How can you compare lengths between the customary and metric systems? 6 ft. ACTIVITY: Customary Measure History

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1 5.7 Converting Measures How can you compare lengts between te customary and metric systems? yd 6 ft ACTIVITY: Customary Measure History COMMON CORE Converting Measures In tis lesson, you will use conversion factors (rates) to convert units of measurement. Learning Standard 6.RP.3d Work wit a partner. 232 Capter 5 Ratios and Rates a. Matc te measure of lengt wit its istorical beginning. Lengt Historical Beginning Inc Foot Yard Mile Te lengt of a uman foot Te widt of a uman tumb Te distance a uman can walk in 000 paces ( pace = 2 steps) Te distance from a uman nose to te end of an outstretced uman arm b. Use a ruler to measure your tumb, arm, and foot. How do your measurements compare to your answers from part (a)? Are tey close to te istorical measures? You know ow to convert measures witin te customary and metric systems. Equivalent Customary Lengts ft = 2 in. yd = 3 ft mi = 5280 ft Equivalent Metric Lengts m = 000 mm m = 00 cm km = 000 m You will learn ow to convert between te two systems. Converting Between Systems in. = 2.54 cm mi.6 km 2.54 cm c m in. 2 3 i in.

2 2 ACTIVITY: Comparing Measures Mat Practice Analyze Givens Wat is te relationsip between te given quantities? Wat are you trying to find? Work wit a partner. Answer eac question. Explain your answer. Use a diagram in your explanation. Metric Customary a. Car Speed: Wic is faster? 80 km/ 60 mi/ b. Trip Distance: Wic is farter? 200 km 200 mi c. Human Heigt: Wo is taller? 80 cm 5 ft 8 in. d. Wrenc Widt: Wic is wider? 8 mm 5/6 in. e. Swimming Pool Dept: Wic is deeper?.4 m 4 ft 3 ACTIVITY: Canging Units in a Rate Work wit a partner. Cange te units of te rate by multiplying by a Magic One. Write your answer as a unit rate. Sow your work. Original Rate Magic One New Units Unit Rate a. Sample: b. c. d. $20 $3 min 2 in. ft 2 ft week 60 min = $20 60 min = $2 min = $ = = in. yd ft yr 4. One problem-solving strategy is called Working Backwards. Wat does tis mean? How can you use tis strategy to find te rates in Activity 3? 5. IN YOUR OWN WORDS How can you compare lengts between te customary and te metric systems? Give examples wit your description. Use wat you learned about converting measures between systems to complete Exercises 4 and 5 on page 236. Section 5.7 Converting Measures 233

3 5.7 Lesson Lesson Tutorials Key Vocabulary U.S. customary system, p. 234 metric system, p. 234 conversion factor, p. 234 unit analysis, p. 234 Te U.S. customary system is a system of measurement tat contains units for lengt, capacity, and weigt. Te metric system is a decimal system of measurement, based on powers of 0, tat contains units for lengt, capacity, and mass. To convert from one unit of measure to anoter, multiply by one or more conversion factors. A conversion factor can be written using fraction notation. Conversion Factor A conversion factor is a rate tat equals. Relationsip Conversion Factors Example m 3.28 ft m 3.28 ft and 3.28 ft m You can use unit analysis to decide wic conversion factor will produce te appropriate units. EXAMPLE Converting Units a. Convert 36 quarts to gallons. Use a conversion factor. 36 qt gal 4 qt = 36 gal 4 = 9 gal gal = 4 qt So, 36 quarts is 9 gallons. b. Convert 20 centimeters to inces. Use a conversion factor. 20 cm in in cm So, 20 centimeters is about 7.87 inces. in. = 2.54 cm Exercises 6 7 Copy and complete te statement. Round to te nearest undredt if necessary.. 48 ft = yd 2. 7 lb = oz 3. 5 g = mg 4. 7 mi km 5. 2 qt L kg lb 234 Capter 5 Ratios and Rates

