1. CUSTOMARY MEASUREMENT UNITS

2. 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.

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 = 3.6 ft Ans
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

5. CONVERSION EXAMPLE Express 4.56 miles as rods = 1460 rods Ans
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

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

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

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

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

10. MULTIPLYING COMPOUND NUMBERS
Multiply each unit by the multiplier
If necessary, simplify each product
Add the units of each product together
Multiply: 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. 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

13. DIVISION 14 yd 2ft 1 yd = 3 ft 4 ft 4 ft 7yd 2ft Ans
Write as division problem and start dividing at left: 15  2 = 7
14 yd 2ft
1 yd
2  7 = 14: write 14 under the and subtract
= 3 ft
4 ft
Convert 1 yd into 3 feet and add it to the 1 foot in the dividend
4 ft
Complete division
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
= 140 sq ft Ans
Note: Rounded to 2 significant digits

17. 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.

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
= cu yd Ans
Note: Rounded to 3 significant digits.

19. 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 in3 Ans
Note: Rounded to 2 significant digits
Express 200 cm3 as liters
= 0.2 L Ans

20. 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

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

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

23. PRACTICE PROBLEMS (Cont)
Express 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

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?

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
yd2
48,000 acres
4,320 cu in
2.647 cu yd
gal
mi/hr
1760 ft/sec
871,200 square feet
23,100 cubic inches