6- Measurement: Changing Customary Units MAIN IDEA Change units in the customary system. New Vocabulary unit ratio Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz ANIMALS The table shows Animal Weight (T) the approximate weights in Grizzly Bear 1 tons of several large land White Rhinoceros animals. One ton is equivalent Hippopotamus 5 to,000 pounds. African Elephant 8 You can use a ratio table, which have columns filled with ratios that have the same value, to convert each weight from tons to pounds. 1. Copy and complete the ratio table. The first two ratios are done for you. See margin. Tons 1 5 8 Pounds,000 8,000 To produce equivalent ratios, multiply the quantities in each row by the same number. Customary Units Type of Measure Larger Unit Smaller Unit Length Weight Capacity. Then graph the ordered pairs (tons, pounds) from the table. Label the horizontal axis Weight in Tons and the vertical axis Weight in Pounds. Connect the points. What do you notice about the graph of these data?. Sample answer: The points lie on a straight line. See margin for graph. The relationships among the most commonly used customary units of length, weight, and capacity are shown in the table below. 1 foot (ft) = 1 inches (in.) 1 yard (yd) = feet 1 mile (mi) = 5,80 feet 1 pound (lb) = 16 ounces (oz) 1 ton (T) =,000 pounds Key Concept 1 cup (c) = 8 fluid ounces (fl oz) 1 pint (pt) = cups 1 quart (qt) = pints 1 gallon (gal) = quarts 98 Chapter 6 Ratios and Proportions
Each of the relationships above can be written as a unit ratio. Like a unit rate, a unit ratio is one in which the denominator is 1 unit. _ ft _,000 lb _ qt 1 yd 1 T 1 gal Notice that the numerator and denominator of each fraction above are equivalent, so the value of each ratio is 1. You can multiply by a unit ratio of this type to convert or change from larger units to smaller units. Convert Larger Units to Smaller Units Multiplying by 1 Although the number and units changed in Example 1, because the measure is multiplied by 1, the value of the converted measure is the same as the original. 1 Convert 0 feet into inches. 1 in. Since 1 foot = 1 inches, the unit ratio is _ 1 ft. 1 in. 0 ft = 0 ft _ Multiply by _ 1 in. 1 ft 1 ft. 1 in. = 0 ft _ Divide out common units, leaving 1 ft the desired unit, inches. = 0 1 in. or 0 in. Multiply. So, 0 feet = 0 inches. GARDENING Clarence mixes cup of fertilizer with soil before planting each bulb. How many ounces of fertilizer does he use per bulb? c = _ 1 8 fl oz c _ 1 c = _ 1 8 fl oz or fl oz Multiply. Since 1 cup = 8 fluid ounces, multiply by _ 8 fl oz. Then, divide out common units. 1 c So, fluid ounces of fertilizer are used per bulb. Review Vocabulary reciprocal The product of a number and its reciprocal is 1; Example: The reciprocal of _ 5 5_ is. (Lesson 5-7) a. 6 yd = ft 108 b. _ T = lb 1,500 c. 1 _ 1 qt = pt To convert from smaller units to larger units, multiply by the reciprocal of the appropriate unit ratio. Convert Smaller Units to Larger Units Convert 15 quarts into gallons. Since 1 gallon = quarts, the unit ratio is _ qt, and its reciprocal is _ 1 gal 1 gal qt. 15 qt = 15 qt _ 1 gal Multiply by _ 1 gal qt qt. = 15 qt _ 1 gal qt = 15 _ 1 Divide out common units, leaving the desired unit, gallons. gal or.75 gal Multiplying 15 by is the same as dividing 15 by. Lesson 6- Measurement: Changing Customary Units 99