4 EXAMPLE 2 Comparing Units Copy and complete te statement using < or >: 25 oz 2 kg. Convert 25 ounces to kilograms. lb = 6 oz lb 0.45 kg 25 oz lb 6 oz 0.45 kg lb = kg 0.70 kg 6 Because 0.70 kilogram is less tan 2 kilograms, 25 oz < 2 kg. EXAMPLE 3 Converting a Rate: Canging One Unit How many liters does te uman eart pump per minute? Pumps 5 quarts of blood per minute 5 qt min 0.95 L qt 4.75 L min qt 0.95 L Te rate of 5 quarts per minute is about 4.75 liters per minute. EXAMPLE 4 Converting a Speed: Canging Bot Units You are riding on a zip line. Your speed is 5 miles per our. Wat is your speed in feet per second? 5 mi 5280 ft ( mi )( 3600 sec) = ft 3600 sec mi = 5280 ft = 3600 sec 79,200 ft = 3600 sec 22 ft = sec Your speed is 22 feet per second. Exercises 20 3 Copy and complete te statement using < or > cm 3 in c 2 L 9. 3 oz 70 g 0. An oil tanker is leaking oil at a rate of 300 gallons per minute. Wat is tis rate in gallons per second?. A tennis ball travels at a speed of 20 miles per our. Wat is tis rate in feet per second? Section 5.7 Converting Measures 235

5 5.7 Exercises Help wit Homework 0 mm. VOCABULARY Is a conversion factor? Explain. cm 2. WRITING Describe ow to convert 2 liters per our to milliliters per second. 3. DIFFERENT WORDS, SAME QUESTION Wic is different? Find bot answers. Convert 5 inces to centimeters. Find te number of inces in 5 centimeters. How many centimeters are in 5 inces? Five inces equals ow many centimeters? 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= Answer te question. Explain your answer. 4. Wic juice container is larger: 2 L or gal? 5. Wic person is eavier: 75 kg or 0 lb? Copy and complete te statement. Round to te nearest undredt if necessary pt = c ml = L oz = lb 9. 2 L qt 0. 4 m ft. 4 ft m lb kg km mi in. cm 5. 7 kg lb 6. 5 cm in mi km 8. ERROR ANALYSIS Describe and correct te error in converting te units. 9. BRIDGE Te Mackinac Bridge in Micigan is te tird-longest suspension bridge in te United States. a. How ig above te water is te roadway in meters? b. Te bridge as a lengt of 26,372 feet. Wat is te lengt in kilometers? 8 L 8 L 0.95 qt L = 8 L 0.95 qt L = 7.6 qt 99 ft 236 Capter 5 Ratios and Rates

6 Copy and complete te statement using < or > kg 30 oz 2. 6 ft 300 cm gal 6 L in. 200 mm g 5 lb m 3000 ft Copy and complete te statement km mi L min = L mi = mi sec km min mi gal qt min 3. 6 cm min = m sec 32. BOTTLE Can you pour te water from a full 2-liter bottle into a 2-quart pitcer witout spilling any? Explain MPH AUTOBAHN Germany suggests a speed limit of 30 kilometers per our on igways. a. Is te speed sown greater tan te suggested limit? b. Suppose te speed sown drops 30 miles per our. Is te new speed below te suggested limit? 34. BIRDS Te table sows te flying speeds of several birds. a. Wic bird is te fastest? Wic is te slowest? b. Te peregrine falcon as a dive speed of 322 kilometers per our. Is te dive speed of te peregrine falcon faster tan te flying speed of any of te birds? Explain. 35. SPEED OF LIGHT Te speed of ligt is about 300,000 kilometers per second. Convert te speed to miles per our. Bird Spine-tailed swift Spur-winged goose Eider duck 36. One liter of paint covers 00 square Mallard feet. How many gallons of paint does it take to cover a room wose walls ave an area of 800 square meters? Speed m/min 29. ft/sec 3.3 m/sec 65 mi/ Find te percent of te number. (Section 5.6) % of % of % of % of MULTIPLE CHOICE Wat is te area of a parallelogram wit a base of 5 centimeters and a eigt of 2 centimeters? (Section 4.) A 90 cm 2 B 75 cm 2 C 80 cm 2 D 205 cm 2 Section 5.7 Converting Measures 237