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Unit 8

Unit 8. CUSTOMARY MEASUREMENT UNITS. CUSTOMARY LINEAR UNITS. Linear Measurement expresses distance between two points or measurement of lengths Make sure you print the conversion sheet if you have not already. It will show all the conversions that this lesson discusses.

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Unit 8

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  1. Unit 8 CUSTOMARY MEASUREMENT UNITS

  2. CUSTOMARY LINEAR UNITS • Linear Measurement expresses distance between two points or measurement of lengths • Make sure you print the conversion sheet if you have not already. It will show all the conversions that this lesson discusses.

  3. CONVERTING UNITS OF MEASURE • Unity fraction method is used to convert between different units of measure • Method multiplies given unit of measure by a fraction equal to one • Unity fraction is set up so that the original unit cancels and the unit being converted to remains.

  4. CONVERSION EXAMPLE Express 43 inches as feet • Use 12 inches = 1 foot equivalence to set up the unity fraction • Since we started with 43 inches, the inches must cancel • We will make our unity fraction = = 3.6 ftAns Note: Rounded to 2 significant digits

  5. CONVERSION EXAMPLE Express 4.56 miles as rods • Use 1 mile = 320 rods equivalence to set up unity fraction • Since we started with miles, they must cancel out • We will make our unity fraction = 1460 rodsAns Note: Rounded to 3 significant digits

  6. ADDING COMPOUND NUMBERS • To add compound numbers, arrange like units in same columns, then add each column. • When necessary, simplify sum • Add:

  7. ADDING COMPOUND NUMBERS • Arrange like units in same columns: • Add each column: • Simplify:

  8. SUBTRACTING COMPOUND NUMBERS • Arrange like units in the same columns • Subtract each column starting from the right • Regroup as necessary Subtract: 3 ft 14 in – 1 ft 21 in

  9. SUBTRACTING COMPOUND UNITS • Arrange like units in same columns • Borrow from 3 ft • Complete subtraction 1 ft 5 in Ans

  10. MULTIPLYING COMPOUND NUMBERS • Multiply each unit by the multiplier • If necessary, simplify each product • Add the units of each product together Multiply: 5 times 2 mi 540 yd

  11. MULTIPLYING COMPOUND NUMBERS • Multiply each unit by 5: 10 mi 2700 yd • Simplify product: 2700 yd = 1 mi 940 yd • Add: 10 mi + 1 mi 940 yd = 11 mi 940 ydAns

  12. DIVIDING COMPOUND NUMBERS • Divide each unit by divisor starting at left • If a unit is not exactly divisible, express remainder as next smaller unit and add to given number of smaller units • Continue process until all units are divided

  13. DIVISION • Write as division problem and start dividing at left: 15  2 = 7 14 yd 2ft 1 yd • 2  7 = 14: write 14 under the 15 and subtract = 3 ft 4 ft • Convert 1 yd into 3 feet and add it to the 1 foot in the dividend 4 ft • Complete division 7yd 2ft Ans

  14. AREA • Two-dimensional measure • Computed as product of two linear measures • Expressed in square units • Square feet • Square inches • yd2

  15. SURFACE AREA • Customary Units of Surface Area • On your conversion sheet you will notice that the middle column is mostly area measurements.

  16. SURFACE AREA CONVERSIONS • Unity fractions are used for surface area conversions as in linear measure • Express 15 square yards as square feet • Use 1 square yard = 9 square feet to set up unity fraction • Square yards must cancel out • Make the unity fraction = 140 sq ftAns Note: Rounded to 2 significant digits

  17. CUSTOMARY VOLUME UNITS • Three-dimensional • Computed as product of three linear measures • Expressed in cubic units • Cubic inches • Cubic yards • Ft3 • You will notice this follows the third column on your conversion chart.

  18. CUSTOMARY VOLUME UNITS CONVERSION • Use unity fractions to express 12,500 cubic inches as cubic yards • No direct equivalence between cubic inches and cubic yards • Use more than one unity fraction = 0.268 cu ydAns Note: Rounded to 3 significant digits.

  19. CAPACITY/WEIGHT CONVERSIONS • Express 1.5 quarts as cubic inches • No direct conversion between quarts and cubic inches, so more than one unity fraction will be needed = 87 in3Ans Note: Rounded to 2 significant digits • Express 200 cm3 as liters = 0.2 L Ans

  20. COMPOUND UNITS • Products or quotients of two or more basic units such as mi/hr or lb/in2 (psi) • Unity fractionsused to convert compound units by placing units on opposite sides of fraction so that they cancel out • Express 60 miles/hour as feet/second

  21. PRACTICE PROBLEMS • Convert numbers and round each to the same number of significant digits as original quantity • 34.52 feet as yards • 2.36 miles as feet • 4.5 yards as inches • Perform the indicated operations and simplify answers • 1 mi 250 rd + 3 mi 225 rd • 7 ft 2 in – 4 ft 9 in

  22. PRACTICE PROBLEMS (Cont) • Perform the indicated operations and simplify all answers • 4 rd 14 ft + 2 rd 12.5 ft + 3 rd 7 ft • 5 yd 1 ¾ ft – 2 yd 2 ½ ft • 4 yd 2 ft × 4 • 5 mi 110 rd  3 • 6 mi 210 rd 7.5 yd × 3 • 6 ft 6 in  4

  23. PRACTICE PROBLEMS (Cont) • Express 163.2 square inches as square feet • Express 543 square rods as square yards • Express 75 square miles as acres • Express 2.5 cubic feet as cubic inches • Express 123,500 cubic inches as cubic yards • Express 13.5 pints as gallons • Express 18.2 ft/min as mi/hr

  24. PRACTICE PROBLEMS (Cont) • A bullet travels at about 1200 miles per hour. How many feet per second is that? • You own hot property on the edge of a city. You have heard a lot of numbers talking about price per square foot, but you only know you own 20 acres. How many square feet do you own? • How many cubic inches are in a 100 gallon tank?

  25. 11.51 yards 12,500 feet 160 inches 5 mi 155 rd 2 ft 5 in 11 rd 0.5 ft 2 yd 21/4 ft 18 yd 2 ft 1 mi 250 rd 19 mi 314 rd 0.5 yd 1 ft 7.5 in 1.133 sq ft 163.35 yd2 48,000 acres 4,320 cu in 2.647 cu yd 1.6875 gal 0.2068 mi/hr 1760 ft/sec 871,200 square feet 23,100 cubic inches PROBLEM ANSWER KEY

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