COSTUMES Umeka needs feet of fabric to make a costume for a play. How many yards of fabric does she need? ft = _ 1 1 yd ft _ ft = 9 _ _ 1 yd 1 Write = _ yd or 1 _ 1 yd Multiply. So Umeka needs 1 _ 1 yards of fabric. _ Since 1 yard = feet, multiply by 1 yd ft. Then, divide out common units. as an improper fraction. Then divide out common factors. d.,60 ft = mi f. 100 oz = lb 6 e. 5 pt = qt g. 76c = gal _ h. c = pt 6 i. 18 in. = ft 1 j. FOOD A -pound pork loin can be cut into 10 smaller pork chops of equal weight. How many ounces does each pork chop weigh?.8 oz You can also convert from one rate to another by multiplying by a unit rate or its reciprocal. Convert Rates 5 HELICOPTERS A helicopter flies at a rate of 158 miles per hour. How many miles per second is this? 1 h Since 1 hour =,600 seconds, multiply by _,600 s. _ 158 mi = _ 158 mi _ 1 h Multiply by _ 1 h h 1 h,600 s,600 s. = _ 158 mi _ 1 h 1 h,600 s _ 0.0 mi 1 s Divide out common units. Simplify. So, a helicopter flies approximately 0.0 mile per second. Real-World Link A swordfish reaches a maximum size of 1 feet and almost 1,00 pounds. Source: Sport Fishing Central k. FISH A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 16,800 ft/h l. WALKING Ava walks at a speed of 7 feet per second. How many feet per hour is this? 5,00 ft/h 00 Chapter 6 Ratios and Proportions
indicates multi-step problem Examples 1, (p. 99) Examples, (pp. 99 00) Example 5 (p. 00) 1. lb = oz 8. 5 1 _ yd = ft 16. 6.5 c = fl oz 5. FISH Grouper are members of the sea bass family. A large grouper can weigh _ 1 ton. About how much does a large grouper weigh to the nearest pound? 667 lb 5. 1 qt = gal 6. 8 in. = ft 7. 15 pt = qt 7 8. VEHICLES The world s narrowest electric vehicle is about 5 inches wide and is designed to move down narrow aisles in warehouses. About how wide is this vehicle to the nearest foot? ft 9. RUNNING The fastest a human has ever run is about 7 miles per hour. How many miles per minute is this? 0.5 mi/min HOMEWORK HELP For Exercises 10 1 5 6 7 HELP See Examples 1 5 Exercise Levels A: 10 7 B: 8 7 C: 8 10. 18 ft = yd 6 11. 7 oz = lb 1. lb = oz 1. gal = qt 16 1. _ 1 pt = c 9 15. c = fl oz 16. mi = ft 10,560 17. 1 _ 1 mi = ft 6,600 18. 5,000 lb = T 19. 1 c = pt 6 0. _ qt = pt 5 1. _ T = lb 6,750 8. PUMPKINS One of the largest pumpkins ever grown weighed about 1 _ ton. How many pounds did the pumpkin weigh? 1,000 lb. SKIING Speed skiing takes place on a course that is _ mile long. How many feet long is the course?,50 ft. BOATING A 0-foot power boat is for sale by owner. About how long is this boat to the nearest yard? 1 yd 5. BLOOD A total of 5 pints of blood were collected at a local blood drive. How many quarts of blood is this? 17 qt 6. GO-KARTS A go-kart s top speed is 607,00 feet per hour. How many miles per hour is this? 115 mi/h 7. BIRDS A peregrine falcon can fly at over 00 miles per hour. How many feet per hour is this? 1,056,000 ft/h Lesson 6- Measurement: Changing Customary Units 01
8. No; + + 7_ + + = 8 1 c punch and a -qt pitcher holds qt _ pt _ 1 qt c 1 pt = c or 8 c. Since PRACTICE EXTRA PRACTICE See pages 68, 709. 8. PUNCH Will a -quart pitcher hold the entire recipe of citrus punch given at the right? Explain your reasoning. 9. WEATHER On Monday, it snowed a total of 15 inches. On Tuesday and Wednesday, it snowed an additional _ 1 inches and 6 _ inches, Recipe: cups orange juice cups grapefruit juice 1 / cup apricot nectar 1 / cup pineapple juice cups ginger ale Citrus Punch Drink 7_ 8 c < 8 c, the 1 pitcher will not respectively. A weather forecaster says that over the last three days, it snowed about _ hold all of the 1 feet. Is this a valid claim? Justify your answer. punch. MEASUREMENT Complete the following statements. 