Unit 8 CUSTOMARY MEASUREMENT UNITS 1 CUSTOMARY LINEAR

  • Slides: 25
Download presentation
Unit 8 CUSTOMARY MEASUREMENT UNITS 1

Unit 8 CUSTOMARY MEASUREMENT UNITS 1

CUSTOMARY LINEAR UNITS • • Linear Measurement expresses distance between two points or measurement

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. 2

CONVERTING UNITS OF MEASURE • Unity fraction method is used to convert between different

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. 3

CONVERSION EXAMPLE Express 43 inches as feet – Use 12 inches = 1 foot

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 ft Ans Note: Rounded to 2 significant digits 4

CONVERSION EXAMPLE Express 4. 56 miles as rods – Use 1 mile = 320

CONVERSION EXAMPLE Express 4. 56 miles as rods – Use 1 mile = 320 rods equivalence to set up unity fraction = 1460 rods Ans Since we started with miles, they must cancel out – Note: Rounded to 3 significant digits We will make our unity fraction – 5

ADDING COMPOUND NUMBERS ¡ To add compound numbers, arrange like units in same columns,

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

ADDING COMPOUND NUMBERS – Arrange like units in same columns: – Add each column:

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

SUBTRACTING COMPOUND NUMBERS ¡ Arrange like units in the same columns ¡ Subtract each

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 8

SUBTRACTING COMPOUND UNITS • Arrange like units in same columns • Borrow from 3

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

MULTIPLYING COMPOUND NUMBERS ¡ Multiply each unit by the multiplier ¡ If necessary, simplify

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 10

MULTIPLYING COMPOUND NUMBERS • Multiply each unit by 5: • Simplify product: 10 mi

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

DIVIDING COMPOUND NUMBERS • Divide each unit by divisor starting at left • If

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 12

DIVISION • Write as division problem and start dividing at left: 15 2 =

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

AREA ¡ Two-dimensional measure ¡ Computed as product of two linear measures ¡ Expressed

AREA ¡ Two-dimensional measure ¡ Computed as product of two linear measures ¡ Expressed in square units l Square feet l Square inches l yd 2 14

SURFACE AREA ¡ Customary Units of Surface Area l On your conversion sheet you

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

SURFACE AREA CONVERSIONS • Unity fractions are used for surface area conversions as in

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 ft Ans Note: Rounded to 2 significant digits 16

CUSTOMARY VOLUME UNITS ¡ ¡ Three-dimensional Computed as product of three linear measures Expressed

CUSTOMARY VOLUME UNITS ¡ ¡ Three-dimensional Computed as product of three linear measures Expressed in cubic units l Cubic inches l Cubic yards l Ft 3 You will notice this follows the third column on your conversion chart. 17

CUSTOMARY VOLUME UNITS CONVERSION ¡ Use unity fractions to express 12, 500 cubic inches

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 yd Ans Note: Rounded to 3 significant digits. 18

CAPACITY/WEIGHT CONVERSIONS ¡ Express 1. 5 quarts as cubic inches – No direct conversion

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 in 3 Ans Note: Rounded to 2 significant digits • Express 200 cm 3 as liters = 0. 2 L Ans 19

COMPOUND UNITS ¡ ¡ ¡ Products or quotients of two or more basic units

COMPOUND UNITS ¡ ¡ ¡ Products or quotients of two or more basic units such as mi/hr or lb/in 2 (psi) Unity fractions used to convert compound units by placing units on opposite sides of fraction so that they cancel out Express 60 miles/hour as feet/second 20

PRACTICE PROBLEMS ¡ Convert numbers and round each to the same number of significant

PRACTICE PROBLEMS ¡ Convert numbers and round each to the same number of significant digits as original quantity 1. 2. 3. ¡ 34. 52 feet as yards 2. 36 miles as feet 4. 5 yards as inches Perform the indicated operations and simplify answers 4. 5. 1 mi 250 rd + 3 mi 225 rd 7 ft 2 in – 4 ft 9 in 21

PRACTICE PROBLEMS (Cont) ¡ Perform the indicated operations and simplify all answers 6. 7.

PRACTICE PROBLEMS (Cont) ¡ Perform the indicated operations and simplify all answers 6. 7. 8. 9. 10. 11. 4 5 6 6 rd 14 ft + 2 rd 12. 5 ft + 3 rd 7 ft yd 1 ¾ ft – 2 yd 2 ½ ft yd 2 ft × 4 mi 110 rd 3 mi 210 rd 7. 5 yd × 3 ft 6 in 4 22

PRACTICE PROBLEMS (Cont) 12. 13. 14. 15. 16. 17. 18. Express feet Express yards

PRACTICE PROBLEMS (Cont) 12. 13. 14. 15. 16. 17. 18. Express feet Express yards Express 163. 2 square inches as square 543 square rods as square yards 75 square miles as acres 2. 5 cubic feet as cubic inches 123, 500 cubic inches as cubic 13. 5 pints as gallons 18. 2 ft/min as mi/hr 23

PRACTICE PROBLEMS (Cont) 19. 20. 21. A bullet travels at about 1200 miles per

PRACTICE PROBLEMS (Cont) 19. 20. 21. 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? 24

PROBLEM ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 11. 51

PROBLEM ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 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 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 19 mi 314 rd 0. 5 yd 1 ft 7. 5 in 1. 133 sq ft 163. 35 yd 2 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 25