Step 2 Step 2: Set that equal to Teresa’s Step 3 Step 3: Cross-multiply. Are the cross products equal? When cross products are EQUAL, it IS a proportion 10,530 27,000 1,625 6,500 68,445,000 43,875,000 When cross products are NOT equal, it is NOT a proportion Since cross products are NOT equal, they do NOT pay a proportional amount of taxes.

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: Step 1 Step 1: Write your empty proportion. Step 2 Step 2: Set up your left side anyway you want. * I’d recommend starting with “ 245 N ” Step 3 Step 3: Find the correct conversion ● ● x Drew bench pressed, about, 55 pounds (lb). 100 ounces (oz) = 6.25 pounds (lb) 8 newtons (N) = 1.8 pounds (lb) 25 ounces (oz) = 6.95 newtons (N)... then write it as your right side ratio. 8 N 1.8 lb Step 4 Step 4: Cross-multiply, then set the cross-products equal to each other... since you’re trying to find weight in pounds, call that x. x lb = 8x8x = 441 Step 5 Step 5: Solve the equation you made. 8 8 x = Since newtons (N) is on top on the left, then put newtons (N) on top on the right. To solve a proportion, cross multiply, set the products equal to each other, then solve.

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 = l chili Now, find the cross products. Jack should use 3.4 tablespoons of lime juice. Let’s set up both ratios as Chili # l = l = l = 3.4 Simplify, then solve

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 Step 1: Write an empty proportion. Step 2: On the left side, write the map scale map scale as a fraction. m Let’s change those fractions to decimals m = m = Step 3: On the right side, fill in the distance given in the problem m = 14 m = 14 map scale m Step 4: Call the missing distance, m. m Step 5: Cross-multiply, then solve for m. The bus ride would be, about, 14 miles.

Finding the Map Scale 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? Step 1 Step 1: Write your empty proportion. = Step 2 Step 2: Set your left side as 1 Step 3map Step 3: Write the map distance. as your numerator (top) … in3450 = x x 1 map scale Why 1 ? Since it’s your map scale, you get to pick the numerator. Why x ? That’s the part you are trying to find. Step 4actual Step 4: Write the actual distance. as your denominator (bottom) Step 5 Step 5: Solve the proportion. The map scale is 1 in mi

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?

1.8 is 124% of what number? (If needed, round to the nearest tenth.) Using the Percent Proportion Proportions compare a part/whole ratio to another part/whole ratio. part whole part whole = 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” Which number is the “whole”? I dunno. Let’s say x. What little word is next to it?“of” Write and solve the proportion 180 = 124x ____ 124 x = is 124% of 1.5 = is of p 100 = 1.8 x This is the percent proportion.

What number is 56.1% of 31? What number is 56.1% of 31? (If needed, round to the nearest tenth.) Using the Percent Proportion Which number is the “is”? x (I dunno ?!) let’s call it x is of _ p _ 100 = x  17.4 Which number is the “of”?it’s 31 Which number is the “percent”?it’s 56.1 Solve for x What percent of 47 is 41 ? What percent of 47 is 41 ? (If needed, round your percent to the nearest tenth.) Which number is the “is”? 41 is of _ p _ 100 = p  87.2% Which number is the “of”? Which number is the “percent”? I dunno…let’s call it p Solve for p 47

In 2009, Loudoun Valley High School had a capacity of 1350 students, but 1497 students are enrolled. What percent of capacity was Valley running? Using the Percent Proportion Which number is the “part”? it’s actually 1497 x  Which number is the “whole”? 1350 Which number is the “percent”? x Solve for x Harvard University accepted 4,983 freshman applications last year. Only 7% of all students who applied were accepted. How many students applied? Which number is the “part”? 4983 part whole _ p _ 100 = x  71,186 Which number is the “whole”? Which number is the “percent”?it’s 7 Solve for x x (I dunno ?!) let’s call it x part whole _ p _ 100 = Valley was running at 110.9% capacity. 71,186 students applied.

Are They Similar? Polygons are similar when: 2. Corresponding sides are in proportion 1.Corresponding angles are congruent. *Put a pair of corresponding sides in a ratio. *Set them equal to another pair of corresponding sides. *Cross-multiply – Are they equal? PR JL QR KL = ? J L K = * QPR KJL * PRQ JLK The triangles are SIMILAR

U W T Finding Missing Measures of Similar Figures V

12 19 x 30

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

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 = ≈ 9.7 yd s 60 yd 6.68 s = ≈ 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 $ oz =0.699≈ $0.70 oz Planters $ oz 0.65≈$0.65 oz