Study Guide and Review
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1 Complete each sentence with the correct term. Choose from the list below. congruent constant of proportionality corresponding parts cross products dilation dimensional analysis indirect measurement inverse proportion nonproportional proportion proportional rate ratio scale scale drawing scale factor scale model similar figures unit rate A statement of equality of two ratios or rates is called a(n). A statement of equality of two ratios or rates is called a proportion. proportion A(n) is a ratio of two measurements having different units. A rate is a ratio of two measurements having different units. rate Proportional relationships can be described by using the equation y = kx, where k is the. Proportional relationships can be described by using the equation y = kx, where k is the constant of proportionality. constant of proportionality esolutions Manual - Powered by Cognero Page 1
2 The ratio of the length on a scale drawing to the corresponding length on the real object is called the. The ratio of the length on a scale drawing to the corresponding length on the real object is called the scale factor. scale factor Figures that have the same shape but not necessarily the same size are called. Figures that have the same shape but not necessarily the same size are called similar figures. similar figures A(n) is a comparison of two quantities by division. A ratio is a comparison of two quantities by division. ratio The process of including units of measurement as factors when computing is called. The process of including units of measurement as factors when computing is called dimensional analysis. dimensional analysis Two quantities are if they have a constant ratio or rate. Two quantities are proportional if they have a constant ratio or rate. proportional esolutions Manual - Powered by Cognero Page 2
3 Express each ratio as a fraction in simplest form. 10 girls out of 24 students 6 red cars to 4 blue cars 10 yards to 8 inches Convert 10 yards to inches. Three are 36 inches in 1 yard. esolutions Manual - Powered by Cognero Page 3
4 18 ounces to 3 cups Convert 3 cups to ounces. Three are 8 ounces in 1 cup. BASEBALL Jean got 12 hits out of 16 times at bat. Express this rate as a fraction in simplest form. Explain its meaning. For every 4 times at bat, Jean got 3 hits or on ; For every 4 times at bat, Jean got 3 hits or on Express each rate as a unit rate. Round to the nearest tenth, if necessary. $25.97 for 8 boxes The unit rate is $3.25 per box. $3.25 per box 400 meters in 5 minutes The unit rate is 80 meters per minute. 80 meters per minute esolutions Manual - Powered by Cognero Page 4
5 $175 for 4 concert tickets The unit rate is $43.75 per ticket. $43.75 per ticket 125 miles in 200 minutes The unit rate is 0.6 mile per minute. 0.6 mile per minute SHOPPING An eight pack of juice boxes costs $4.79, and a twelve pack of juice boxes costs $6.59. Which is a better buy? Explain. The eight pack costs $0.60 per juice box. The twelve pack of juice boxes costs $0.55 per juice box. The twelve pack is a better buy because the cost per juice box is less. 12 juice boxes for $6.59; Sample answer: The eight pack of juice boxes costs $0.60 per juice box and the twelve pack of juice boxes costs $0.55 per juice box. Complete each conversion. Round to the nearest hundredth esolutions Manual - Powered by Cognero Page 5
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7 340.2 PLANES A plane is flying at a speed of 425 miles per hour. How far will the plane travel in 0.75 hour? The plane will travel miles mi WATER A swimming pool is being drained at a rate of 50 gallons per hour. How many milliliters per second is this? The pool is being drained at a rate of about 52.6 milliliters per second milliliters per second esolutions Manual - Powered by Cognero Page 7
8 Determine whether the set of numbers in each table is proportional. Explain. Write the rate of boxes to pens in simplest form. Each rate is equal to. So, the number of boxes is proportional to the number of pens. Yes; each rate is equal to. Write the rate of number of people to brownies eaten in simplest form. The rates are not equal. So, the number of people is not proportional to the brownies eaten. No; the rates are not equal. esolutions Manual - Powered by Cognero Page 8
9 FESTIVALS A customer at the ring toss booth gets 8 rings for $2. Write an equation relating the cost to the number of rings. At this same rate, how much would a customer pay for 11 rings? for 20 rings? Find the constant of proportionality. The cost is $0.25 times the number of rings, r. The equation is c = 0.25r. To find the cost of 11 rings, substitute 11 for r. 11 rings cost $2.75. To find the cost of 20 rings, substitute 20 for r. 20 rings cost $5. c = 0.25r, 11 rings cost $2.75; 20 rings cost $5 Solve each proportion. 12 esolutions Manual - Powered by Cognero Page 9
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11 REAL ESTATE A homeowner whose house is assessed for $120,000 pays $1800 in taxes. At the same rate, what is the tax on a house assessed at $135,000? Let t represent the tax on a house assessed at $135,000. The tax on a house assessed at $135,000 is $2025. $2025 On the scale drawing of a museum, the scale is 0.5 inch = 10 feet. Find the actual length of each gallery. Let x = the actual length of the Modern Art gallery. The actual length of the Modern Art gallery is 120 feet. 120 ft esolutions Manual - Powered by Cognero Page 11
12 Let x = the actual length of the Renaissance gallery. The actual length of the Renaissance gallery is 85 feet. 85 ft Let x = the actual length of the Egypt gallery. The actual length of the Egypt gallery is 150 feet. 150 ft MAPS The length of a highway is 900 miles. If 0.5 inch on a map represents 50 miles, what is the length of the highway on the map? Let x = the length of the highway on the map. The length of the highway on the map is 9 inches. 9 in. esolutions Manual - Powered by Cognero Page 12
13 The figures are similar. Determine each missing measure. Since ABC ~ WXY, the corresponding sides are proportional. The length of is 7.2 in. 7.2 in. Since Figure EFGH ~ RUST, the corresponding sides are proportional. The length of is 8 cm. 8 cm esolutions Manual - Powered by Cognero Page 13
14 MOSAIC A mosaic is created using rectangular blocks. Block A has a length of 5 centimeters and a width of 2.5 centimeters. Block B is similar to block A and has a length of 7 centimeters. What is the width of block B? Since Block A ~ Block B, the length and width are proportional. The width of Block B is 3.5 cm. 3.5 cm HISTORY The largest known pyramid is the Pyramid of Khufu. At a certain time of day, a vertical yard stick casts a shadow 1.5 feet long, and the pyramid casts a shadow 241 feet long. How tall is the pyramid? The pyramid is 482 feet tall. 482 ft esolutions Manual - Powered by Cognero Page 14
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