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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
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
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
7
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
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
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
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
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
2ft 7ydft1 yd152
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 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
17
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
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
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.
19
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
20
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
21
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
22
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
23
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
24
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?
25
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