Unit 8

CUSTOMARY MEASUREMENT 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

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 =inft

121

= 3.6 ft Ans ftft

in

ftin583.3

12

43

.12

1

1

.43

Note: Rounded to 2 significant digits

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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

mi

rodmi

1

320

1

56.4 = 1460 rods Ans

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: ft3

12yd2ft

4

32yd3

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ADDING COMPOUND NUMBERS

– Arrange like units in same columns:

– Add each column:

– Simplify: ft121

5yd5

ft31

2yd2

ft43

2 yd3

ft121

2yd1ft121

5

Ansft121

2yd6ft121

2yd1yd5

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

9

• Arrange like units in same columns

• Borrow from 3 ft

• Complete subtraction

SUBTRACTING COMPOUND UNITS

in21ft1

in14ft3

in21ft1

in26ft2

1 ft 5 in Ans

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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

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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

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• 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

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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

2ft 7ydft1 yd152

7yd 2ft Ans

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AREA

Two-dimensional measure

Computed as product of two linear measures

Expressed in square units

Square feet

Square inches

yd2

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SURFACE AREA

Customary Units of Surface Area On your conversion sheet you will

notice that the middle column is mostly area measurements.

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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 yd sq1

ft sq9

ft sq 135 ydsq 1

ft sq 9

1

ydsq 15 = 140 sq ft Ans

Note: Rounded to 2 significant digits

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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.

CUSTOMARY VOLUME UNITS

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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

3

3

3

3

33

26792.27

1

1728

1

1

12500yd

ft

yd

in

ftin

= 0.268 cu yd Ans

Note: Rounded to 3 significant digits.

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CAPACITY/WEIGHT CONVERSIONS

33

in86.625gal1

in231

qt4

gal1

1

qt1.5

= 87 in3 AnsNote: Rounded to 2 significant digits

• Express 200 cm3 as liters

1000mL

1L

1cm

1mL

1

200cm3

3

= 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

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COMPOUND UNITS

Anssec

ft88

sec60

min1

min60

hr1

mi1

ft5280

hr

mi60

Products or quotients of two or more basic units such as mi/hr or lb/in2 (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

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PRACTICE PROBLEMS

Convert numbers and round each to the same number of significant digits as original quantity

1. 34.52 feet as yards2. 2.36 miles as feet3. 4.5 yards as inches

Perform the indicated operations and simplify answers

4. 1 mi 250 rd + 3 mi 225 rd5. 7 ft 2 in – 4 ft 9 in

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PRACTICE PROBLEMS (Cont)

Perform the indicated operations and simplify all answers

6. 4 rd 14 ft + 2 rd 12.5 ft + 3 rd 7 ft7. 5 yd 1 ¾ ft – 2 yd 2 ½ ft8. 4 yd 2 ft × 49. 5 mi 110 rd 310. 6 mi 210 rd 7.5 yd × 311. 6 ft 6 in 4

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PRACTICE PROBLEMS (Cont)

12. Express 163.2 square inches as square feet

13. Express 543 square rods as square yards14. Express 75 square miles as acres15. Express 2.5 cubic feet as cubic inches16. Express 123,500 cubic inches as cubic

yards17. Express 13.5 pints as gallons18. Express 18.2 ft/min as mi/hr

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PRACTICE PROBLEMS (Cont)

19. A bullet travels at about 1200 miles per hour. How many feet per second is that?

20. 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?

21. How many cubic inches are in a 100 gallon tank?

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PROBLEM ANSWER KEY

1. 11.51 yards2. 12,500 feet3. 160 inches4. 5 mi 155 rd5. 2 ft 5 in6. 11 rd 0.5 ft7. 2 yd 21/4 ft8. 18 yd 2 ft9. 1 mi 250 rd

10. 19 mi 314 rd 0.5 yd11. 1 ft 7.5 in12. 1.133 sq ft13. 163.35 yd2

14. 48,000 acres15. 4,320 cu in16. 2.647 cu yd17. 1.6875 gal18. 0.2068 mi/hr19. 1760 ft/sec20. 871,200 square feet21. 23,100 cubic inches