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.
2
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 equivalence to set up the unity fraction
–
Since we started with 43 inches, the inches must cancel
–
We will make our unity fraction =
1 ft
12in
43in.
1ft
43ft


 3.583ft = 3.6 ft Ans
1
12in.
12
Note: Rounded to 2 significant digits
4
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
–
4.56mi 320rod

= 1460 rods Ans
1
1mi
Note: Rounded to 3 significant digits
5
ADDING COMPOUND NUMBERS

To add compound numbers, arrange like
units in same columns, then add each
column.

When necessary, simplify sum

Add: 3 yd 2 3 ft  2 yd 2 1 ft
4
3
6
ADDING COMPOUND NUMBERS
–
Arrange like units in
same columns:
–
Add each column:
3
ft
4
1
2 yd 2 ft
3
Simplify:
5 yd 5
–
3 yd 2
5
1
ft
12
1
1
ft  1 yd 2 ft
12
12
1
1
5 yd  1 yd 2 ft  6 yd 2 ft Ans
12
12
7
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 ft
3 ft 14 in
 1 ft 21 in
2 ft 26 in
 1 ft 21 in
•
Complete subtraction
1 ft 5 in Ans
9
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 2700 yd
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 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 = 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
7yd 2ft
2 15yd 1ft
14 yd 2ft
1 yd
= 3 ft
4 ft
4 ft
7yd 2ft Ans
13
AREA



Two-dimensional measure
Computed as product of two linear
measures
Expressed in square units

Square feet

Square inches

yd2
14
SURFACE AREA

Customary Units of Surface Area

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
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
9 sq ft
– Make the unity fraction
1 sq yd
15 sq yd
9 sq ft

 135 sq ft = 140 sq ft Ans
1
1 sq yd
Note: Rounded to 2 significant digits
16
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.
17
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
12500 in
1
3

1 ft
3
1728 in
3

1 yd
27 ft
3
3
 .26792 yd
3
= 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 between quarts and cubic
inches, so more than one unity fraction will be
needed
3
3
1.5 qt 1 gal 231 in

1

4 qt

1 gal
 86.625 in
= 87 in3 Ans
Note: Rounded to 2 significant digits
• Express 200 cm3 as liters
200cm
1
3

1mL
1cm
1L

3
1000mL
= 0.2 L Ans
19
COMPOUND UNITS



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
60 mi 5280 ft
1 hr
1 min
88 ft




Ans
hr
1 mi
60 min 60 sec
sec
20
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.
8.
9.
10.
11.
4
5
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
Express
Express
Express
yards
Express
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
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 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 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
25