Chapter 08

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Measurement units

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Unit 8:

Unit 8 CUSTOMARY MEASUREMENT UNITS

CUSTOMARY LINEAR UNITS:

2 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. CUSTOMARY LINEAR UNITS

CONVERTING UNITS OF MEASURE:

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 .

CONVERSION EXAMPLE:

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 ft Ans Note: Rounded to 2 significant digits

CONVERSION EXAMPLE :

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 rods Ans Note: Rounded to 3 significant digits

ADDING COMPOUND NUMBERS:

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

ADDING COMPOUND NUMBERS:

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

SUBTRACTING COMPOUND NUMBERS :

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

SUBTRACTING COMPOUND UNITS :

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

MULTIPLYING COMPOUND NUMBERS:

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

MULTIPLYING COMPOUND NUMBERS:

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 yd Ans

DIVIDING COMPOUND NUMBERS:

12 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 DIVIDING COMPOUND NUMBERS

DIVISION:

13 DIVISION Write as division problem and start dividing at left: 15  2 = 7 14 yd 2ft 1 yd = 3 ft 4 ft 4 ft 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 7yd 2ft Ans

AREA:

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

SURFACE AREA:

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

SURFACE AREA CONVERSIONS:

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 ft Ans Note: Rounded to 2 significant digits

CUSTOMARY VOLUME UNITS:

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

CUSTOMARY VOLUME UNITS CONVERSION:

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 yd Ans Note: Rounded to 3 significant digits.

CAPACITY/WEIGHT CONVERSIONS:

19 CAPACITY/WEIGHT CONVERSIONS = 87 in 3 Ans Note: Rounded to 2 significant digits Express 200 cm 3 as liters = 0.2 L Ans Express 1.5 quarts as cubic inches No direct conversion between quarts and cubic inches, so more than one unity fraction will be needed

COMPOUND UNITS:

20 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

PRACTICE PROBLEMS:

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

PRACTICE PROBLEMS (Cont):

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

PRACTICE PROBLEMS (Cont):

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

PRACTICE PROBLEMS (Cont):

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?

PROBLEM ANSWER KEY:

25 PROBLEM ANSWER KEY 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 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

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