9. No; 15 in. + 0. If 16 c = 1 gal, then 1 _ 1 gal = c 0 in. + 6 _ 1. If 1,760 yd = 1 mi, then 880 yd = mi in. = 6 in. and 6 _. If 6 in. = 1 yd, then. yd = in. 8.8 1 =. So, it 16. ESTIMATION Cristos is a member of the swim team and trains by swimming snowed a total of an average of,000 yards a day. About how many miles would he swim by _ ft training at this rate for 5 days, to the nearest half-mile? 16 or about ft, about 8 mi not ft. MEASUREMENT For Exercises y 7, use the graph at the right. H.O.T. Problems 8. Sample answer: Annabelle is making brownies. The recipe calls for cups of sour cream. She has pints of sour cream. Does she have enough sour cream to make the brownies?. What does an ordered pair from this graph represent? See margin. 1 5. Find the slope of the line. 0 6 8 10 x 6. Use the graph to find the See margin. Capacity in Quarts capacity in quarts of a.5-gallon container. Explain your reasoning. 7. Use the graph to predict the capacity in gallons of a 1-quart container. Explain your reasoning. gal; Sample answer: the graph increases by 1 gallon for every quarts. 8. OPEN ENDED Write a problem about a real-world situation in which you would need to convert pints to cups. REASONING Replace each with <, >, or = to make a true sentence. Justify your answers. 9 1. See margin for justification. 9. 16 in. 1 _ 1 ft < 0. 8 _ gal qt > 1..7 T 86,00 oz =. CHALLENGE To whiten fabrics, a certain Web site recommends that you soak them in a mixture of _ cup vinegar, quarts water, and some salt. Does a mixture that contains 1.5 ounces vinegar and 16 ounces water have the same vinegar-to-water ratio as the recommended mixture? Explain. See margin.. MATH Use multiplication by unit ratios of equivalent measures to convert 5 square feet to square inches. Justify your answer. See margin. WRITING IN Capacity in Gallons 0 Chapter 6 Ratios and Proportions
. Which situation is represented by the graph? D 5. How many cups of milk are shown below? G 18 15 1 9 6 O y 1 5 6x A conversion of inches to yards B conversion of feet to inches C conversion of miles to feet D conversion of yards to feet F _ c H _ 1 c G 1 _ 1 c J 10 c 6. How many ounces are in 7 _ pounds? A 1 oz C 10 oz A B 1 oz D 11 oz 7. Use the information in the table to find the rate of change in dollars per hour. (Lesson 6-) $9 per h Wage ($) 0 9 18 7 Time (h) 0 1 8. GROCERIES Find the unit price if Anju spent $ for six oranges. Round to the nearest cent if necessary. (Lesson 6-) $0. per orange 9. MEASUREMENT By doubling just the length of the rectangular ice skating rink in Will s backyard from 16 to feet, he increased its area from 18 square feet to 56 square feet. Find the width of both rinks. (Lesson -6) 8 ft ALGEBRA For Exercises 50 5, use the pay stub at the right. (Lesson -) 50. Write and solve an equation to find the regular hourly wage. 0r = 00; $7.50/h 51. Write and solve an equation to find the overtime hourly wage. v =.50; $11.5/h 5. Write and solve an equation to find how many times greater Grace s overtime hourly wage is than her regular hourly wage. 7.5t = 11.5; 1.5 Martin, Grace Employee #: 11 Description: Regular hours: Overtime hours: Hours: 0 Earnings ($): 00.00.50 PREREQUISITE SKILL Multiply. (p. 67) 5. 1.5 8. 118.9 5. 7.0.6.8 55. 9.9 15. 1.17 56. 1.8 16.7 0.78 Lesson 6- Measurement: Changing Customary Units 0